Talk_id  Date  Speaker  Title 
31514

Monday 1/9 4:10 PM

Anna Weigandt, Massachusetts Institute of Technology

Combinatorial Aspects of Determinantal Varieties
 Anna Weigandt, Massachusetts Institute of Technology
 Combinatorial Aspects of Determinantal Varieties
 01/09/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Sabrina M Walton (waltons3@msu.edu)
Schubert calculus has its origins in enumerative questions asked by the geometers of the 19th century, such as “how many lines meet four fixed lines in threespace?” These problems can be recast as questions about the structure of cohomology rings of geometric spaces such as flag varieties. Borel’s isomorphism identifies the cohomology of the complete flag variety with a simple quotient of a polynomial ring. Lascoux and Schützenberger (1982) defined Schubert polynomials, which are coset representatives for the Schubert basis of this ring. However, it was not clear if this choice was geometrically natural. Knutson and Miller (2005) provided a justification for the naturality of Schubert polynomials via antidiagonal Gröbner degenerations of matrix Schubert varieties, which are generalized determinantal varieties. Furthermore, they showed that preexisting combinatorial objects called pipe dreams govern this degeneration. In this talk, we study the dual setting of diagonal Gröbner degenerations of matrix Schubert varieties, interpreting these limits in terms of the “bumpless pipe dreams” of Lam, Lee, and Shimozono (2021). We then use the combinatorics of Ktheory representatives for Schubert classes to compute the CastelnuovoMumford regularity of matrix Schubert varieties, which gives a bound on the complexity of their coordinate rings.

31521

Tuesday 1/10 4:10 PM

Nathaniel Bottman, Max Planck Institute

What analysis, combinatorics, and quilted spheres can tell us about symplectic geometry
 Nathaniel Bottman, Max Planck Institute
 What analysis, combinatorics, and quilted spheres can tell us about symplectic geometry
 01/10/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Sabrina M Walton (waltons3@msu.edu)
A central tool for studying symplectic manifolds is the Fukaya category. In this talk, I will describe my program to relate the Fukaya categories of different symplectic manifolds. The key objects are "witch balls", which are coupled systems of PDEs whose domain is the Riemann sphere decorated with circles and points, and "2associahedra", the configuration spaces of these domains. I will describe applications to symplectic geometry and algebraic geometry, and highlight the role of degenerating families of elliptic PDEs.

31519

Wednesday 1/11 4:10 PM

Aver St. Dizier, University of Illinois

A Polytopal View of Schubert Polynomials
 Aver St. Dizier, University of Illinois
 A Polytopal View of Schubert Polynomials
 01/11/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Sabrina M Walton (waltons3@msu.edu)
Schubert polynomials are a family of multivariable polynomials whose product can be used to solve problems in enumerative geometry. Despite their many known combinatorial formulas, there remain mysteries surrounding these polynomials. I will describe Schubert (and the special case of Schur) polynomials with a focus on polytopes. From this perspective, I will address questions such as vanishing of Schubert coefficients, relative size of coefficients, and interesting properties of their support. Time permitting, I'll talk about my current work on generalizing the Gelfand–Tsetlin polytope, and its connections with representation theory and Bott–Samelson varieties.

31511

Thursday 1/12 4:10 PM

Demetre Kazaras, Duke University

The geometry of scalar curvature and mass in general relativity
 Demetre Kazaras, Duke University
 The geometry of scalar curvature and mass in general relativity
 01/12/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Sabrina M Walton (waltons3@msu.edu)
In general relativity, the space we inhabit is modeled by a Riemannian manifold. The fundamental restriction this theory places upon spatial geometry is a lower bound on this manifold's scalar curvature. It is an important problem in pure geometry to understand the geometric and topological features of this condition. For instance, if a manifold has positive scalar curvature, what may we conclude about the lengths of its curves, the areas of its surfaces, and the topology of the underlying manifold? I will explain many results (originally proven by SchoenYau and GromovLawson) in this direction, and sketch proofs by analyzing objects I call 'spacetime harmonic functions.' Leveraging these new ideas, I will also describe progress on geometric versions of the following questions: How flat is a gravitational system with little total mass? How can we tell when matter will coalesce to form a black hole?

31528

Friday 1/13 4:10 PM

Alexander Watson, University of Minnesota

Mathematics of novel materials from atomic to macroscopic scales
 Alexander Watson, University of Minnesota
 Mathematics of novel materials from atomic to macroscopic scales
 01/13/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Sabrina M Walton (waltons3@msu.edu)
Materials' electronic properties arise from the complex dynamics of electrons flowing through the material. These dynamics are quantum mechanical and present many surprising phenomena without classical analogues. I will present analytical and numerical work clarifying these dynamics in three novel materials which have attracted intense theoretical and experimental attention in recent years: graphene, the first ``2D'' material, whose electronic properties can be captured by an effective Dirac equation, topological insulators, whose edges host surprising oneway edge currents, and twisted bilayer graphene, an aperiodic material whose properties can be captured by an effective system of Dirac equations with periodic coefficients. I will then present ongoing and future work focused on further clarifying the properties of twisted bilayer graphene, which was recently shown to superconduct when twisted to the ``magic'' twist angle 1 degree.

31510

Tuesday 1/17 4:10 PM

Cesar Cuenca, Harvard University

Random matrices and random partitions at varying temperatures
 Cesar Cuenca, Harvard University
 Random matrices and random partitions at varying temperatures
 01/17/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Sabrina M Walton (waltons3@msu.edu)
I will discuss the globalscale behavior of ensembles of random matrix eigenvalues and random partitions which depend on the "inverse temperature" parameter beta. The goal is to convince the audience of the effectiveness of the moment method via Fourierlike transforms in characterizing the Law of Large Numbers and Central Limit Theorems in various settings. We focus on the regimes of high and low temperatures, that is, when the parameter beta converges to zero and infinity, respectively. Part of this talk is based on joint projects with F. BenaychGeorges  V. Gorin, and M. Dolega  A. Moll.

31524

Wednesday 1/18 4:10 PM

Charles Ouyang, UMass Amherst

Compactifications of Hitchin components
 Charles Ouyang, UMass Amherst
 Compactifications of Hitchin components
 01/18/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Sabrina M Walton (waltons3@msu.edu)
Hitchin components are natural generalizations of the classical Teichmüller space. In the setting of SL(3,R), the Hitchin component parameterizes the holonomies of convex real projective structures, which are related to hyperbolic affine spheres. By studying Blaschke metrics, which are Riemannian metrics associated to hyperbolic affine spheres, along with their limits, we obtain a compactification of the SL(3,R)Hitchin component. We show the boundary objects are hybrid structures, which are in part flat metric and in part laminar. These hybrid objects are natural generalizations of measured laminations, which are the boundary objects in Thurston's compactification of Teichmüller space.

31518

Thursday 1/19 4:10 PM

March Tian Boedihardjo, ETH Zurich

Freeness and matrices
 March Tian Boedihardjo, ETH Zurich
 Freeness and matrices
 01/19/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Sabrina M Walton (waltons3@msu.edu)
I will begin by giving some background on Free Probability motivated by the freeness in free groups. I will then demonstrate how Free Probability can be used to obtain a sharp nonasymptotic random matrix estimate for general use. This talk will be concluded by a recent application of our result to the Matrix Spencer Conjecture. Joint work with Afonso Bandeira and Ramon van Handel.

31512

Monday 1/23 4:10 PM

Zhongshan An, University of Michigan

Geometric boundary conditions for the Einstein equations and quasilocal mass
 Zhongshan An, University of Michigan
 Geometric boundary conditions for the Einstein equations and quasilocal mass
 01/23/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Sabrina M Walton (waltons3@msu.edu)
The Einstein equations are the most fundamental equations for spacetimes in general relativity. They relate the geometry (curvatures) of a spacetime with its physical property. When a spacetime has nonempty boundary, it is natural to ask what geometric boundary conditions are wellposed for the Einstein equations. The investigation of geometric boundary conditions both gives rise to interesting geometric PDE problems in differential geometry, and also plays an important role in the study of quasilocal mass for compact spacetimes in general relativity. In this talk, we will discuss geometric boundary conditions for the vacuum Einstein equations, from both the hyperbolic and elliptic aspects. Furthermore, we will talk about applications of these geometric boundary value problems in the construction of quasilocal mass.

30460

Thursday 2/23 4:10 PM

Brendan Hassett, Brown University

TBA
 Brendan Hassett, Brown University
 TBA
 02/23/2023
 4:10 PM  5:00 PM
 Online (virtual meeting)
 Joseph Waldron (waldro51@msu.edu)
No abstract available.

29375

Thursday 3/2 4:10 PM

Katy Craig, UCSB

TBA
 Katy Craig, UCSB
 TBA
 03/02/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
 Olga Turanova (turanova@msu.edu)
TBA

29404

Thursday 3/16 4:10 PM

John Baldwin, Boston College

TBA
 John Baldwin, Boston College
 TBA
 03/16/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
 Joseph Waldron (waldro51@msu.edu)
No abstract available.

29388

Sunday 3/26 4:10 PM

Robin Walters, Northeastern University

TBA
 Robin Walters, Northeastern University
 TBA
 03/26/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
 Olga Turanova (turanova@msu.edu)
TBA

29381

Thursday 3/30 4:10 PM

Tim Hoheisel, McGill University

TBA
 Tim Hoheisel, McGill University
 TBA
 03/30/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
 Olga Turanova (turanova@msu.edu)
TBA

29382

Thursday 4/6 4:10 PM

Michael Brannan, University of Waterloo

TBA
 Michael Brannan, University of Waterloo
 TBA
 04/06/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
 Olga Turanova (turanova@msu.edu)
TBA

30453

Thursday 4/13 4:10 PM

David Fisher, Indiana University Bloomington

TBA
 David Fisher, Indiana University Bloomington
 TBA
 04/13/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
 Olga Turanova (turanova@msu.edu)
TBA

29405

Thursday 4/20 4:10 PM

Robert Pollack, Boston University

TBA
 Robert Pollack, Boston University
 TBA
 04/20/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
 Joseph Waldron (waldro51@msu.edu)
No abstract available.

29406

Thursday 4/27 4:10 PM

Tony Feng, University of California, Berkeley

TBA
 Tony Feng, University of California, Berkeley
 TBA
 04/27/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
 Joseph Waldron (waldro51@msu.edu)
No abstract available.
