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.

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. 

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.

<p>The Hopf fibration of <span class="math-tex">\(S^3 \space by \space S^1\)</span></p>

This workshop will bring together researchers at the frontiers of geometric analysis and Riemannian geometry, with a focus on recent advances on geometric flows, geometric problems in mathematical relativity, global Riemannian geometry, and minimal submanifolds. These areas have shown highly intriguing interactions in recent years and we expect this workshop will provide a unique opportunity to facilitate these emerging links.

The analysis of solutions to nonlinear geometric PDEs with higher-dimensional singular sets has seen some notable recent advances, but many fundamental questions still remain open. This workshop will bring together a wide array of researchers working in differential geometry, gauge theory, nonlinear PDEs, microlocal analysis, the calculus of variations and geometric measure theory, with the goal of describing recent advances, advertising recent technical breakthroughs and forging new connections.

AI-generated interpretation of a random network

This two-day workshop will bring together researchers from discrete mathematics, probability theory, theoretical computer science, and statistics to explore topics at their interface. The focus will be on probability and statistics of random discrete structures, as well as their applications, including in computer science and physical systems. 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.

Visualization of a network constructed using simple probabilistic rules, showing the emergence of hubs and other macroscopic network phenomenon. From https://graph-tool.skewed.de

Networks, graph driven algorithms, and dynamics on graphs such as epidemics, random walks and centrality measures all play a major role, both in our daily lives as well as many scientific and engineering disciplines. This introductory workshop will bring together experts and junior researchers in combinatorics, probability, and statistics to share a broad vision of major challenges and objectives, with a primary focus on models of random graphs and their limits, network inference, dynamic processes on networks and algorithms and optimization on random structures. 

The purpose of this workshop is to bring together promising early-career researchers in extremal combinatorics who are women or from underrepresented minorities so that they can meet with, forge connections with, and be inspired by the leading figures in the area. The workshop will include lectures, time for collaborative research, and an informal panel discussion session among female and minority researchers on career issues.

This workshop will feature leading experts in several major areas of graph theory, including extremal, probabilistic and structural aspects of the field. Introductory lectures will form an important part of the program, providing background and motivation, and aimed at a general mathematical audience. Complementing these, research talks will share exciting recent developments in graph theory.

A degree 7 curve passing through 35 points in the plane

Many exciting breakthroughs in combinatorics involve innovative applications of techniques from a wide range of areas such as harmonic analysis, polynomial and linear algebraic methods, spectral graph theory, and representation theory. This workshop will present recent developments in this area and facilitate discussions of research problems.

Recovering communities in a network.

In a growing number of applications, one needs to analyze and interpret data coming from massive networks. The statistical problems arising from such applications lead to important mathematical challenges: building novel probabilistic models, understanding the possibilities and limitations for statistical detection and inference, designing efficient algorithms, and understanding the inherent limitations of fast algorithms. The workshop will bring together leading researchers in combinatorial statistics, machine learning, and random graphs in the hope of cross-fertilization of ideas.

The Connections workshop will bring together leading experts working at the intersection of kinetic theory and stochastic partial differential equations (SPDEs).

The joint introductory workshop for the programs in Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups and Topological and Geometric Structures in Low Dimensions will feature lectures introducing subjects of interest to both programs, including Teichmuller Theory, geometry in higher rank, foliations and flows, Anosov groups and thermodynamic formalism,  mapping class groups, counting and equidistribution, and related topics. Minicourses will be targeted at early career researchers as well as specialists looking to find connections between the different subjects.

Foliations around a pseudo-Anosov singularity (Image credit: Chi Cheuk Tsang)

This workshop will bring together ideas from diverse areas of mathematics that meet in the setting of geometry and topology in low dimensions.  This includes the study of flows, foliations, and fibrations of three-manifolds and the related study of geometry (e.g. hyperbolic or conformal structures) of the manifolds and of the leaves or fibers, and their mapping class groups.  This is a rich and interconnected area and many adjacent topics will also be featured.

This workshop will focus on recent advances on geometric and dynamical approaches to the study of discrete subgroups of higher rank Lie groups and their deformation spaces. The goal will be to present results and exchange ideas from different areas of mathematics, and we hope to create bonds between several different mathematical communities.