This workshop aims to prepare the participants for the main program: Special Geometric Structures and Analysis.
There will be introductory lectures to recent results in geometry and analysis; more precisely in Kähler geometry, special holonomy, microlocal analysis and geometric measure theory.

The spatial Schwarzschild space with minimal surface boundary foliated by the inverse mean curvature flow

This workshop will include introductory lectures on each of the four main topics of the program: geometric flows, geometric problems in mathematical relativity, global Riemannian geometry, and minimal submanifolds. The workshop will also have semi-expository lectures on recent advances and breakthroughs involving interactions between the four main topics. This will set the stage and provide important context for the semester-long program itself. 

Geosurface

This three-day workshop will consist of various talks given by prominent women mathematicians on topics of differential geometry and geometric analysis. These will be appropriate for graduate students, postdocs, and researchers in areas related to the two Fall 2024 programs at SLMath.  The workshop will also include activities to promote interaction and connection between participants. This workshop is open to all mathematicians.

Many long-standing conjectures in commutative algebra have been solved in recent years, often through the introduction of new methods that are quickly becoming central to the field.  This workshop will bring together a wide array of researchers in commutative algebra and related fields, with the goal of forging new connections among topics, and with a particular emphasis on transformative new methods.

Optical illusion staircase

This workshop will give an overview of recent developments in non-commutative algebraic geometry, including NC projective AG, NC resolutions, semiorthogonal decompositions, enhancements of derived categories, and connections to homological mirror symmetry, to enumerative AG, to moduli spaces and to birational geometry. It will in particular focus on speakers who have built new bridges between these topics.

A paper fortune teller illustrating the Atiyah flop.

This introductory workshop will consist of a combination of minicourses addressing core topics in noncommutative algebraic geometry and research lectures describing recent developments in the field.  The workshop will focus on subjects connected to algebraic geometry, category theory, and mirror symmetry such as categorical and noncommutative resolutions, deformation theory, derived categories in algebraic geometry, derived algebraic geometry, infinity categories, and enumerative geometry.

This two-day workshop will feature the work of mathematicians in noncommutative geometry who identify as women or another marginalized gender. The talks will be appropriate for graduate students, post-docs, and researchers in areas related to the program. This meeting aims to support young researchers.

The workshop will focus on recent developments in noncommutative algebraic geometry including Derived Algebraic Geometry, Categorical and Noncommutative Resolutions, Deformation Theory, and Enumerative Geometry.

The format will include plenary talks, a poster session, panel discussions, as well as the opportunity for informal discussions and connections in noncommutative geometry. The workshop is open to all mathematicians, and members of historically excluded groups and identities are especially encouraged to attend.

Fractal behavior of local cohomology. For details, see arXiv:2210.03656 by Gao and Raicu

The Introductory Workshop will feature lecture series devoted to some recent breakthrough results in commutative algebra, and to new developments in core areas of the field.  It will also highlight links to other areas such as arithmetic geometry, representation theory, noncommutative geometry, and singularity theory.

This two-day workshop will feature the work of mathematicians in commutative algebra who identify as women or another marginalized gender. The talks will be appropriate for graduate students, post-docs, and researchers in areas related to the program. This meeting aims to support young researchers. The format will include plenary talks, poster sessions, panel discussions, as well as the opportunity for informal discussions and connections.  The workshop is open to all mathematicians, and members of historically excluded groups and identities are especially encouraged to attend.

The workshop is aimed at exploring core subjects in the field of market and mechanism design, such as the design of non-convex auction markets, the design of matching markets with preferences, algorithmic mechanism design, and learning in games. These topics are interrelated and deeply rooted in mathematics and computer science. Each day of the 4-day workshop is devoted to one of these topics with talks by leading scholars in the field and panel discussions on major open problems.

This workshop will look at the idea of fairness and neutrality in algorithms and decision-making. How it relates to the idea of randomization and how randomization can be employed in the pursuit of neutrality and fairness. The goal is both to bring together state-of-the-art research and explore the implications and limitations of the deployment in the real world.

This workshop is multifaceted. In addition to familiarizing graduate students and other junior participants to the topics of the program, the workshop will also reinforce common ground and language among computer scientists and economists and provide an on-ramp introduction for interested mathematicians.

The Connections Workshop will consist of invited talks from leading researchers at all career stages in the field of market design.  Particular attention will be paid to real-world applications.  There will also be an AMA focused on career paths with highly visible individuals in the field, and a social event intended to help workshop attendees network with each other.

Image generated by an AI process.

In this workshop, we will bring together speakers who are engaged in the active areas of scholarship around algorithmic fairness, the disparate impacts of facially impartial systems, and the ways that algorithms can be enmeshed in governance and decisionmaking—for better and worse.  The speakers will introduce themes that will be picked up throughout the semester program on "Algorithms, Fairness, and Equity."

The Connections Workshop will welcome participants of all genders and identities, with the scope of fostering a sense of community, amplifying voices of those who identify as women, and providing avenues to allies to be helpful. The workshop particularly aims to increase visibility among junior women in fields adjacent to the topics of the general program, including but not limited to game-theoretic fairness, mechanism design, partition, networks, redistricting, and fairness in machine learning. This two-day workshop will include keynote speakers, lightning talks from participants, panel discussions on career advancement, breakout sessions by research areas, opportunities for networking, and other mentoring activities.

A genus 2 curve over the reals and various p-adics. Image created by Prof. Jennifer Balakrishnan .

In recent years, a number of techniques have led to outstanding progress on Lang-Vojta conjectures, such as the Subspace Theorem, p-adic approaches to finiteness, and modular methods. Similarly, spectacular progress has been achieved on unlikely intersection conjectures thanks to new methods and tools, such as height formulas for special points, connections to model theory, refined counting results, and new theorems of Ax-Shanuel type (bi-algebraic geometry). The goal of this workshop is to create the opportunity for these two groups to interact, to share their techniques, to update on the most recent progress, and to attack the outstanding open questions in the field.

Some Gaussian periods for the 29,070-th cyclotomic extension. Image credit: E. Eischen, based on earlier work by W. Duke, S. R. Garcia, T. Hyde, and R. Lutz

The topical workshop will be dedicated to Shouwu Zhang, to mark the occasion of his 60th birthday, and to honour his numerous beautiful contributions to the theory of Shimura varieties and special values of L-functions. It will highlight cutting edge work on topics such as the construction of Euler systems; relations between special cycles on Shimura varieties and L-functions, such as generalized Gross-Zagier formulas and the Tate conjecture; the construction of Galois representations in cohomology; and related aspects of the theory of automorphic forms.

Rational points on a general type surface. Image by Hector Pasten.

This will be a hybrid workshop with both in-person and virtual participation.

This workshop will feature expository lectures about  current developments in  Diophantine geometry. This includes  the uniform Mordell—Lang for rational points on curves,  the  Andre—Oort conjecture for special points on Shimura varieties, and effective results via Chabauty method, and related topics in  Arakelov theory, unlikely intersections, arithmetic statistics, arithmetic dynamics, and p-adic Hodge theory.

This will be a hybrid workshop with both in-person and virtual participation.

This workshop will highlight talks on various aspects of Diophantine Geometry. The goal of the workshop is to bring together researchers at different career stages and of various backgrounds in order to establish new collaborations and mentoring relationships. Although we will showcase the research of mathematicians who identify as women or gender minorities, this workshop is open to all.

Image credit: Vincent J. Matsko, 6-adic Koch-like fractal. For details, see http://www.vincematsko.com/Art/ICERM.html

This will be a hybrid workshop with both in-person and virtual participation.

The Introductory Workshop aims to provide a coherent overview of current research in algebraic cycles, L-values, Euler systems, and the many connections between them. This includes the study of special cycles on Shimura varieties and moduli spaces of shtukas, integral representations of L-values and the construction of p-adic L-functions, and the construction of Euler systems from special elements in Chow groups or higher Chow groups of Shimura varieties. Workshop lectures will be organized into short lecture series, so as to allow each series to begin with expository lectures on foundational results before moving on to current research. This workshop is held in honor of mathematician Bernadette Perrin-Riou.

David Lowry-Duda. Modular form of weight 32 and level 3. For details, see http://davidlowryduda.com/trace-form/

This will be a hybrid workshop with both in-person and virtual participation.

The Connections Workshop features presentations by both leading researchers and promising newcomers whose research has contact with the interrelated topics of algebraic cycles, L-values, and Euler systems. The goal is to present a variety of diverse results, so as to forge new connections, foster collaborative projects, and establish mentoring relationships. While emphasis will be placed on the work of women mathematicians, the workshop is open to all researchers. This workshop is held in honor of mathematician Bernadette Perrin-Riou.

This will be a hybrid workshop with in-person participation only available to members of the semester-long program and invited guests.  Online participation will be open to all who register.  Due to limited capacity, mathematicians who have not received an official invitation will not be permitted to enter the institute.

The workshop will focus on the interaction between homotopy theory and symplectic topology and low dimensional topology that is mediated by Floer theory. Among the topics covered are foundational questions, applications to concrete geometric questions, and the relationship with finite dimensional approaches.

Image drawn by Dr. Lotte Hollands

This will be a hybrid workshop with in-person participation only available to members of the semester-long program and invited guests.  Online participation will be open to all who register.  Due to limited capacity, mathematicians who have not received an official invitation will not be permitted to enter the institute.

This workshop will bring together researchers working on new four-dimensional gauge theories from the perspectives of differential geometry, algebraic geometry, and physics. Over the last 25 years, physicists have made tantalizing conjectures relating the Vafa–Witten equation to modular forms and the Kapustin–Witten and Haydys–Witten equations to knot theory and the geometric Langlands programme. The analytical challenges in the way of establishing these predictions are now being pursued vigorously.  More recently, algebraic geometers have had enormous success in confirming and refining Vafa–Witten's predictions for projective surfaces. The workshop will serve as a platform for reporting on recent progress and exchanging ideas in all of these areas, with the aim of strengthening existing and fostering new interactions.

A Fleur Homotopy.

This will be a hybrid workshop with in-person participation by members of the semester-long program and speakers. Online participation will be open to all who register. 

Over the last decade, there has been a wealth of new applications of homotopy-theoretic techniques to Floer homology in low-dimensional topology and symplectic geometry, including Manolescu’s disproof of the high-dimensional Triangulation Conjecture and Abouzaid-Blumberg’s proof of the Arnol’d Conjecture in finite characteristic. Conversely, results in Floer theory and categorification have opened new directions of research in homotopy theory, from string topology to S-Lie algebras. The goal of this workshop is to introduce researchers in Floer theory to modern techniques and questions in homotopy theory and, conversely, introduce researchers in homotopy theory to ideas underlying Floer theory and its applications.

An illustration of a generic Heegaard quadruple by K. Hendricks, J. Hom, M. Stoffregen, and I. Zemke

This will be a hybrid workshop with in-person participation by members of the semester-long program, speakers and a limited number of invited participants. Online participation will be open to all who register. 

This workshop will feature talks by experts in Floer theory (and its applications to low-dimensional topology) and homotopy theory. It will include two expository lectures aimed at graduate students and other researchers who are new to the field, as well as a sequence of research talks and a contributed talks session. There will also be a panel discussion focusing on professional development. The majority of the speakers and panelists for this event will be women and gender minorities, and members of these groups and of other underrepresented groups are especially encouraged to attend. This workshop is open to all mathematicians.

Portion of a letter from Maxwell to Tait dated December 4, 1867 computing the linking number of two curves

This will be a hybrid workshop with in-person participation by members of the semester-long program and speakers. Online participation will be open to all who register. 

The workshop will highlight the utility and impact of gauge theory in other areas of math. Mini-courses will cover the historical utility and impact of gauge theory in areas including low-dimensional topology, algebraic geometry, and the analysis of PDE; additional talks will cover more recent directions.

The nilpotent cone in red over the 0, and the points A, B and C, lying over the C*-fow and of the Hitchin section respectively.

This will be a hybrid workshop with in-person participation by members of the semester-long program, speakers and a limited number of invited participants. Online participation will be open to all who register. 

This two-day workshop will consist of various talks given by prominent female mathematicians on topics of analytic and geometric aspects of gauge theory. These will be appropriate for graduate students, post-docs, and researchers in areas related to the program.  The meeting aims to support young researchers working in analytic and geometric aspects of gauge theory by   facilitating mentoring from senior colleagues and helping towards the development of crucial professional skills. The format will include mentoring pairings, panel discussions, and Q&A sessions as well as the opportunity for informal discussions and connections.

Image by Scott Kaschner

This workshop will focus on complex dynamics in one and several variables. We will bring toghether experts in rational dynamics, transcendental dynamics, and dynamics in several complex variables in order to get new perspective and foster discussions in a warm and stimulating atmosphere. A special focus will be put on the interactions between one dimensional and higher dimensional complex dynamics, and on connections with adjacent areas of mathematics.

Image by Prof. Amanda Turner

The aim of this workshop is to bring together researchers whose work contributes to the study of random structures that exhibit some form of conformal self-similarity. Notable examples include the Schramm-Loewner evolution SLE, the Brownian map and random trees, Liouville Quantum Gravity, and Conformal Field Theory. A particular focus will be the discussion of analytic tools needed to address the challenges arising from the often rough underlying sets and spaces.

Parameter space for the family $e^z+c$

This will be a hybrid workshop with in-person participation by members of the semester-long program. Online participation will be open to all who register. 

This workshop is built around four minicourses that will introduce the participants to a range of recent techniques in various areas of holomorphic dynamics, given by specialists in these topics. The event is complemented by a series of talks by leaders in the field, aimed at a large audience and presenting current research directions in the area.

This will be a hybrid workshop with in-person participation by members of the semester-long program. Online participation will be open to all who register. 

This workshop will feature lectures on a variety of topics in complex dynamics, given by prominent researchers in the field, as well as presentations by younger participants. It precedes the introductory workshop and will preview the major research themes of the semester program. There will be a panel discussion focusing on issues particularly relevant to junior researchers, women, and minorities, as well as other social events. This workshop is open to all mathematicians.

Interface for the critical Ising model, approaching an SLE curve in the scaling limit (image by Dr. Malin P. Forsström)

This will be a hybrid workshop with in-person participation by members of the semester-long program. Online participation will be open to all who register. 

This workshop will introduce some of the major themes in probability and geometric analysis that will be relevant for the semester-long program. A series of short mini-courses will give participants the opportunity to learn about important subjects such as the Schramm-Loewner evolution (SLE) or the Gaussian free field (GFF), for example. The workshop will also include "visionary" lectures by prominent researchers who will outline fruitful directions for future research.

Simulation of the discrete planar Gaussian free field. Image by Dr. Ellen Powell.

This will be a hybrid workshop with in-person participation by members of the semester-long program. Online participation will be open to all who register.

The Connections Workshop will feature talks on a variety of topics related to the analysis and geometry of random spaces. It will preview the research themes of the semester program and will highlight the work of women in the field. There will be a panel discussion as well as other social events. This workshop is directly prior to the Introductory Workshop, and participants are encouraged to participate in both workshops. This workshop is open to all mathematicians.

Image by Alexei Borodin.

This will be a hybrid workshop with in-person participation by members of the semester-long program. Online participation will be open to all who register.  This workshop will focus on the integrable aspect of random matrix theory and other related probability models such as random tilings, directed polymers, and interacting particle systems. The emphasis is on communicating diverse algebraic structures in these areas which allow the asymptotic analysis possible. Some of such structures are determinantal point processes, Toeplitz and Hankel determinants, Bethe ansatz, Yang-Baxter equation, Karlin-McGregor formula, Macdonald process, and stochastic six vertex model.

An illustration of the TASEP interface growth by Leonid Petrov and Hao Yu Li.

This will be a hybrid workshop with in-person participation by members of the semester-long program. Online participation will be open to all who register.

This workshop aims at providing participants with an overview of some of the recent developments in the topics of the semester, with a particular emphasis on universality and applications. This includes universality for Wigner matrices and band matrices and quantum unique ergodicity, universality for beta ensembles and log/coulomb gases, KPZ universality class, universality in interacting particle systems, the connection between random matrices and number theory.

In addition, this workshop will also explore connections with other branches of mathematics and applications to sciences and engineering. The workshop will feature presentations by both leading researchers and promising newcomers. There will be some special activities originally planned for the Connections Workshop: We will have a panel discussion of topics relevant to junior researchers, women, and minorities; a poster session for students and recent PhDs; and other social events.

This workshop is open to and welcomes all mathematicians.

An illustration of the TASEP interface growth by Leonid Petrov and Hao Yu Li.

This will be a hybrid workshop with in-person participation by members of the semester-long program. Online participation will be open to all who register. This workshop aims at providing participants with an overview of some of the recent developments in the topics of the semester, with a particular emphasis on universality and applications. This includes universality for Wigner matrices and band matrices and quantum unique ergodicity, universality for beta ensembles and log/coulomb gases, KPZ universality class, universality in interacting particle systems, the connection between random matrices and number theory.

Water waves

The aim of the workshop is to bring together a broad array of researchers working on incompressible fluid dynamics. Some of the key topics to be covered are Euler flows, Navier Stokes equations as well as water wave flows and associated model equations. Some emphasis will also be placed on numerical analysis of the above evolutions.

This workshop will be held online.  The Zoom link will be provided at a later time. You must register for the workshop to receive the password.  The workshop is held in Pacific Standard Time.

The workshop will address topics in the PDE analysis of the basic equations of the incompressible fluid dynamics (the Euler equations for inviscid flows, the Navier Stokes equations for viscous flows), interface problems (water waves), and other related equations. Open problems and connections to related branches of mathematics will be discussed, including the phenomena of turbulence and the zero viscosity limit. Both theoretical and numerical aspects of these topics will be considered. There will be some colloquium style lectures as well as shorter research talks. The workshop is open to all.

Image by Noomann Bassou

This workshop will be held online.  The Zoom link will be provided at a later time. You must register for the workshop to receive the password.  The workshop is held in Pacific Standard Time.

This workshop will feature talks by prominent female mathematicians whose research lies in and interfaces with mathematical fluids featuring water waves,  free boundaries, fluid structures,  viscous fluids and turbulence. The talks will be appropriate for graduate students, post-docs, and researchers in areas above mentioned. There will also be a panel discussion. This workshop is open to all mathematicians.

This Introductory workshop will take place virtually, over the course of three weeks.  There will be two mini-courses and two talks by MSRI Postdoctoral Fellows each week.

The link to this online workshop is: https://msri.zoom.us/j/999860976

This workshop will focus on recent developments in factorization homology, parametrized homotopy theory, and algebraic K-theory.  These seemingly disparate topics are unified by a common methodology, which leverages universal properties and unforeseen descent by way of higher category theory. Furthermore, they enjoy powerful and complementary roles in application to the cyclotomic trace.  This workshop will be a venue for experts in these areas to present new results, make substantive connections across fields, and suggest and contextualize outstanding questions and problems.  It will consist of 4 two-part lecture series and 10 one-hour talks. The lecture series will be given by Thomas Nikolaus, Akhil Mathew, David Ben-Zvi and a split Martina Rovelli and Viktoriya Ozornova.

Topological field theory studies the interplay of algebraic and topological structure (image credit Kevin Walker)

Link to stream workshop: https://msri.zoom.us/j/226801541

***Due to the COVID-19 virus outbreak, the 2020 Tensor categories and topological quantum field theories workshop will no longer be held onsite at MSRI, rather it will take place online from March 16-20 as scheduled***

The decision to move this workshop online is based on the available scientific data on COVID-19, and the strong advice from experts to avoid gatherings of large groups.

Announcement: Workshop Moved Online

Download Official Notice of Change

A formal Notice of Change letter is available here, which can be shared with your institution, funding agency, and others.

relations among 2-morphisms in the 2-dimensional unoriented bordism bicategory

This workshop will survey notable developments and applications of higher category theory; it will be a venue for end-users to share their vision of how to apply the theory, as well as developers to share technical advancements.  It will consist of 6 series of 3 lectures, each given by instrumental end-users & developers of higher category theory, together with a few question-answer sessions.  Each lecture series will be tailored to a diverse audience, accessible to graduate students and non-expert researchers with some background in homological also algebra.  The content of these lecture series will concern the following topics.

• K-theory: categorification, non-commutative motives, trace methods; 
• TQFT: functorial field theories, factorization homology.
• Parametrized higher category theory: stratifications, equivariant homotopy theory, operads, deformation theory and Koszul duality. 
• Synthetic higher category theory: model-independent characterizations, cosmoi.  

Picture of a Feynman graph.

This two-day workshop will survey notable developments in the foundations and applications of higher category theory. It will consist of two mini-courses given by emerging female leaders in the subject: Claudia Scheimbauer and Nathalie Wahl.  This will be paired with a problem sessions lead by selected "TA's", themselves experts in higher structures.  Each lecture series will be tailored to a diverse audience, accessible to graduate students and non-expert researchers with some background in homological algebra.  

The majority of the speakers and panelists for this event will be women and gender minorities, and members of these groups and of other underrepresented groups are especially encouraged to attend. This workshop is open to all mathematicians.

Jellyfish floating to the surface, as in the evaluation algorithm for certain planar algebras.

This workshop will consist of introductory minicourses on key topics in Quantum Symmetry: fusion categories, modular tensor categories, Hopf algebras, subfactors and planar algebras, topological field theories, conformal nets, and topological phases of matter.  These minicourses will be introductory and are aimed at giving semester participants exposure to the main ideas of subfields other than their own.

Photo by drmakete lab on Unsplash

This workshop will feature several talks by experts, along with numerous 5-minute presentations by junior mathematicians, on topics related to Quantum Symmetry. Such topics will include tensor categories, subfactors, Hopf algebras, topological quantum field theory and more. There will also be a panel discussion on professional development. The majority of the speakers and panelists for this event will be women and gender minorities, and members of these groups and of other underrepresented groups are especially encouraged to attend. This workshop is open to all mathematicians.

An example of a spectral network associated to the group SL(4).

Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In some cases the areas themselves (such as stability conditions on Fukaya-type categories, links to quantum integrable systems, or the physically derived construction of so-called spectral networks) are new, while in others the novelty lies more in the role of the holomorphic differentials (for example in the study of billiards in polygons, special - Hitchin or higher Teichmuller - components of representation varieties, asymptotic properties of Higgs bundle moduli spaces, or in new interactions with algebraic geometry).

It is remarkable how widely scattered are the motivating questions in these areas, and how diverse are the backgrounds of the researchers pursuing them. Bringing together experts in this wide variety of fields to explore common interests and discover unexpected connections is the main goal of our program. Our workshop will be of interest to those working in many different fields, including low-dimensional dynamical systems (via the connection to billiards); differential geometry (Higgs bundles and related moduli spaces); and different types of theoretical physics (electron transport and supersymmetric quantum field theory).

Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory, hyperbolic dynamical systems, probability… As this description shows microlocal analysis has become a very broad area. Due to its breadth, it is a challenge for researchers to be aware of what is happening in other parts of the field, and the impact this may have in their own research area. The purpose of this workshop is thus to bring together researchers from different parts of microlocal analysis and its applications to facilitate the transfer of new ideas. 

Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory… This workshop will provide a comprehensive introduction to the field for postdocs and graduate students as well as specialists outside the field, building up from standard facts about the Fourier transform, distributions and basic functional analysis.

This workshop will provide a gentle introduction to a selection of applications of microlocal analysis.  These may be drawn from among geometric microlocal analysis, inverse problems, scattering theory, hyperbolic dynamical systems,  quantum chaos and relativity.  The workshop will also provide  a panel discussion, a poster session and an introduction/research session. 

This workshop is open to all mathematicians.

Some holomorphic differentials on a genus 2 surface, with close up views of singular points, image courtesy Jian Jiang.

Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In this introductory workshop, we will bring junior and senior researchers from this diverse range of subjects together in order to explore common themes and unexpected connections.

Some holomorphic differentials on a genus 2 surface, with close up views of singular points, image courtesy Jian Jiang.

This two-day workshop will consist of various talks given by prominent female mathematicians on topics of new developments in the role of holomorphic differentials on Riemann surfaces. These will be appropriate for graduate students, post-docs, and researchers in areas related to the program.  

This workshop is open to all mathematicians.

This workshop will bring together researchers at various frontiers, including arithmetic geometry, representation theory, mathematical physics, and homotopy theory, where derived algebraic geometry has had recent impact. The aim will be to explain the ideas and tools behind recent progress and to advertise appealing questions. A focus will be on moduli spaces, for example of principal bundles with decorations as arise in many settings, and their natural structures.    

A picture of a singularity, courtesy of Herwig Hauser

The workshop will survey several areas of algebraic geometry, providing an introduction to the two main programs hosted by MSRI in Spring 2019. It will consist of 7 expository mini-courses and 7 separate lectures, each given by top experts in the field. 

Image created by Tristan Hübsch

This workshop will be on different aspects of Algebraic Geometry relating Derived Algebraic Geometry and Birational Geometry. In particular the workshop will focus on connections to other branches of mathematics and open problems. There will be some colloquium style lectures as well as shorter research talks. The workshop is open to all.

An invariant set inhibiting transport in a two degree-of-freedom Hamiltonian system (courtesy J. D. Szezech)

This is a main workshop of the program “Hamiltonian systems, from topology to applications through analysis.”  It  will feature current developments pertaining to finite and infinite-dimensional Hamiltonian systems, with a mix of rigorous theory and applications.  A broad range of topics will be included, e.g., existence of and transport about invariant sets (Arnold diffusion, KAM, etc.),  techniques for projection/reduction of infinite to finite systems, and the role of topological invariants in applications.

Depiction of the standard nontwist map (courtesy of G.Miloshevich).

This is a main workshop of the program “Hamiltonian systems, from topology to applications through analysis” and is a companion to the workshop next month (November 26-30).  Both workshops will feature current developments pertaining to finite and infinite-dimensional Hamiltonian systems, with a mix of rigorous theory and applications.  A broad range of topics will be included, e.g., existence of and transport about invariant sets (Arnold diffusion, KAM, etc.),  techniques for projection/reduction of infinite to finite systems, and the role of topological invariants in applications.

Representing the orbits of the standard map for K = 1.2

This workshop will feature lectures on a variety of topics in Hamiltonian dynamics given by leading researchers in the area. The talks will focus on recent developments in subjects closely related to the program such as Arnold diffusion, celestial mechanics, Hamilton-Jacobi equations, KAM methods, Aubry-Mather theory and symplectic topological techniques, and on applications. The workshop is open to all mathematicians in areas related to the program.

The workshop will bring together key researchers working in various areas of Group Representation Theory to strengthen the interaction and collaboration between them and to make further progress on a number of basic problems and conjectures in the field. Topics of the workshop include
-- Global-local conjectures in the representation theory of finite groups
-- Representations and cohomology of simple, algebraic and finite groups
-- Connections to Lie theory and categorification, and
-- Applications to group theory, number theory, algebraic geometry, and combinatorics.

The purpose of the workshop is to bring together specialists to work on understanding the many-faceted mathematical structures underlying problems in enumerative geometry. Topics represented at the workshop will include: geometric representation theory, supersymmetric gauge theory, string theory, knot theory, and derived geometry, all of which have had a profound effect on the development of modern enumerative geometry.

The workshop will survey various important and active areas of the representation theory of finite and algebraic groups, and introduce the audience to several basic open problems in the area. It will consist of 6 series of 3 lectures each given by top experts in the field. The lectures are designed for a diverse audience and will be accessible to non-specialists and graduate students with some background in representation theory. Topics covered include Representation theory of algebraic groups, Decomposition numbers of finite groups of Lie type, Deligne-Lusztig theory,  Block theory, Categorification, and Local-global-conjectures.

This intensive two day workshop will introduce graduate students and recent PhD’s to some current topics of research in Representation Theory. It will consists of a mixture of survey talks on the hot topics in the area given by leading experts and research talks by junior mathematicians covering subjects such as new developments in character theory, group cohomology, representations of Lie algebras and algebraic groups, geometric representation theory, and categorification. 

This workshop is open to all mathematicians.

This workshop will consist of expository mini-courses and lectures introducing various aspects of modern enumerative geometry, among which: enumeration via intersection theory on moduli spaces of curves or sheaves, including Gromov-Witten and Donaldson-Thomas invariants; motivic and K-theoretic refinement of these invariants; and categorical invariants (derived categories of coherent sheaves, Fukaya categories).

This two-day workshop will provide an overview of significant developments and open problems in modern enumerative geometry, from the perspectives of both algebraic geometry and symplectic topology. 

This workshop is open to all mathematicians.

This workshop will focus on the interaction between Combinatorics, Geometry and Topology, including recent developments and techniques in areas such as 

-- polytopes and cell complexes,
-- simplicial complexes and higher order graph theory,
-- methods from equivariant topology and configuration spaces,
-- geometric combinatorics in optimization and social choice theory,
-- algebraic and algebro-geometric methods.

The introductory workshop will present the main topics that will be the subject of much of the Geometric and Topological Combinatorics Program at MSRI.  Key areas of interest are point configurations and matroids, hyperplane and subspace arrangements, polytopes and polyhedra, lattices, convex bodies, and sphere packings. This workshop will consist of introductory talks on a variety of topics, intended for a broad audience. 

This workshop will feature lectures on a variety of topics in geometric and topological combinatorics, given by prominent women and men in the field. It precedes the introductory workshop and will preview the major research themes of the semester program. There will be a panel discussion focusing on issues particularly relevant to junior researchers, women, and minorities, as well as other social events. This workshop is open to all mathematicians.

This workshop will consist of several short courses related to high dimensional convex geometry, high dimensional probability, and applications in data science. The lectures will be accessible for graduate students.

This workshop will be on topics connected with Asymptotic Geometric Analysis - a relatively new field, the young finite dimensional cousin of Banach Space theory, functional analysis and classical convexity. We study high, but finite, dimensional objects, where the disorder of many parameters and many dimensions is regularized by convexity assumptions.  This workshop is open to all mathematicians.

This workshop will be focused on presenting the latest developments in analytic number theory, including (but not restricted to) recent advances in sieve theory, multiplicative number theory, exponential sums, arithmetic statistics, estimates on automorphic forms, and the Hardy-Littlewood circle method.

The introductory workshop will present, through short minicourses and introductory lectures, the main topics that will be the subject of much of the Analytic Number Theory Programme at MSRI. These topics include the theory of multiplicative functions, the theory of modular forms and L-functions, the circle method, sieve methods, and the theory of exponential sums over finite fields

This workshop will consist of lectures on the current state of research in analytic number theory, given by prominent women and men in the field.  The workshop is open to all graduate students, post-docs, and researchers in areas related to the program; it will also include a panel discussion session among female researchers on career issues, as well as other social events

This week-long workshop will serve as an introduction for graduate students, postdocs, and other researchers to the main themes of the program.  It will feature accessible talks by a number of leading harmonic analysts, including several short courses on the core ideas and techniques in the field.  There will also be a problem session, to which all participants are encouraged to contribute. 

This workshop will highlight the work of several prominent women working in harmonic analysis, including some of the field's rising stars.  There will also be a panel discussion.  There will also be a contributed poster session.  This workshop is open to, and poster contributions are welcome from all mathematicians.

The main theme of the workshop is the spectrum of analytic properties running from Kazhdan's property (T) at one end to von Neumann's amenability at the other, that forms a foundational organizing structure for infinite groups and spaces. These properties can be described both analytically, via unitary representation theory, and geometrically, using embedding properties for discrete spaces. Connections with probability and combinatorics will likewise be addressed during the meeting.

A four-day workshop with research-level talks on the latest advances in the geometry of mapping class groups and Out(F_n), and spaces on which they act.

The theme of the workshop is algebraic, geometric and analytical aspects of groups that act by isometries on spaces of non-positive curvature known as CAT(0) spaces. The world of CAT(0) spaces includes classical spaces such as symmetric spaces and buildings, as well as more avant-garde arrivals, such as CAT(0) cube complex. The workshop will bring together researchers studying various aspects of such groups and spaces to discuss recent developments and chart new directions in the field. 

This will be an introductory workshop to the MSRI jumbo program Geometric Group Theory being held during the Fall Semester of 2016. The purpose of the workshop is to provide an overview of key areas of research to be covered in the program, including an introduction to open problems of current interest.

The workshop will concentrate on parabolic methods in both Riemannian and complex geometry. The topics will include

- Ricci flow. Analytic questions about Ricci flow in three dimensions. Possible applications of Ricci flow to 4-manifold topology. Ricci flow in higher dimensions under curvature assumptions.

- Kähler-Ricci Flow. Applications to the Kähler-Einstein problem. Connections to the minimal model program. Study of Kähler-Ricci solitons and limits of Kähler-Ricci flow.

- Mean curvature flow. Singularity analysis. Generic mean curvature flow.

- Other geometric flows such as Calabi flow and pluriclosed flow.

The workshop will integrate elements from complex differential geometry with Einstein metrics and their generalizations. The topics will include

- Existence of Kähler-Einstein metrics and extremal Kähler metrics. Notions of stability in algebraic geometry such as Chow stability, K-stability, b-stability, and polytope stability. Kähler-Einstein metrics with conical singularities along a divisor.

- Calabi-Yau metrics and collapsed limit spaces. Connections with physics and mirror symmetry.

- Einstein metrics and their moduli spaces, ε-regularity, noncompact examples such as ALE, ALF, and Poincaré-Einstein metrics. Generalizations of the Einstein condition, such as Bach-flat metrics and Ricci solitons.

- Sasaki-Einstein metrics and metrics with special holonomy. New examples and classification problems.

The week will be devoted to an introduction to modern techniques in Riemannian geometry. This is intended to help graduate students and younger researchers get a headstart, in order to increase their participation during the main semester programs and research lectures. To increase outreach, the week will focus on Riemannian geometry and should be largely accessible. Some minicourses on topics of recent interest will be included. The workshop will also have semi-expository lectures dealing with aspects of spaces with curvature bounded from below, since such spaces will occur throughout the semester. We expect that many Berkeley mathematicians and students will participate in the introductory workshop.

The purpose of this meeting is to help junior female researchers to become familiar with the focus topics of the main MSRI program, and also for the junior researchers to have an opportunity to get acquainted with more senior women researchers in differential geometry.

This workshop is open to all mathematicians.

This workshop serves to bring into focus the fundamental aim of the jumbo program by both a)  showcasing the spectacular progress in recent years in the study of both nonlinear dispersive as well as stochastic partial differential equations and b) bringing to the fore the key challenges for the future in quantitatively analyzing the dynamics of solutions arising from the flows generated by deterministic and non-deterministic evolution differential equations, or dynamical evolution of large physical systems.  

During the two weeks long workshop, we intertwine talks on a wide array of topics by some of the key researchers in both communities and aim at highlighting the most salient ideas, proofs and questions which are important and fertile for `cross-pollination’ between PDE and SPDE. Topics include:  Global dynamics and singularity formation for geometric and physical nonlinear wave and dispersive models (critical and supercritical regimes); dynamics of infinite dimensional systems (critical phenomena, multi scale dynamics and metastability); symplectic structures of infinite dimensional dynamical systems; randomization and long time dynamics, invariant Gibbs and weighted Wiener measures; derivation of effective dynamics in quantum systems; weak turbulence phenomena; optimization and learning algorithms: distributed, stochastic and parallel.

The purpose of the program New Challenges in PDE: Deterministic Dynamics and Randomness in High and Infinite Dimensional Systems is to bring together a core group of mathematicians from the dispersive PDE and the SPDE communities whose research contains an underlying and unifying problem:  analyzing high or infinite dimensional dynamics, where dynamics is understood in a broad sense and arising from the flows generated by either deterministic or stochastic partial differential equations, or from dynamical evolution of large physical systems.

The introductory workshop will serve as an overview to the program.  It aims at familiarizing graduate students, postdocs, and other researchers to the major topics of the program through short courses and discussions.

This workshop will consist of various talks given by prominent female mathematicians whose research lies in and interfaces with the fields of nonlinear evolution dispersive PDE, wave phenomena and stochastic processes.  These talks will be appropriate for graduate students, post-docs, and researchers in areas above mentioned.  The workshop will allocate ample time for group discussions and will include a professional development session.

This workshop is open to all mathematicians.

The Advances in Homogeneous Dynamics workshop will feature the speakers whose work is at the forefront of the field. There will be a panel discussion accompanied by an open problem session to lay out possible directions for the research in homogeneous dynamics. Talks will be in a broad range of topics and this will help to build more connections between researchers interested in dynamical systems, number theory and geometry. For example we hope that the involvement of the participants of the other program held at MSRI during the same academic year (Dynamics on Moduli Spaces of Geometric Structures, Spring 2015) would create new connections between the topics. There will be shorter talks presented by early-career researchers

The Research Workshop of the ``Dynamics on moduli spaces of geometric structures'' will concentrate on some of the following general interrelated themes:

(1) Geometric structures on the spaces of geometric structures which extend and generalize classical constructions on Teichmüller spaces, such as the Weil-Petersoon metric, the pressure metric, the Teichmüller metric and its geodesic flow, Fenchel-Nielsen coordinates, Fock-Goncharov Thurson-Penner coordinates, and the symplectic and Poisson  geometries

(2) Relations with harmonic maps, Riemann surfaces, complex geometry:  specifically Higgs  bundles, holomorphic differentials (quadratic, cubic, etc.) as parameters  for representations  of the fundamental group, hyperkähler and complex symplectic geometry of  moduli spaces,   lifts of Teichmüller geodesic flows to flat bundles of character varieties

(3) Asymptotic properties of higher Teichmüller spaces, including generalized measured geodesic laminations, Culler-Morgan-Shalen asymptotics of character varieties, degenerations of geometric structures and discrete subgroups

(4) Actions of mapping class groups and outer automorphism groups,  properness criteria for Anosov representations and their generalizations,  properness criteria for non-discrete representations, chaotic actions of  mapping class groups and the monodromy map from structures to  representations

(5) Classification of exotic geometric structures, tameness criteria, generalizations of ending lamination-type invariants to higher rank structures, rigidity and flexibility for thin subgroups, arithmeticity conditions, and geometric transitions

This Introductory Workshop will consist of several introductory lectures and series of lectures on the recent trends in the field, given by experts in the domain. In addition, there will be several shorter talks by young researchers.

Please note that immediately preceding this workshop there is a Connections for Women workshop which will also be introductory in nature.

This workshop will consist of several mini-courses given by prominent female mathematicians in the field, intended for graduate students, post-docs, and researchers in areas related to the program. The workshop will also include an informal panel discussion session among female researchers on career issues. This workshop is open to all mathematicians.

The deformation theory of geometric structures on manifolds  is a subfield of differential geometry and topology, with a heavy infusion of Lie theory. Its richness stems from close relations to dynamical systems, algebraic geometry, representation theory, Lie theory, partial differential equations, number theory, and complex analysis.

The introductory workshop will serve  as an overview to the  program.   It aims to familiarize graduate students, post-docs, and other researchers to the major topics of the program. There will be a number of short courses.

This two-day workshop will consist of various talks given by prominent female mathematicians in the field.  These will be appropriate for graduate students, post-docs, and researchers in areas related to the program.  The workshop will also include a professional development session.

This workshop is open to all mathematicians.

L-functions attached to Galois representations coming from algebraic geometry contain subtle arithmetic information (conjectures of Birch and Swinnerton-Dyer, Deligne, Beilinson, Bloch and Kato, Fontaine and Perrin-Riou). Langlands has predicted the existence of a correspondence relating these L-functions to L-functions of automorphic forms which are much better understood. The workshop will focus on recent developments related to Langlands correspondence (construction of Galois representations attached to automorphic forms via the cohomology of Shimura varieties, modularity of Galois representations...) and arithmetic of special values of L-functions.

It will be dedicated to Michael Harris as a tribute to his enormous influence on the themes of the workshop.

The workshop will focus on the role of categorical structures in number theory and harmonic analysis, with an emphasis on the setting of the Langlands program. Celebrated examples of this theme range from Lusztig's character sheaves to Ngo's proof of the Fundamental Lemma. The workshop will be a forum for researchers from a diverse collection of fields to compare problems and strategies for solutions.

Geometric Representation Theory is a very active field, at the center of recent advances in Number Theory and Theoretical Physics. The principal goal of the Introductory Workshop will be to provide a gateway for graduate students and new post-docs to the rich and exciting, but potentially daunting, world of geometric representation theory. The aim is to explore some of the fundamental tools and ideas needed to work in the subject, helping build a cohort of young researchers versed in the geometric and physical sides of the Langlands philosophy.

Within the broad range of geometric representation theory the Connections Workshop will focus on three research topics in which we expect particularly striking new developments within the next few years:
* Categorical and geometric structures in representation theory and Lie superalgebras
* Geometric construction of representations via Shimura varieties and related moduli spaces
* Hall algebras and representations

The workshop will bring together researchers from these different topics within geometric representation theory and will thus facilitate a successful start of the semester program. It will give junior researchers from each of these parts of geometric representation theory a broader picture of possible applications and of new developments, and will establish a closer contact between junior and senior researchers.
This workshop is aimed at encouraging and increasing the active participation of women and members of under-represented groups in the MSRI program. 

All are welcome to participate in the scientific portions of the workshop and the panel discussion, regardless of gender.

The goal of this workshop is to give a practical introduction to some of the main topics and techniques related to the August-December 2014 MSRI program, "New geometric methods in number theory and automorphic forms."   The workshop is aimed at graduate students and interested researchers in number theory or related fields.  

There will be  lecture series on periods of automorphic forms, Shimura varieties, and representations of p-adic groups,as well as more advanced topics, including p-adic Hodge theory and the cohomology of arithmetic groups.  

This 2-day workshop will showcase the contributions of female mathematicians to the three main themes of the associated MSRI program: Shimura varieties, p-adic automorphic forms, periods and L-functions. It will bring together women who are working in these areas in all stages of their careers, featuring lectures by both established leaders and emerging researchers. In addition, there will be a poster session open to all participants and an informal panel discussion on career issues.

The workshop will feature talks in a range of topics where model theory interacts with other parts of mathematics, especially number theory and arithmetic geometry, including: motivic integration, algebraic dynamics, diophantine geometry, and valued fields.

Recent innovations in higher category theory have unlocked the potential to reimagine the basic tools and constructions in algebraic topology. This workshop will explore the interplay between these higher and $\infty$-categorical techniques with classical algebraic topology, playing each off of the other and returning the field to conceptual, geometrical intuition.

The development of model theory has always been influenced by its potential applications.
Recent years have seen a remarkable flowering of that development, with many exciting applications of model theory in number theory and algebraic geometry. The introductory workshop will aim to increase these interactions by exposing the techniques of model theory to the number theorists and algebraic geometers, and the problems of number theory and algebraic geometry to the model theorists. The Connections for Women workshop will focus on presenting current research on the borders of these subjects, with particular emphasis on the contributions of women. In addition, there will be some social occasions to allow young women and men to make connections with established researchers, and a panel discussion addressing the challenges faced by all young researchers, but especially by women, in establishing a career in mathematics.

Model theory is a branch of mathematical logic whose structural techniques have proven to be remarkably useful in arithmetic geometry and number theory. We will introduce in this workshop some of the main themes of the program.

In particular, we will be offering the following tutorials:
1. An Introduction to Stability-Theoretic Techniques, by Pierre Simon.
2. Model Theory and Diophantine Geometry, by Antoine Chambert-Loir, Ya'acov Peterzil, and  Anand Pillay.
3. Valued Fields and Berkovich Spaces, by Deirdre Haskell and Martin Hils.
4. Model Theory and Additive Combinatorics, by Lou van den Dries.

In addition to the tutorials there will be several "state of the art" lectures on the program topics, indicating recent results as well as directions for future work. Speakers include Ekaterina Amerik, Ehud Hrushovski, Alice Medvedev, Terence Tao, and Margaret Thomas.

The introductory workshop aims to familiarize graduate students, postdocs, and non-experts to major and new topics of the current program. Though the audience is expected to have a general mathematical background, knowledge of technical terminology and recent findings is not assumed.

Algebraic topology is a rich, vibrant field with close connections to many branches of mathematics. This workshop will describe the state of the field, focusing on major programs, open problems, exciting new tools, and cutting edge techniques.

The introductory workshop serves as an overview to the overlying programmatic theme. It aims to familiarize graduate students, postdocs, and non-experts to major and new topics of the current program. Though the audience is expected to have a general mathematical background, knowledge of technical terminology and recent findings is not assumed.

This two-day workshop will consist of short courses given by prominent female mathematicians in the field. These introductory courses will be appropriate for graduate students, post-docs, and researchers in related areas. The workshop will also include a panel discussion featuring successful women at various stages in their mathematical careers.

The purpose of this workshop is to gather researchers working in various areas of geometry in infinite dimensions in order to facilitate collaborations and sharing of ideas. Topics represented include optimal transport and geometries on densities, metrics on shape spaces, Euler-Arnold equations on diffeomorphism groups, the universal Teichmuller space, geometry of random Riemann surfaces, metrics on spaces of metrics, and related areas. The workshop will be held on the campus of University of California Berkeley (60 Evans Hall) the weekend of December 7-8, 2013. It is funded by an NSF grant.

This workshop discusses recent developments both in the study of the properties of initial data for Einstein's equations, and in the study of solutions of the Einstein evolution problem. Cosmic censorship, the formation and stability of black holes, the role of mass and quasi-local mass, and the construction of solutions of the Einstein constraint equations are focus problems for the workshop. We highlight recent developments, and examine major areas in which future progress is likely.

The workshop will be devoted to emerging approaches to fluid mechanical, geophysical and kinetic theoretical flows based on optimal transportation. It will also explore numerical approaches to optimal transportation problems.

Mathematical relativity is a very widely ranging area of mathematical study, spanning differential geometry, elliptic and hyperbolic PDE, and dynamical systems. We introduce in this workshop some of the leading areas of current interest associated with problems in cosmology, the theory of black holes, and the geometry and physics of the Cauchy problem (initial data constraints and evolution) for the Einstein equations.

The introductory workshop serves as an overview to the overlying programmatic theme. It aims to familiarize graduate students, postdocs, and non-experts to major and new topics of the current program. Though the audience is expected to have a general mathematical background, knowledge of technical terminology and recent findings is not assumed.

Ever since the epic work of Yvonne Choquet-Bruhat on the well-posedness of Einstein's equations initiated the mathematical study of general relativity, women have played an important role in many areas of mathematical relativity. In this workshop, some of the leading women researchers in mathematical relativity present their work.

The workshop is intended to give an overview of the research landscape surrounding optimal transportation, including its connections to geometry, design applications, and fully nonlinear partial differential equations.

As such, it will feature some survey lectures or minicourses by distinguished visitors and/or a few of the organizers of the theme semester, amounting to a kind of summer school. These will be complemented by a sampling of research lectures and short presentations from a spectrum of invited guests and other participants, including some who attended the previous week's {\em Connections for Women} workshop.

The introductory workshop aims to familiarize graduate students, postdocs, and non-experts to major and new topics of the current program. Though the audience is expected to have a general mathematical background, knowledge of technical terminology and recent findings is not assumed.

This two-day event aims to connect women graduate students and beginning researchers with more established female researchers who use optimal transportation in their work and can serve as professional contacts and potential role-models. As such, it will showcase a selection of lectures featuring female scientists, both established leaders and emerging researchers.

These lectures will be interspersed with networking and social events such as lunch or tea-time discussions led by successful researchers about (a) the particular opportunities and challenges facing women in science---including practical topics such as work-life balance and choosing a mentor, and (b) promising new directions in optimal transportation and related topics. Junior participants will be paired with more senior researchers in mentoring groups, and all participants will be encouraged to stay for the Introductory Workshop the following week, where they will have the opportunity to propose a short research communication.

The workshop will examine the interplay between measures of singularities coming both from characteristic p methods of commutative algebra, and invariants of singularities coming from birational algebraic geometry. There is a long history of this interaction which arises via the "reduction to characteristic p" procedure. It is only in the last few years, however, that very concrete objects from both areas, namely generalized test ideals from commutative algebra and multiplier ideals from birational geometry, have been shown to be intimately connected. This workshop will explore this connection, as well as other topics used to study singularities such as jets schemes and valuations.

In recent years there have been increasing interactions between noncommutative algebra/representation theory on the one hand and algebraic geometry on the other. This workshop would aim to examine these interactions and, as importantly, to encourage the interactions between the three areas. The precise topics will become more precise nearer the time, but will certainly include:

Noncommutative algebraic geometry; Noncommutative resolutions of singularities and Calabi-Yau algebras; Symplectic reflection and related algebras; D-module theory; Deformation-quantization
 

The workshop will focus on recent breakthroughs in understanding and applications of free resolutions and on interactions of commutative algebra and representation theory, where algebraic geometry often appears as a third player. A specific goal is to stimulate further interaction between these fields.

This workshop will provide several short lecture series consisting two or three lectures each to introduce postdocs, graduate students and non-experts to some of the major themes of the conference. While the precise topics may change to reflect developments in the area, it is likely that we will run mini-series in the following subjects:

Noncommutative algebraic geometry; D-Module Theory; Derived Categories; Noncommutative Resolutions of Singularities; Deformation-Quantization; Symplectic Reflection Algebras; Growth Functions of Infinite Dimensional Algebras.

The Connections for Women workshop associated to the MSRI program in noncommutative algebraic geometry and representation theory is intended to bring together women who are working in these areas in all stages of their careers.

As the first event in the semester, this workshop will feature a "tapas menu" of current research and open questions: light but intriguing tastes, designed to encourage further exploration and interest. Talks will be aimed at a fairly general audience and will cover diverse topics within the theme of the program. In addition, there will be a poster session for graduate students and recent PhD recipients and a panel discussion on career issues, as well as free time for informal discussion.

This workshop on Combinatorial Commutative Algebra aims to bring together researchers studying toric algebra and degenerations, simplicial objects such as monomial ideals and Stanley-Reisner rings, and their connections to tropical geometry, algebraic statistics, Hilbert schemes, D-modules, and hypergeometric functions.

Cluster algebras provide a unifying algebraic/combinatorial framework for a wide variety of phenomena in settings as diverse as quiver representations, Teichmuller theory, Poisson geometry, Lie theory, discrete integrable systems, and polyhedral combinatorics.

The workshop aims at presenting a broad view of the state-of-the-art understanding of the role of cluster algebras in all these areas, and their interactions with each other.

This workshop will take place at the opening of the MSRI special programs on Commutative Algebra and on Cluster Algebras. It will feature lecture series at different levels, to appeal to a wide variety of participants. There will be minicourses on the basics of cluster algebras, and others developing particular aspects of cluster algebras and commutative algebra.

This workshop will present basic notions from Commutative Algebra and Cluster Algebras, with a particular focus on providing background material. Additionally, the workshop aims to encourage and facilitate the exchange of ideas between researchers in Commutative Algebra and researchers in Cluster Algebras.

The field of random media has been the object of intensive mathematical research over the last thirty years. It covers a variety of models, mainly from condensed matter physics, physical chemistry, and geology, where one is interested in materials which have defects or inhomogeneities. These features are taken into account by letting the medium be random. It has been found that this randomness can cause very unexpected effects in the large scale behavior of these models; on occasion these run contrary to the prevailing intuition. A feature of this area, which it has in common with other areas of statistical physics, is that what was initially thought to be just a simple toy model has turned out to be a major mathematical challenge.

Our understanding of the scaling limits of discrete statistical systems has shifted in recent years from the physicists' field-theoretical approaches to the more rigorous realm of probability theory and complex analysis. The aim of this workshop is to combine both discrete and continuous approaches, as well as the statistical physics/combinatorial and the probabilistic points of view. Topics include quantum gravity, planar maps, discrete conformal analysis, SLE, and other statistical models such as loop gases.

Over the last ten years there has been spectacular progress in the understanding of geometrical properties of random processes. Of particular importance in the study of these complex random systems is the aspect of their phase transition (in the wide sense of an abrupt change in macroscopic behavior caused by a small variation in some parameter) and critical phenomena, whose applications range from physics, to the performance of algorithms on networks, to the survival of a biological species.

Recent advances in the scope of rigorous scaling limits for discrete random systems, most notably for 2D systems such as percolation and the Ising model via SLE, have greatly contributed to the understanding of both the critical geometry of these systems and the behavior of dynamical stochastic processes modeling their evolution. While some of the techniques used in the analysis of these systems are model-specific, there is a remarkable interplay between them. The deep connection between percolation and interacting particle systems such as the Ising and Potts models has allowed one model to successfully draw tools and rigorous theory from the other.

The aim of this workshop is to share and attempt to push forward the state-of-the-art understanding of the geometry and dynamic evolution of these models, with a main focus on percolation, the random cluster model, Ising and other interacting particle systems on lattices.

Research at the interface of lattice statistical mechanics and combinatorial problems of ``large sets" has been and exciting and fruitful field in the last decade or so. In this workshop we plan to develop a broad spectrum of methods and applications, spanning the spectrum from theoretical developments to the numerical end. This will cover the behaviour of lattice models at a macroscopic level (scaling limits at criticality and their connection with SLE) and also at a microscopic level (combinatorial and algebraic structures), as well as efficient enumeration techniques and Monte Carlo algorithms to generate these objects.

This 2-day workshop will bring together researchers from discrete mathematics, probability theory, theoretical computer science and statistical physics to explore topics at their interface. The focus will be on combinatorial structures, probabilistic algorithms and models that arise in the study of physical systems. This will include the study of phase transitions, probabilistic combinatorics, Markov chain Monte Carlo methods, and random structures and randomized algorithms.

Since discrete lattice models stand at the interface of these fields, the workshop will start with background talks in each of the following three areas: Statistical and mathematical physics; Combinatorics of lattice models; Sampling and computational issues. These talks will describe the general framework and recent developments in the field and will be followed with shorter talks highlighting recent research in the area.

The workshop will celebrate academic and gender diversity, bringing together women and men at junior and senior levels of their careers from mathematics, physics and computer science.

Geometric problems which are inherently quantitative occur in various aspects of theoretical computer science, including
a) Algorithmic tasks for geometric questions such as clustering and proximity data structures.
b) Geometric methods in the design of approximation algorithms for combinatorial optimization problems, including the analysis of semidefinite programs and embedding methods.
c) Geometric questions arising from computational complexity, particularly in hardness of approximation. These include isoperimetric and Fourier analytic problems. These include isoperimetric and Fourier analytic problems.

This workshops aims to present recent progress in these directions.

This workshop is devoted to various kinds of embeddings of metric spaces into Banach spaces, including biLipschitz embeddings, uniform embeddings, and coarse embeddings, as well as linear embeddings of finite dimensional spaces into low dimensional $\ell_p^n$ spaces. There will be an emphasis on the relevance to geometric group theory, and an exploration into the use of metric differentiation theory to effect embeddings.

"Probabilistic Reasoning in Quantitative Geometry" refers to the use of probabilistic techniques to prove geometric theorems that do not have any a priori probabilistic content. A classical instance of this approach is the probabilistic method to prove existence of geometric objects (examples include Dvoretzky's theorem, the Johnson-Lindenstrauss lemma, and the use of expanders and random graphs for geometric constructions). Other examples are the use of probabilistic geometric invariants in the local theory of Banach spaces (sums of independent random variables in the context of type and cotype, and martingale-based invariants), the more recent use of such invariants in metric geometry (e.g., Markov type in the context of embedding and extension problems), probabilistic tools in group theory, the use of probabilistic methods to prove geometric inequalities (e.g., maximal inequalities, singular integrals, Grothendieck inequalities), the use of probabilistic reasoning to prove metric embedding results such as Bourgain's embedding theorem (where the embedding is deterministic, but its analysis benefits from a probabilistic interpretation), probabilistic interpretations of curvature and their applications, and the use of probabilistic arguments in the context of isoperimetric problems (e.g., Gaussian, rearrangement, and transportation cost methods).

Quantitative Geometry deals with geometric questions in which quantitative or asymptotic considerations occur. The workshop will provide a mathematical introduction, a foretaste, of the many themes this exciting topic comprises: geometric group theory, theory of Lipschitz functions, large scale and coarse geometry, embeddings of metric spaces, quantitative aspects of Banach space theory, geometric measure theory and of isoperimetry, and more.

This workshop will provide an introduction to the program on Quantitative Geometry. There will be several short lecture series, given by speakers chosen for the accessibility of their lectures, designed to introduce non-specialists or students to some of the major themes of the program.

Our workshop will highlight some work relevant to or carried out during our program at the MSRI, including statistical results about ranks for elliptic curves, zeros of L-functions, curves over finite fields, as well as algorithms for L-functions, point counting, and automorphic forms.

Many problems in physics, industry, finance, biology, and other areas can be described by partial differential equations that exhibit apriori unknown sets, such as interfaces, moving boundaries, shocks, etc. The study of such sets, also known as free boundaries, often occupies a central position in such problems. The main objective of the workshop is to bring together experts in various theoretical an applied aspects of free boundary problems.

Our Introductory Workshop will focus largely on the background, recent work, and current problems regarding: Selmer groups and Mordell-Weil groups, and the distribution of their ranks (and "sizes") over families of elliptic curves, including recent work of Manjul Bhargava and Arul Shankar where they have shown that the average size of the 2-Selmer group of an elliptic curve over Q is 3, and thereby obtains information about the average rank of Mordell-Weil groups; related work on the asymptotics of number fields; certain natural families of L-functions, and the statistical distribution of their zeros and values; complementary algorithmic methods and experimental results regarding L-functions, automorphic forms, elliptic curves and number fields; the statistical behavior of eigenvalues of Frobenius elements in Galois representations.


 

The format of this 2-day workshop will be colloquium-style presentations that will introduce some of the major topics touched on by the "Arithmetic Statistics" program. They will be pitched so as to be understandable to researchers with a variety of mathematical backgrounds. The talks are designed broadly as a lead-in to the program's initial workshop (taking place the following week) and will include topics such as the Sato-Tate conjecture, random matrix theory, and enumeration of number fields. The purpose will be to provide background but also to present the exciting areas where progress is happening fast, where major problems have been solved, or where there are significant open questions that need to be tackled. With this we aim to provide motivation for the Connections participants to involve themselves with the remainder of the program.

 

Many problems in physics, industry, finance, biology, and other areas can be described by partial differential equations that exhibit a priori unknown sets, such as interfaces, moving boundaries or shocks for example. The study of such sets, also known as free boundaries, often plays a central role in the understanding of such problems. The aim of this workshop is to introduce several free boundary problems arising in completely different areas.

Contributions of women working in areas related to free boundary problems will be presented. It will include survey lectures on current problems and on standard techniques used in this field, as well as more specific new results of individual researchers. One of the major goals besides the scientific aspect, is to encourage women mathematicians to interact and to build networks. It addresses also to graduate students who are very welcome. A discussion on women’s experiences in the mathematical community should help them to find their way in their mathematical career.

 

Random matrix theory (RMT) was introduced into the theoretical physics community by Eugene Wignerinthe 1950s as a model for the scattering resonances of neutrons off large nuclei. In multivariate statistics, random matrix models were introduced in the late 1920s by John Wishart and subsequently developed by Anderson, James and others. Since these early beginnings RMT has found an extraordinary variety of mathematical, physical and engineering applications that, to name some, include number theory, stochastic growth models, tiling problems and wireless communications.

 

Inverse Problems are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. Applications include a number of medical as well as other imaging techniques, location of oil and mineral deposits in the earth's substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes, and modelling in the life sciences.
The speakers in the workshop will cover a broad range of the most recent developments in the theory and applications of inverse problems.





 

Topics covered in this workshop will include fundamental problems in random matrices, including universality questions and connections to physics, free probability, Riemann Hilbert problems and applications to other areas of mathematics such as number theory and numerical analysis.

In the spring of 1999, MSRI hosted a very successful and influential one-semester program on RMT and its applications. At the workshops during the semester, there was a sense of excitement as brand new and very recent results were reported. The goal of the 2010 Program is to showcase the many remarkable developments that have taken place since 1999 and to spur further developments in RMT and Related areas of interacting particle systems (IPS) and integrable systems (IS) as well as to highlight various applications of RMT.

Inverse Problems are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. Applications include a number of medical as well as other imaging techniques, location of oil and mineral deposits in the earth’s substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modelling in the life sciences.
 

Inverse Problems are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. Applications include a number of medical as well as other imaging techniques, location of oil and mineral deposits in the earth’s substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modelling in the life sciences.

Sponsor: Hayashibara Foundation




Symplectic geometry originated as a mathematical language for Hamiltonian mechanics, but during the last 3 decades it witnessed both, spectacuar development of the mathematical theory and discovery of new connections and applications to physics. Meanwhile, non-commutative geometry naturally entered into this picture.

The first week of May 2010 coincides with the first year anniversary of Alan Weinstein's retirement from UC Berkeley; Weinstein has been one of the most influential figures in symplectic geometry, Poisson geometry and analysis in the past forty years. Weinstein's fundamental work inspired many others and led to the development of central concepts in symplectic and Poisson geometry, as well as to the establishment of symplectic geometry as an independent discipline within mathematics. This conference will be a forum to celebrate Weinstein's fundamental contributions to geometry and mathematics at large.

This workshop will focus on recent progress in central problems in
symplectic and contact topology and Hamiltonian dynamics such as
rigidity of Lagrangian submanifolds, algebra/topology/geometry of
symplectomorphism and contactomorphism groups, exotic symplectic and
contact structures, and existence of
periodic orbits of Hamiltonian systems and Reeb flows.
It will explain applications of the "large machines"
such as Floer Theory, Symplectic Field Theory and Fukaya categories,
showing where these machines do not yet provide satisfactory
answers. Special attention will also be paid to articulating
new problems and
directions, as well as to explaining
interactions between symplectic and contact
topology and other fields.

Link homology is a young and rapidly-developing area drawing on many branches of mathematics. The subject has its roots in representation theory, and it has benefitted from its interactions with low-dimensional, classical, and quantum topology and symplectic geometry. Indeed, several recent developments have underscored the close parallels between link homology and Floer homological invariants for low-dimensional manifolds.

This workshop will introduce the main branches in the study of knot homology theories. It will consist of three mini-courses, one on knot Floer homology and related topics; one on the various approaches to
Khovanov and Khovanov-Rozansky homology; and one on categorification on quantum groups. (There will also be several stand-alone lectures.) The techniques involved in the three branches are quite different; in
particular, Heegaard Floer theory is analytic in nature, with its origin in gauge theory and symplectic geometry, while both Khovanov homology and categorification are more algebraic in nature, with origins in representation theory and algebraic geometry. The workshop will provide an opportunity for graduate students and researchers
outside the field to gain entry, as well as for researchers working in one part of the field to learn about techniques and developments in other parts.

This 2-day workshop will serve as a prelude to the introductory workshop for the semester-long program on homology theories of knots and links. Survey talks in the mornings will position the work in Khovanov and Heegaard Floer homology in a broader context, focusing on:

1) applications to classical questions in low-dimensional topology, and
2) connections to contact and symplectic topology.

Research talks in the afternoons will highlight the range of current activity in the field. We plan a format of no more than four talks each day to allow ample time for presentation opportunities for younger researchers and formal and informal discussions.

One of the successes of tropical geometry is its applications to a number of different areas of recently developing mathematics. Among these are enumerative geometry, symplectic field theory, mirror symmetry, dimer models/random surfaces, amoebas and algas, instantons, cluster varieties, and tropical compactifications. While these fields appear quite diverse, we believe the common meeting ground of tropical geometry will provide a basis for fruitful interactions between participants.

The theory of holomorphic curves in symplectic manifolds leads
to rich algebraic structures. The study of these structures is
increasingly important both for understanding the theory itself, and
for actual computations and applications. The aim of the workshop
is to survey ongoing developments in the area. Some of the topics
of interest are: cohomological field theories; relative and tropical
Gromov-Witten invariants; Symplectic Field Theory (SFT) and connections
with string topology; theories of holomorphic curves with Lagrangian
boundary conditions, such as relative SFT, open Gromov-Witten theory,
and Fukaya categories.

This workshop will concentrate on tropical methods in Combinatorics
and Algebra. Some of the topics we expect to explore are
tropical ideas and methods in combinatorial linear algebra and in
combinatorial representation theory, as well as computational issues and applications of tropical methods in algebraic statistics.

This workshop is to lay the foundations for the upcoming program. Mini-courses comprising lectures and exercise/discussion sessions will cover the foundational aspects of tropical geometry as well as its connections with adjacent areas: symplectic geometry, several complex variables, algebraic geometry (in particular enumerative and computational aspects) and geometric combinatorics. The mini-courses will be augmented by research talks on current tropical develpoments to open the scene and set up new goals in the beginning semester.

The aim of this workshop is to introduce advanced graduate students and postdocs to tropical geometry. Various aspects of this multi-faceted field will be highlighted in two short-courses comprising lectures and exercise/discussion sessions as well as in research talks. The workshop will thus provide the participants with
an excellent introduction to the forthcoming events of the program. The scientific part will be complemented by a round table discussion on career issues of female mathematicians.

This workshop aims both to introduce
people to a broad swath of the field
and to frame its most important problems.
Each day will be organized around a
basic topic, such as how to count holomorphic
curves with boundary on a Lagrangian submanifold (which
leads to various versions of Floer theory)
or how to understand the general structure of
symplectic and contact manifolds.
There will also be an introduction to the
analytic and algebraic aspects of symplectic
field theory, and a discussion of some applications.

This will form a bridge between
the graduate student workshop which will just be ending and
the Introductory workshop. After some
elementary talks describing some of the main questions
in the field, there will be an extended discussion session
intended to explain basic concepts to those unfamiliar with the area.
There will also be an opportunity for young researchers in the field
to present their work, and an evening social event.

This workshop will present the state of the art in combinatorial, enumerative, and toric algebraic geometry. It
will highlight this part of modern algebraic geometry within the context of the broader parent program at MSRI, and convey its scope to young researchers.

This workshop will convene experts specializing on the minimal model program, derived categories and moduli
spaces in an informal environment to facilitate the cross-fertilization of ideas across these different fields of algebraic geometry.
 

The main theme of the workshop will be to explore modern approaches to
problems originating in Classical Algebraic Geometry, and at the same time
offer an introduction to various subfields to the younger participants in
the semester-long program.

This workshop is part of the semester program on Algebraic Geometry, and
additional funding will be available for participants to attend the associated
"Introductory workshop: Classical algebraic geometry," January 26-30, 2009.

 

This workshop will bring together researchers interested in the topology of stratified spaces. It will focus roughly on four topics: topology of complex varieties, signature theory on singular spaces, L² and intersection cohomology, and mixed Hodge theory and singularities. Aside from talks on current research, there will be a series of introductory lectures on these themes. These talks will be aimed at strengthening the connections among the various topology research groups and the connections between topology researchers and researchers at the program on Analysis of Singular Spaces, running concurrently.

This four-day program will be an introduction to the main themes of the Analysis on Singular Spaces program, geared toward graduate students and postdocs. It will consist of several minicourses, covering topics in
spectral and scattering theory, index theory, and $L²$-cohomology, as well as developing the technical tools needed as background.

This two-day program will consist of a "crash course" in topics in PDE relevant to the Analysis on Singular Spaces main program, and in particular will attempt to get graduate students, postdocs, and even advanced
undergraduates ready for the Introductory Workshop the following week. The focus will be topics in analysis on smooth manifolds whose generalizations to singular spaces will be the focus of the main program.

The goal of the Introductory Workshop is to survey current and recent developments in the field. The talks will focus on tableaux, reflection groups, finite groups, geometry and mathematical physics in the realm of Combinatorial Representation Theory.

Complex physical, biological, geophysical and environmental systems display variability over a broad range of spatial and temporal scales. To make progress in understanding and modelling such systems, a combination of computational, analytical, and experimental techniques is required. There are issues that emerge prominently in each of these categories and in all these stochastic methods are playing a fundamental role.

Mirror duality has demonstrated the striking effectiveness of concepts of modern physics in enuerative geometry. It is of the same type as the simple radius inversion duality seen in string compactifications on S1. This type was discovered early because it shows up in every term in the string genus expansion and can be studied in 2d conformal field theory.

This workshop is jointly sponsored by MSRI and CRM and will be held at the Banff International Research Station in Banff, Canada.

NOTE: This workshop is to be held at the International House Berkeley on the UC Berkeley campus, at 2299 Piedmont Avenue.

The purpose of this program is to introduce new topological concepts in physics to young research mathematicians from both South and North America. The lectures given during the first week will provide the necessary background; these will be supplemented, primarily during the second week, with lectures by leading researchers on recent progress. That week serves as the Opening Workshop for the MSRI program, Spring, 2006, in New Topological Structures in Physics.

NOTE: This workshop is to be held at the International House on the UC Berkeley campus, at 2299 Piedmont Avenue. On site registration for the workshop will be at the International House, starting at 8:30 AM Monday and ending at 3:30 PM Monday.

NOTE: This workshop is to be held at the International House on the UC Berkeley campus, at 2299 Piedmont Avenue, except for the Tuesday session, which will be held at the Lawrence Berkeley National Laboratory. On site registration for the workshop will start at 8:30 AM Monday and end at 3:30 PM Monday.

This workshop seeks to bring together (a) mathematicians studying the math
properties of particular models, and (b) experts in various network
fields who can survey the successes and challenges of modeling within
their field.

This workshop is aimed at faculty who wish to learn about this exciting field and would like to enrich a variety of undergraduate courses with new examples and applications. The workshop is being held in collaboration with the Mathematical Association of America as part of the MAA's Professional Enhancement Program (PREP). See the PREP website for information about registration and participant support.

The topics of this workshop include phase transitions in connection to
random graphs, boolean functions, satisfiability problems, coding,
reconstruction on trees and spinglasses.

Special focus will be given to the study of the interplay
between the replica method, local weak convergence and algorithmic aspects of
reconstruction.

Recent years have seen the rapid development of techniques for the analysis of MCMC algorithms, with applications in all the above areas. These techniques draw from a wide range of mathematical disciplines, including combinatorics, discrete probability, functional analysis, geometry and statistical physics, and there has been significant cross-fertilization between them. This workshop aims to bring together practitioners from all these domains with the aim of furthering this interplay of ideas.

MSRI Program on Probability, Algorithms and Statistical Physics, Spring 2005 --- OPENING DAY, Thursday 13 January, 2005

This workshop will be part of MSRI's Special Semester in Hyperplane Arrangements and Applications.

This workshop will focus on the following topics: Characteristic varieties and resonance varieties, homotopy types of arrangements, moduli of arrangements, Gauss-Manin connections, KZ and qKZ equations, elliptic hypergeometric functions, and hypergeometric functions associated with curves of arbitrary genus.

LOCATION: The Banff Conference Centre, Banff, Canada

To be held at the Banff International Research Station in Banff, Alberta, Canada.

Presented jointly with IPAM, and held in Los Angeles. See IPAM website for details.

To be held at the Banff Conference Centre in Banff (Alberta), Canada

The first week will focus on Infinite-dimensional Algebras, Conformal Field Theory and Integrable Systems, and the second week would be devoted to Supersymmetry in Mathematics and Physics.

Discussion of the important developments in the geometric Langlands correspondence in the last few years

The field of algebraic stacks has gathered a huge momentum and is bound to become one of the main tools of the working mathematician.

The purpose of the workshop will be to bring together people working on different aspects of inverse problems, to appraise the current status of development of the field, and to encourage interaction between mathematicians and scientists and engineers working directly with the applications.

This workshop will concentrate on several topics in representation theory and geometric analysis of homogeneous spaces for which techniques in integral geometry play a key role.

see program webpage at http://zeta.msri.org/calendar/programs/ProgramInfo/52/show_program

see program webpage at http://zeta.msri.org/calendar/programs/ProgramInfo/51/show_program

This workshop will focus on problems of a scattering theoretic nature for geometric operators on manifolds with asymptotically regular
geometries, and also on spectral theory and related questions of invertibility of such operators on singular spaces. The emphasis will be on the consideration of new problems and the dissemination of new techniques.

This meeting will be joint for the first two days with the MSRI workshop on Quantization and Non-commutative Geometry, and during the three-day period April 29 - May 1 will function as a closing conference for the 2000-01 MSRI program on Operator Algebras.

These two topics have been scheduled in a joint workshop because the confluence of their research is likely to influence future advances in both fields.

This workshop will study the spectral theory of geometric operators, including: spectral invariants, applications in conformal geometry, classification of 4-manifolds, index theory and scattering theory.

The Free Probability section of the workshop will cover several aspects of the subject: applications to von Neumann algebras and C*-algebras of free product type, connections with random matrix theory, free stochastic processes and free stochastic integration, combinatorial approach via noncrossing partitions, free entropy.

The Non-commutative Banach Space section will cover the central concepts of the recently developed theory of operator spaces such as: exactness, local reflexivity and injectivity with applications to C* tensor products, operator algebras and operator modules. The non-commutative Lp-spaces, which play an important role in this theory, provide many points of contact with free probability.

This workshop will focus on the development of explicit and computational methods in arithmetic
geometry, as well as the complexity analysis of existing algorithms.

These two areas have had a strong interaction in the last two decades, leading to exciting and closely related mathematics.

This workshop will focus on number-theoretic aspects of cryptography, and will be cross-cultural, where the the cultures in question are "mathematics" and "computer science."

As part of the full-year 2000-2001 program on Operator Algebras, MSRI will host a one-week NATO
ADVANCED RESEARCH WORKSHOP on Simple C*-algebras and Non-commutative Dynamical
Systems, September 25-29, 2000.

This workshop introduces graduate students and other scientists to the exciting area of Operator
Algebras.

This workshop will have lecture series covering the basic areas of algorithmic number theory,
aimed at graduate students and mathematicians without extensive experience in the field.

For more information about this event, please see the original web page at:
http://www.msri.org/activities/programs/9900/noncomm/hopfalg/index.html

For more information about this conference, please visit the original web page at
http://msri.org/activities/programs/9900/noncomm/vonneumann/

Please see the workshop web page at http://www.msri.org/activities/programs/9899/random/qc/ for more information.