Current Graduate
Upcoming Graduate
Past Graduate

GTC Graduate Seminar: Introduction to Lattice Polytopes
Location: SLMath: Baker Board Room Speakers: Mónica Blanco Gómez (University of Cantabria)This is a preparatory talk for Ben Braun’s Tuesday seminar.
Updated on Aug 25, 2017 02:41 PM PDT 
Graduate Student Lunch Seminar
Location: SLMath: Baker Board RoomCreated on Sep 03, 2015 04:06 PM PDT 
Graduate Student Lunch Seminar
Location: SLMath: Baker Board RoomCreated on Sep 03, 2015 04:04 PM PDT 
Graduate Student Lunch Seminar
Location: SLMath: Baker Board RoomCreated on Sep 03, 2015 04:03 PM PDT 
Graduate Student Lunch Seminar
Location: SLMath: Eisenbud AuditoriumCreated on Sep 03, 2015 04:02 PM PDT 
Graduate Student Lunch Seminar
Location: SLMath: Eisenbud AuditoriumDear friends,
here's the topic of the next graduate student lunch meeting:
The idea is to further explore the concept of "invariant measure" associated to the flow of a Hamiltonian PDE. The starting point would be BurqTzvetkov's 2007 "Invariant measure for a 3d nonlinear wave equation" and some ideas from DengTzvetkovVisciglia's "Invariant measures and long time behavior for the BenjaminOno equation" (depending on my reading speed).
I have chosen those papers based on the following considerations. The paper by Burq and Tzvetkov is the first in their series of papers on the randomized approach to the wave equation, and it looks easier to read than the others. My hope is that it will provide some insight into the construction of invariant measures without too many technical complications. The paper by Deng, Tzvetkov and Visciglia is interesting because it obtains information on an infinitedimensional flow by using an invariant measure and the Poincare's recurrence theorem. This is an idea that we have never seen in previous meetings.
As usual you will find the bibliography at the following Dropbox link:
https://www.dropbox.com/sh/g54iliv2muckzni/AACNEpr4_pJseLutUrcfqSSwa?dl=0
All the best
Giuseppe
Hi, this sounds good.
I also suggest finish reading the previous paper of Bourgain,We are still left with several "harder" case.I think it will be rewarding to finish this.If people are interested, I can also try to do a presentation.Best,ChenjieCreated on Sep 03, 2015 04:01 PM PDT 
Graduate Student Lunch Seminar
Location: SLMath: Baker Board RoomUpdated on Sep 03, 2015 03:59 PM PDT 
Graduate Student Lunch Seminar
Location: SLMath: Baker Board Room Speakers: Xueying Yu (Oregon State University), Haitian Yue (University of Massachusetts Amherst)We are fortunate to have Haitian and Xueying presenting results on the cubic NLS next Thursday, starting at 11am. See the message below.
best,PeterDear Prof. Bates.We plan to introduce the almost sure LWP result for cubic NLS on the torus T^2, essentially based on Bourgain's paper(attached below). For the X^{s,b} part, we need also refer to the lecture #2 of Bourgain's lecture notes(attached below) and the section 2.6 of Tao's book: Nonlinear Dispersive Equations: Local and Global Analysis.Since there are too many cases, maybe we will just sketch a outline of the whole proof, and cover a few simple cases.Best,Haitian Yue & Xueying YuCreated on Sep 03, 2015 08:59 AM PDT 
Graduate Student Lunch Seminar
Location: SLMath: Baker Board RoomCreated on Sep 03, 2015 08:57 AM PDT 
Postdoc Symposium (Part I): Wave maps with large data
Location: SLMath: Eisenbud Auditorium Speakers: Andrew Lawrie (Massachusetts Institute of Technology)The wave maps equation is perhaps the simplest incarnation of a geometric wave equation  the nonlinearity arises naturally from the Riemannian structure of the target manifold. It is the hyperbolic analogue of the (elliptic) harmonic maps equation and the (parabolic) harmonic map heat flow.
We will review some of the significant developments from the past decade concerning the asymptotic dynamics of solutions to the energy critical wave maps equation, emphasizing the crucial role that harmonic maps play in singularity formation. We will also discuss new phenomena that arise when curvature is introduced in the domain, focusing on the theory of wave maps on hyperbolic space that is being developed jointly with SungJin Oh and Sohrab Shahshahani.Updated on Sep 18, 2015 11:31 AM PDT 
Graduate Student Lunch Seminar
Location: SLMath: Baker Board RoomCreated on Sep 03, 2015 08:56 AM PDT 
Graduate Student Lunch Seminar
Location: SLMath: Baker Board RoomCreated on Sep 03, 2015 08:55 AM PDT 
Graduate Student Lunch Seminar
Location: SLMath: Baker Board RoomUpdated on Sep 03, 2015 02:19 PM PDT 
Graduate Student Lunch Seminar
Location: SLMath: Baker Board RoomUpdated on Aug 28, 2015 03:58 PM PDT 
Computing critical values of quadratic Dirichlet Lfunctions, with an eye toward their moments.
Location: SLMath: Eisenbud Auditorium Speakers: Matthew AldersonMoments of Lfunctions has been a topic of intense research in recent years. Through the integration of random matrix theory and multiple Dirichlet series with traditional number theoretic arguments, methods for studying the moments of Lfunctions have been developed and, in turn, have lead to many wellposed conjectures for their behavior. In my talk, I will discuss the (integral) moments of quadratic DIrichlet Lfunctions evaluated at the critical point s=1/2. In particular, I will present formulas for computing the critical values for such Lfunctions and then compare the data for the corresponding moments to the (aforementioned) conjectured moments.Updated on Aug 09, 2023 08:34 AM PDT 
FBPInformal Seminar
Location: SLMath: Baker Board Room Speakers: TBA, Lihe WangUpdated on Aug 09, 2023 08:34 AM PDT 
Moment Polynomials for the Riemann Zeta Function
Location: SLMath: Eisenbud Auditorium Speakers: Shuntaro YamagishiI will explain how we calculated the coefficients of moment
polynomials for the Riemann zeta function for k = 4,5.., 13
and numerically tested them against the moment polynomial conjecture.
Updated on Aug 09, 2023 08:34 AM PDT 
"Computing Lfunctions in SAGE"
Location: SLMath: Eisenbud Auditorium Speakers: RishikeshUpdated on Aug 09, 2023 08:34 AM PDT 
Elliptic curves of arbitrarily large rank (Over Function Fields)
Speakers: Kevin Wilson
Updated on Aug 09, 2023 08:34 AM PDT 
Empirical Evidence for an Arithmetic Analogue of Nevanlinna's Five Value Theorem
Location: SLMath: Baker Board Room Speakers: James Weigandt
Updated on Aug 09, 2023 08:34 AM PDT 
A problem related to the ABC conjecture
Speakers: Danial Kane (Harvard University)
Updated on Aug 09, 2023 08:34 AM PDT 
Postdoctoral and Graduate Student Seminar TBA
Location: SLMath: Eisenbud AuditoriumPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
Gluing semiclassical resolvent estimates via propagation of singularities.
Location: SLMath: Baker Board Room Speakers: Kiril Datchev (Purdue University)Pizza Lunch
Updated on Aug 09, 2023 08:34 AM PDT 
Lower bounds for the volume of the nodal sets
Location: SLMath: Eisenbud Auditorium Speakers: Hamid Hezari (University of California, Irvine)Pizza Lunch
Updated on Aug 09, 2023 08:34 AM PDT 
Nonintersecting Brownian Motions at a Tacnode: Soft and Hard Edge Case.
Location: SLMath: Eisenbud AuditoriumPizza Lunch
Updated on Aug 09, 2023 08:34 AM PDT 
Harmonic maps into conic surfaces with cone angles less than $2\pi$
Updated on Aug 09, 2023 08:34 AM PDT 
A tale of two tiling problems
Speakers: Benjamin Young (University of Oregon)
Updated on Aug 09, 2023 08:34 AM PDT 
Postdoctoral and Graduate Student Seminar TBA
Location: SLMath: Baker Board RoomPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
Dihedral symmetry and the RazumovStroganov ExConjecture
Location: SLMath: Baker Board RoomPizza Lunch
Updated on Aug 09, 2023 08:34 AM PDT 
Geometric structures in the study of the geodesic ray transform
Location: SLMath: Eisenbud Auditorium Speakers: JuhaMatti PerkkioPizza Lunch
Updated on Aug 09, 2023 08:34 AM PDT 
"Edge scaling limits for nonHermitian random matrices"
Location: SLMath: Eisenbud Auditorium Speakers: Martin Bender (Bergische UniversitätGesamthochschule Wuppertal (BUGH))
Updated on Aug 09, 2023 08:34 AM PDT 
Postdoctoral and Graduate Student Seminar TBA
Location: SLMath: Eisenbud AuditoriumPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
From Oscillatory Integrals to a Cubic Random Matrix Model"
Speakers: Alfredo Deaño (Universidad Carlos III de Madrid)Pizza Lunch
Updated on Aug 09, 2023 08:34 AM PDT 
Application of RiemannHilbert Problems in Modelling of Cavitating Flow
Location: SLMath: Eisenbud Auditorium Speakers: Anna Zemlyanova (Kansas State University)Pizza Lunch
Updated on Jan 08, 2024 09:20 AM PST 
Albrecht Durer, Magic Squares, and Unitary Matrix Integrals
Location: SLMath: Eisenbud Auditorium Speakers: Jonathan Novak (University of California, San Diego)Pizza Lunch
Updated on Aug 09, 2023 08:34 AM PDT 
Integrable Equations for Random Matrix Spectral Gap Probabilities
Location: SLMath: Eisenbud Auditorium Speakers: Igor RumanovPizza Lunch
Connections are exposed between integrable equations for spectral gap probabilities of unitary invariant ensembles of random matrices (UE) derived by different  TracyWidom (TW) and AdlerShiotavan Moerbeke (ASvM)  methods. Simple universal relations are obtained between these probabilities and their ratios on one side, and variables of the approach using resolvent kernels of Fredholm operators on the other side. A unified description of UE is developed in terms of universal, i.e. independent of the specific probability measure, PDEs for gap probabilities, using the correspondence of TW and ASvM variables. These considerations are based on the threeterm recurrence for orthogonal polynomials (OP) and onedimensional Toda lattice (or TodaAKNS) integrable hierarchy whose flows are the continuous transformations between different OP bases. Similar connections exist for coupled UE. The gap probabilities for onematrix Gaussian UE (GUE) or joint gap probabilities for coupled GUE satisfy various PDEs whose number grows with the number of spectral endpoints. With the above connections serving as a guide, minimal complete sets of independent lowest order PDEs for the GUE and for the largest eigenvalues of twomatrix coupled GUE are found.Updated on May 13, 2013 11:01 PM PDT 
Imaging Edges in Random Media
Location: SLMath: Eisenbud Auditorium Speakers: Fernando Guevara VasquezPizza Lunch
Consider the problem of imaging a reflector (target) from recordings of the echoes resulting from probing the medium with waves emanating from an array of transducers (the array response matrix). We present an algorithm that selectively illuminates the edges or the interior of an extended target by choosing particular subspaces of the array response matrix. For a homogeneous background medium, we characterize these subspaces in terms of the singular functions of a space and wave number restricting operator, which are also called generalized prolate spheroidal wave functions. We discuss results indicating what can be expected from using this algorithm when the medium fluctuates around a constant background medium and the fluctuations can be modeled as a random field.Updated on May 13, 2013 11:01 PM PDT 
E. Nordenstam's Talk
Location: SLMath: Eisenbud Auditorium Speakers: Eric NordenstamPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
The Inverse Calderon Problem for Schrödinger Operator on Riemann Surfaces
Location: SLMath: Eisenbud Auditorium Speakers: Leo tzouPizza Lunch
We show that on a smooth compact Riemann surface with boundary (M0, g) the Dirichletto Neumann map of the Schrödinger operator â g + V determines uniquely the potential V . This seemingly analytical problem turns out to have connections with ideas in symplectic geometry and differential topology. We will discuss how these geometrical features arise and the techniques we use to treat them. This is joint work with Colin Guillarmou of CNRS Nice. The speaker is partially supported by NSF Grant No. DMS0807502 during this work.Updated on May 13, 2013 11:01 PM PDT 
Resistor Networks and Optimal Grids for Electrical Impedance Tomography with Partial Boundary Measurements
Location: SLMath: Baker Board Room Speakers: Alexander MamonovPizza Lunch
The problem of Electrical Impedance Tomography (EIT) with partial boundary measurements is to determine the electric conductivity inside a body from the simultaneous measurements of direct currents and voltages on a subset of its boundary. Even in the case of full boundary measurements the nonlinear inverse problem is known to be exponentially illconditioned. Thus, any numerical method of solving the EIT problem must employ some form of regularization. We propose to regularize the problem by using sparse representations of the unknown conductivity on adaptive finite volume grids known as the optimal grids. Then the discretized partial data EIT problem can be reduced to solving the discrete inverse problems for resistor networks. Two distinct approaches implementing this strategy are presented. The first approach uses the results for the EIT problem with full boundary measurements, which rely on the use of resistor networks with circular graph topology. The optimal grids for such networks are essentially one dimensional objects, which can be computed explicitly. We solve the partial data problem by reducing it to the full data case using the theory of extremal quasiconformal (Teichmuller) mappings. The second approach is based on resistor networks with the pyramidal graph topology. Such network topology is better suited for the partial data problem, since it allows for explicit treatment of the inaccessible part of the boundary. We present a method of computing the optimal grids for the networks with general topology (including pyramidal), which is based on the sensitivity analysis of both the continuum and the discrete EIT problems. We present extensive numerical results for the two approaches. We demonstrate both the optimal grids and the reconstructions of smooth and discontinuous conductivities in a variety of domains. The numerical results show two main advantages of our approaches compared to the traditional optimizationbased methods. First, the inversion based on resistor networks is orders of magnitude faster than any iterative algorithm. Second, our approaches are able to correctly reconstruct the conductivities of very high contrast, which usually present a challenge to the iterative or linearizationbased inversion methods.Updated on May 13, 2013 11:01 PM PDT