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Colloquium
 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.

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Geometry and Topology

 G&T Seminar Organizational Meeting
 01/10/2023
 2:30 PM  3:00 PM
 C304 Wells Hall
 Peter Kilgore Johnson (john8251@msu.edu)
No abstract available.
Colloquium
 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.

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Colloquium
 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.

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Applied Mathematics
 Simon Foucart, Texas A&M University
 ZOOM TALK (Passcode: the smallest prime > 100 ): Three uses of semidefinite programming in approximation theory
 01/12/2023
 2:30 PM  3:30 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Mark A Iwen (iwenmark@msu.edu)
In this talk, modern optimization techniques are publicized as fitting computational tools to attack several extremal problems from Approximation Theory which had reached their limitations based on purely analytical approaches. Three such problems are showcased: the first problemminimal projectionsinvolves minimization over measures and exploits the moment method; the second problemconstrained approximationinvolves minimization over polynomials and exploits the sumofsquares method; and the third problemoptimal recovery from inaccurate observationsis highly relevant in Data Science and exploits the Sprocedure. In each of these problems, one ends up having to solve semidefinite programs.
Colloquium
 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?

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Colloquium
 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.

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Colloquium
 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.

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Colloquium
 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.

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Applied Mathematics
 Madeleine Udell, Stanford University
 ZOOM TALK (Passcode: the smallest prime > 100 ): Low rank approximation for faster optimization
 01/19/2023
 2:30 PM  3:30 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Mark A Iwen ()
Low rank structure is pervasive in realworld datasets. This talk shows how to accelerate the solution of fundamental computational problems, including eigenvalue decomposition, linear system solves, composite convex optimization, and stochastic optimization (including deep learning), by exploiting this low rank structure. We present a simple method based on randomized numerical linear algebra for efficiently computing approximate top eigendecompositions, which can be used to replace large matrices (such as Hessians and constraint matrices) with low rank surrogates that are faster to apply and invert. The resulting solvers for linear systems (NystromPCG), composite convex optimization (NysADMM), and deep learning (SketchySGD) demonstrate strong theoretical and numerical support, outperforming stateoftheart methods in terms of speed and robustness to hyperparameters.
Colloquium
 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.

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Dynamical Systems
 Fan Yang, Michigan State University
 Lorenz attractor and singular flows: expansivity, entropy, and equilibrium states
 01/20/2023
 3:00 PM  5:00 PM
 C304 Wells Hall
 Fan Yang (yangfa31@msu.edu)
No abstract available.

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Colloquium
 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.

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CoIntegrate Mathematics
 Vince Melfi, MSU; Jenny Green, MSU; John Keane, MSU
 Fostering a Culture of Instructional Development in the Department of Statistics and Probability: Our Journey with FirstYear Graduate Teaching Assistants
 01/24/2023
 1:00 PM  2:30 PM
 115 Erickson Hall
 Lisa Keller (kellerl@msu.edu)
How do we support graduate students to teach introductory statistics classes, which themselves are undergoing dramatic transformation? In this talk, we will get to engage with
lessons learned and questions still unanswered as we embarked on the journey of developing an instructional mentoring program for the Department of Statistics and Probability.

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Combinatorics and Graph Theory
 Yibo Gao, University of Michigan
 CANCELLED: Symmetric structures in the strong Bruhat order
 01/25/2023
 3:00 PM  3:50 PM
 C304 Wells Hall
 Bruce E Sagan (bsagan@msu.edu)
The Bruhat order encodes algebraic and topological information of Schubert varieties in the flag manifold and possesses rich combinatorial properties. In this talk, we discuss three interrelated stories regarding the Bruhat order: selfdual Bruhat intervals, BilleyPostnikov decompositions and automorphisms of the Bruhat graph. This is joint work with Christian Gaetz.
Probability
 Wlodzimierz Bryc, University of Cincinnati
 Stationary measures of the KardarParisiZhang equation and their limits
 01/25/2023
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Konstantin Matetski (matetski@msu.edu)
I will overview recent results of [Corwin and Knizel, 2021] on the existence of stationary measures for the KPZ equation on an interval and [Barraquand and Le Doussal, 2022], [B.KuznetsovWangWesolowski, 2022] who found two different probabilistic descriptions of the stationary measures as a Markov process and as a measure with explicit RadonNikodym derivative with respect to the Brownian motion. The Markovian description leads to rigorous proofs of some of the limiting results claimed in [Barraquand and Le Doussal, 2022]. I shall discuss how the stationary measures of the KPZ equation on [0,L] behave at large scale as L goes to infinity which according to [Barraquand and Le Doussal, 2022] depending on the normalization, should correspond to stationary measures of a hypothetical KPZ fixed point on [0,1], to the stationary measure for the KPZ equation on the halfline, and to the stationary measure of a hypothetical KPZ fixed point on the halfline.
The talk is based mostly on a joint work with Alexey Kuznetsov (ALEA 2022).
Mathematics Education Colloquium Series
 Katie Lewis, University of Washington
 Disability Equity in Mathematics Education: Accessibility, Remediation, and CompensationAbstract
 01/25/2023
 3:30 PM  5:00 PM
 252 EH
(Virtual Meeting Link)
 Lisa Keller (kellerl@msu.edu)
Equity in mathematics education research has only recently begun to consider students with disabilities. In this talk, I focus specifically on students with mathematics disabilities – students who have a neurological difference in how their brains process numerical information. Prior research on mathematics disabilities (i.e., dyscalculia) has predominantly taken up a deficit frame, documenting the ways in which students with dyscalculia are deficient in terms of speed and accuracy. In my work, I argue that this deficit orientation is problematic, and I offer an alternative. I take up an explicitly antideficit framing and draw upon sociocultural learning theories and Disability Studies to orient my work. In this talk I use multiple case studies to explore ideas about accessibility, remediation, and compensation across a range of mathematical topics. This antideficit work provides an alternative vantage point to understand disability in mathematics education and suggests avenues to work towards equity. I close by considering ways that mathematics education equity research can be in service of and in partnership with the populations that we study. Zoom option: https://msu.zoom.us/j/95059549382 Passcode: PRIME

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Operator Algebras Reading
 Lucas Hall, MSU
 Approximately Finite Dimensional C*algebras
 01/30/2023
 4:00 PM  5:30 PM
 C517 Wells Hall
 Brent Nelson (banelson@msu.edu)
I’ll tour through the study of finite dimensional C*algebras and homomorphisms between them, and use this as a basis to define and study approximately finite dimensional (AF) algebras.

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Algebra
 Theodore Voronov, University of Manchester
 From homotopy Lie brackets to thick morphisms of supermanifolds and nonlinear functionalalgebraic duality (NOTE UNUSUAL DAY)
 01/31/2023
 3:00 PM  4:00 PM
 C204A Wells Hall
 Michael Shapiro (mshapiro@msu.edu)
I will give a motivation for homotopy Lie brackets and the corresponding morphisms preserving brackets "up to homotopy" (more precisely, for Linfinity morphisms and Linfinity algebras), and show how to describe them using supergeometry. So, instead of a single Poisson or Lie bracket, there is a whole sequence of operations with n arguments, n=1,2,3,..., satisfying a linked infinite sequence of identities replacing the familiar Jacobi identity for a Lie bracket; and, instead of a morphism as a linear map mapping a bracket to a bracket, there is a sequence of multilinear mappings mixing brackets with different numbers of arguments, and, in particular, the binary bracket is preserved only up to an (algebraic) homotopy. Geometrically, such a sequence of multilinear mappings assembles into one nonlinear map of supermanifolds.
For the case of homotopy brackets of functions ("higher Poisson" or "homotopy Poisson" structure), this leads us to the question about a natural construction of nonlinear mappings between algebras of smooth functions generalizing the usual pullbacks. I discovered such a construction some years ago. These are "thick morphisms" of (super)manifolds generalizing ordinary smooth maps. From a more general perspective, we arrive in this way at a nonlinear analog of the classical functionalalgebraic duality between spaces and algebras.
