MONDAY - 3/31/25

Combinatorics Seminar

Location:  Kassar 105

Time: 12:00-1:00pm

Speaker: Daoji Huang, IAS

Title: Fine multidegree, universal Gröbner basis, and matrix Schubert varieties

Abstract: A universal Gröbner basis of an ideal is a Gröbner basis under any term order. While general results guarantees the existence of universal Gröbner basis of an ideal, few examples are known. We give a criterion for a collection of polynomials to be a universal Gröbner basis for an ideal in terms of the multidegree of the closure of the corresponding affine variety in (ℙ^1)^N. In the context of Schubert calculus, Gröbner theory of matrix Schubert varieties bridges geometry and combinatorics of Schubert polynomials. We use our criterion to give a universal Gröbner basis for the ideals of a family of matrix Schubert varieties.This is based on joint work with Matt Larson.

Algebra Seminar

Location:  Kassar 105

Time: 4:00-5:00pm

Speaker: Shiva Chidambaram, University of Wisconsin-Madison

Title: Cohen-Lenstra type conjectures for p-torsion in characteristic p

Abstract: The Cohen-Lenstra conjectures for ell-part of class-groups of number fields extend naturally to ell-torsion in Jacobians of curves over F_p, when p is not equal to ell. When p = ell, Cais--Ellenberg--Zureick-Brown set up a framework of random Dieudonne modules to make predictions about the distribution of various statistics (a-number, p-rank etc) for p-divisible groups. These predictions align with results on codimensions of strata inside moduli spaces of abelian varieties. For hyperelliptic curves in characteristic 3, the recent work of Garton--Thunder--Weir proves that the codimensions of a-number strata are different from expected, and proposes a different heuristic for the distribution of a-numbers. We will survey these heuristics and discuss ongoing work extending the latter result to other families of curves in characteristic 2.

TUESDAY - 4/1/25

Graduate Student Seminar

Location:  Kassar 105

Time: 12:00-1:00pm

Speaker: Beckett Sanchez, AnaMaria Perez, Fernando Benito Fernandez de la Cigona, Hanieh Ghorbani

Title: What is?  Day 1

Abstract: There will be four talks going over various AMS "What Is" articles.

GLESPA Seminar

Location:  Kassar 105

Time: 4:00-5:30pm

Speaker: Carlos A.C.C. Perelo, Brown University

Title: On the existence of 2D locally optimal, stationary and ergodic matchings

Abstract: We disprove the existence of a locally optimal, stationary and ergodic matching between two Poisson Point Processes in \mathbb{R}^2, which extends the literature on matchings between points sampled uniformly at random from a bounded domain to the plane, and connects this highly-geometric problem with (discrete) optimal transport.

The main tool used in this analysis is the so-called Harmonic approximation theorem introduced by Goldman, Huessmann and Otto, which quantitavely analyses the well-known fact that the Monge-Ampere equation near the Lebesgue measure linearises to be the Poisson equation. All work is based on (https://arxiv.org/abs/2109.13590).

WEDNESDAY - 4/2/25

Geometry & Topology Seminar

Location:  Kassar 105

Time: 3:00-4:00pm

Speaker: Genevieve Walsh, Tufts University

Title: Flappy trees and L2 homology

Abstract: We discuss group properties of right-angled Coxeter groups that are virtually 3-dimensional pseudomanifolds. We are able to show that in many cases these groups are virtually algebraically fibered and incoherent, using the computation of L2 homology.  One of the main tools is the use of flappy trees which I will describe. This is joint work with Lorenzo Ruffoni.

THURSDAY - 4/3/25

Geometric Analysis Seminar

Location:  Kassar 105

Time: 4:00-5:00pm

Speaker: Brian Harvie, Columbia University

Title: Weak Inverse Mean Curvature Flow in Hyperbolic Space

Abstract: Inverse mean curvature flow (IMCF) is a geometric flow that expands hypersurfaces by mean curvature. IMCF has many geometric applications, but a key obstacle to these is the formation of finite-time singularities. To deal with this, Huisken and Ilmanen developed a theory of weak solutions of IMCF which flow beyond these singularities and out to infinity. The flow surfaces of weak IMCF may not be smooth and may vary discontinuously in the time variable, a phenomenon known as a "jump". Furthermore, the asymptotic behavior of weak solutions is poorly understood in manifolds with negative curvature, e.g. hyperbolic space.

In this talk, I will show that a weak IMCF in hyperbolic space eventually becomes a classical IMCF for arbitrary closed initial data-- that is, the flow surfaces become smooth and the jumps cease after an explicit time depending on the initial hypersurface. The proof is based on an Alexandrov reflection method in the Poincare ball. Then, I will apply this regularity result to prove two Minkowski inequalities in hyperbolic space. One of these implies a Penrose-type inequality in general relativity.

FRIDAY - 4/4/25

Algebraic Geometry Seminar

Location:  Kassar 105

Time: 3:00-4:00pm

Speaker: Andrei Caldararu, University of Wisconsin

Title: Introduction to categorical enumerative invariants

Abstract: I will present the construction of categorical enumerative invariants (CEI) associated to a Calabi-Yau category and a splitting of its Hodge filtration. Computed in families, these CEI give analogs of higher genus Gromov-Witten potentials. My talk will have two parts. In the first part I will discuss recent results of Deshmukh giving a conceptual understanding of the construction of CEI. In the second part I will present an effectively computable definition of CEI (joint with Costello and Tu). Throughout the talk I will emphasize the connections with topological field theory.

PDE Seminar

Location:  170 Hope Street, Room 108

Time: 3:00-4:00pm

Speaker: Francisco Gancedo, University of Seville

Title: TBA

Abstract: TBA