Previous Conferences & Workshops

Oct
24
2024

Joint PU/IAS Number Theory

$p$-Adic $L$-Functions for $P$-Ordinary Hida Families On Unitary Groups
David Marcil
3:30pm|314 Fine Hall

I will first discuss the notion of automorphic representations on a unitary group that are $P$-ordinary (at $p$), where $P$ is some parabolic subgroup. In the “ordinary” setting (i.e. when $P$ is minimal), such a representation $\pi$ has a...

Oct
24
2024

Geometry of Matroid Workshop

Valuated Delta Matroids and Principal Minors
Cynthia Vinzant
2:30pm|Simonyi 101

Abstract: Delta matroids are a generalization of matroids, encompassing combinatorial structures such as matchings of graphs and principal minors of symmetric matrices. In this talk, I will discuss a notion of valuated Delta matroids and their...

Oct
24
2024

Geometry of Matroid Workshop

Baker-Bowler Theory for Lagrangian Grassmannians
Donggyu Kim
12:00pm|Simonyi 101

Abstract: Baker and Bowler (2019) showed that the Grassmannian can be defined over a tract, a field-like structure generalizing both partial fields and hyperfields.

This notion unifies theories for matroids over partial fields, valuated matroids, and...

Oct
24
2024

Geometry of Matroid Workshop

Paths to Matroid Representations
Tong Jin
10:00am|Simonyi 101

Abstract: In this talk, I will first review previous works on matroid representations initiated by Tutte in 1958, generalized by Dress and Wenzel in the 1980s, and refined by Baker, Bowler, and Lorscheid more recently using the language of F1...

Oct
23
2024

Mathematical Conversations

Dynamics, Computation, and Real Circuit Theory
6:00pm|Birch Garden, Simons Hall

Some people think that the brain is something like a (conscious) computer. But if a brain can compute, why can't a rock, or a river stream? This basic question has been considered by philosophers, physicists, and mathematicians.

It is not entirely...

Oct
23
2024

Geometry of Matroid Workshop

Multimatroids and Rational Curves with Cyclic Action
12:00pm|Simonyi 101

Abstract: I will share with you a connection between multimatroids and moduli spaces of rational curves with cyclic action. Multimatroids are generalizations of matroids and delta-matroids that naturally arise from topological graph theory. The main...

Oct
23
2024

Geometry of Matroid Workshop

The External Activity Complex of a Pair of Matroids
10:30am|Simonyi 101

Abstract: I will introduce the external activity complex of an ordered pair of matroids on the same ground set. This is the combinatorial analogue of the Schubert variety of an ordered pair of linear subspaces of a fixed space, which is also new...

Oct
23
2024

Geometry of Matroid Workshop

Towards Generalized Schubert Varieties and Anabelian Matroids
9:00am|Simonyi 101

Abstract: The groundbreaking results by Huh (further extended in joint work with Adiprasito and Katz) allowed to associate to a matroid a class in the Chow ring of the permutohedral variety. The technique turned out to be especially powerful, as...

Oct
22
2024

Joint IAS/PU Groups and Dynamics Seminar

Algebraic Equations Characterizing Hyperbolic Surface Spectra
Anshul Adve
4:30pm|314 Fine Hall

Given a compact hyperbolic surface together with a suitable choice of orthonormal basis of Laplace eigenforms, one can consider two natural spectral invariants: 1) the Laplace spectrum $\Lambda$, and 2) the 3-tensor $C_{ijk}$ representing pointwise...

Oct
22
2024

Geometry of Matroid Workshop

Tropicalizing Principal Minors of Positive Definite Matrices
Josephine Yu
2:30pm|Simonyi 101

Abstract: We study the tropicalization of principal minors of positive definite matrices over a real valued field. This tropicalization forms a subset of M-concave functions on the discrete n-dimensional cube. We show that it coincides with a linear...