• Speaker: Anna Weigandt, Massachusetts Institute of Technology
• Title: Combinatorial Aspects of Determinantal Varieties
• Date: 01/09/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: 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 three-space?”  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 pre-existing 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 K-theory representatives for Schubert classes to compute the Castelnuovo-Mumford regularity of matrix Schubert varieties, which gives a bound on the complexity of their coordinate rings.

• Speaker: Nathaniel Bottman, Max Planck Institute
• Title: What analysis, combinatorics, and quilted spheres can tell us about symplectic geometry
• Date: 01/10/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: 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 "2-associahedra", 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.

• Speaker: Simon Foucart, Texas A&M University
• Title: ZOOM TALK (Passcode: the smallest prime > 100 ): Three uses of semidefinite programming in approximation theory
• Date: 01/12/2023
• Time: 2:30 PM - 3:30 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: 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 problem---minimal projections---involves minimization over measures and exploits the moment method; the second problem---constrained approximation---involves minimization over polynomials and exploits the sum-of-squares method; and the third problem---optimal recovery from inaccurate observations---is highly relevant in Data Science and exploits the S-procedure. In each of these problems, one ends up having to solve semidefinite programs.

• Speaker: Alexander Watson, University of Minnesota
• Title: Mathematics of novel materials from atomic to macroscopic scales
• Date: 01/13/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: 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 one-way 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.

• Speaker: Charles Ouyang, UMass Amherst
• Title: Compactifications of Hitchin components
• Date: 01/18/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: 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.

• Speaker: March Tian Boedihardjo, ETH Zurich
• Title: Freeness and matrices
• Date: 01/19/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: 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 non-asymptotic 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.

• Speaker: Zhongshan An, University of Michigan
• Title:  Geometric boundary conditions for the Einstein equations and quasi-local mass
• Date: 01/23/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: 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 well-posed 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 quasi-local 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 quasi-local mass.

• Speaker: Wlodzimierz Bryc, University of Cincinnati
• Title: Stationary measures of the Kardar-Parisi-Zhang equation and their limits
• Date: 01/25/2023
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: 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.-Kuznetsov-Wang-Wesolowski, 2022] who found two different probabilistic descriptions of the stationary measures as a Markov process and as a measure with explicit Radon-Nikodym 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 half-line, and to the stationary measure of a hypothetical KPZ fixed point on the half-line. The talk is based mostly on a joint work with Alexey Kuznetsov (ALEA 2022).

• Speaker: Katie Lewis, University of Washington
• Title: Disability Equity in Mathematics Education: Accessibility, Re-mediation, and CompensationAbstract
• Date: 01/25/2023
• Time: 3:30 PM - 5:00 PM
• Place: 252 EH (Virtual Meeting Link)
• Contact: 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 anti-deficit 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, re-mediation, and compensation across a range of mathematical topics. This anti-deficit 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

• Speaker: Theodore Voronov, University of Manchester
• Title:  From homotopy Lie brackets to thick morphisms of supermanifolds and non-linear functional-algebraic duality (NOTE UNUSUAL DAY)
• Date: 01/31/2023
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall
• Contact: 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 L-infinity morphisms and L-infinity 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 multi-linear 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 multi-linear mappings assembles into one non-linear 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 non-linear mappings between algebras of smooth functions generalizing the usual pull-backs. 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 non-linear analog of the classical functional-algebraic duality between spaces and algebras.

• Speaker: Igor Rapinchuk, MSU
• Title: Profinite groups and infinite Galois theory
• Date: 02/01/2023
• Time: 3:00 PM - 4:00 PM
• Place: C329 Wells Hall
• Contact: Igor Rapinchuk (rapinchu@msu.edu)

No abstract available.

• Speaker: James Murphy, Tufts University
• Title: ZOOM TALK (password the smallest prime > 100) - Towards Intrinsically Low-Dimensional Models in Wasserstein Space: Geometry, Statistics, and Learning
• Date: 02/02/2023
• Time: 2:30 PM - 3:30 PM
• Place: C304 Wells Hall
• Contact: Mark A Iwen ()

We consider the problems of efficient modeling and representation learning for probability distributions in Wasserstein space. We consider a general barycentric coding model in which data are represented as Wasserstein-2 (W2) barycenters of a set of fixed reference measures. Leveraging the Riemannian structure of W2-space, we develop a tractable optimization program to learn the barycentric coordinates when given access to the densities of the underlying measures. We provide a consistent statistical procedure for learning these coordinates when the measures are accessed only by i.i.d. samples. Our consistency results and algorithms exploit entropic regularization of the optimal transport problem, thereby allowing our barycentric modeling approach to scale efficiently. We also consider the problem of learning reference measures given observed data. Our regularized approach to dictionary learning in Wasserstein space addresses core problems of ill-posedness and in practice learns interpretable dictionary elements and coefficients useful for downstream tasks. Applications to image and natural language processing will be shown throughout the talk.

• Speaker: Wenjie Fang, Graz University of Technology
• Title: Parabolic Tamari Lattices in Linear Type B
• Date: 02/08/2023
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

We study parabolic aligned elements associated with the type-B Coxeter group and the so-called linear Coxeter element. These elements were introduced algebraically in (Mühle and Williams, 2019) for parabolic quotients of finite Coxeter groups and were characterized by a certain forcing condition on inversions. We focus on the type-B case and give a combinatorial model for these elements in terms of pattern avoidance. Moreover, we describe an equivalence relation on parabolic quotients of the type-B Coxeter group whose equivalence classes are indexed by the aligned elements. We prove that this equivalence relation extends to a congruence relation for the weak order. The resulting quotient lattice is the type-B analogue of the parabolic Tamari lattice introduced for type A in (Mühle and Williams, 2019). These lattices have not appeared in the literature before. As work in progress, we will also talk about various combinatorial models and bijections between them. Joint work with Henri Mühle and Jean-Christophe Novelli.

• Speaker: Alexander Volberg, MSU
• Title: Noncommutative Bohnenblust--Hille inequalities and application to learning the quantum observables
• Date: 02/08/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Willie Wai-Yeung Wong (wongwil2@msu.edu)

Bohnenblust--Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow sub-exponentially in the degree (Defant—Mastylo—Peres). Such inequalities have found great applications in learning low degree Boolean functions (Eskenazis—Ivanisvili). Motivated by learning quantum observables, a quantum counterpart of Bohnenblust--Hille inequality for Boolean cubes was recently conjectured in Cambyse Rouz\’e, Melchior Wirth, and Haonan Zhang: ``Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions.” arXiv preprint, arXiv:2209.07279, 2022. Haonan Zhang and myself prove such noncommutative Bohnenblust--Hille inequalities with constants that are dimension-free and of exponential growth in the degree. As applications, we study learning problems of quantum observables. (Speaker will present remotely)

• Speaker: Keerthi Madapusi Pera, Boston College
• Title: Derived cycles on Shimura varieties
• Date: 02/13/2023
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Georgios Pappas (pappasg@msu.edu)

I’ll explain how methods from derived algebraic geometry can be applied to give a uniform definition of special cycle classes on integral models of Shimura varieties of Hodge type, verifying some consequences of Kudla’s conjectures on the modularity of generating series of cycles on Shimura varieties of Hermitian type.

• Speaker: Ian Montague , Brandeis University
• Title: TBA
• Date: 02/21/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

No abstract available.

• Speaker: Yuehaw Khoo, U Chicago
• Title: TBA
• Date: 02/24/2023
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Mark A Iwen (iwenmark@msu.edu)

TBA

• Speaker: Ryan Stees, Indiana University
• Title: TBA
• Date: 02/28/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

No abstract available.

• Speaker: Katy Craig, UCSB
• Title: TBA
• Date: 03/02/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Olga Turanova (turanova@msu.edu)

TBA

• Speaker: John Baldwin, Boston College
• Title: TBA
• Date: 03/16/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Joseph Waldron (waldro51@msu.edu)

No abstract available.

• Speaker: John Sheridan, Princeton University
• Title: TBA
• Date: 03/20/2023
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Francois Greer (greerfra@msu.edu)

No abstract available.

• Speaker: Katrina Morgan, Northwestern University
• Title: TBA
• Date: 03/22/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Willie Wai-Yeung Wong (wongwil2@msu.edu)

TBA

• Speaker: Tim Hoheisel, McGill University
• Title: TBA
• Date: 03/30/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Olga Turanova (turanova@msu.edu)

TBA

• Speaker: Matt Jacobs, Purdue
• Title: TBA
• Date: 04/05/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Olga Turanova (turanova@msu.edu)

TBA

• Speaker: Sam Gunningham, Montana State
• Title: RTG Seminar: TBA
• Date: 04/10/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Vijay B Higgins (higgi231@msu.edu)

TBA

• Speaker: Leonardo Abbrescia, Vanderbilt University
• Title: A localized picture of the maximal development for shock forming solutions of the 3D compressible Euler equations
• Date: 04/12/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Willie Wai-Yeung Wong (wongwil2@msu.edu)

Understanding the behavior of solutions to the compressible Euler equations for large times necessitates a sharp analysis of possible singularities that can form. Our understanding of shock singularities in three space dimensions has enjoyed a dramatic surge in progress in the past two decades due in part to the mathematical techniques that were developed to study Einstein’s equations. In this talk, I will discuss my recent work which provides a sharp localized description of a shock singularity as part of the boundary of maximal development of smooth data. The set of Cartesian spacetime points on which a singularity occurs, which we call the singular boundary $\mathcal{B}$, has the structure of an embedded hypersurface with very degenerate causal properties. I will give an overview of the difficulties that occur in the construction of the singular boundary, and if time permits, also discuss the construction of the Cauchy horizon which emanates from the past boundary of $\mathcal{B}$.

• Speaker: Siddhi Krishna, Columbia University
• Title: RTG Seminar: TBA
• Date: 04/17/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

No abstract available.

• Speaker: Siddhi Krishna, Columbia University
• Title: TBA
• Date: 04/18/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

No abstract available.

• Speaker: Jaclyn Lang, Temple
• Title: TBA (note unusual day)
• Date: 04/21/2023
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Preston Wake (wakepres@msu.edu)

No abstract available.

• Speaker: Sarah Petersen, University of Colorado, Boulder
• Title: RTG Seminar: TBA
• Date: 04/24/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

No abstract available.

• Speaker: Sarah Petersen, University of Colorado, Boulder
• Title: TBA
• Date: 04/25/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

No abstract available.

• Speaker: Tony Feng, University of California, Berkeley
• Title: TBA
• Date: 04/27/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Joseph Waldron (waldro51@msu.edu)

No abstract available.