Previous Conferences & Workshops

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...

Oct
22
2024

Symplectic Geometry Seminar

Quantitative Almost-Existence in Dimension Four
Rohil Prasad
1:00pm|Rubenstein Commons | Meeting Room 5

In 1987, Hofer and Zehnder showed that for any smooth function $H$ on $\mathbb{R}^{2n}$, almost every compact and regular level set contains at least one closed characteristic. I'll show that, when $n = 2$, almost every compact and regular level set...

Oct
22
2024

Geometry of Matroid Workshop

Spaces of Lorentzian Polynomials
Mario Kummer
12:00pm|Simonyi 101

Abstract: We characterize the topology of the space of Lorentzian polynomials with a given support in terms of the local Dressian. We prove that this space can be compactified to a closed Euclidean ball whose dimension is the rank of the Tutte group...

Oct
22
2024

Computer Science/Discrete Mathematics Seminar II

Sheaves on Graphs, the Hanna Neumann Conjecture, and My Debt to Number Theory and Algebraic Geometry
Joel Friedman
10:30am|Rubenstein Commons | Meeting Room 5

I will discuss the Hanna Neumann conjecture of the 1950's and some tools in graph theory that I used to solve it.  The tools include sheaf theory on graphs, Galois theory for graphs, and the preservation of "local properties" under base change (for...

Oct
22
2024

Geometry of Matroid Workshop

Cohomologically Tropical Varieties
Kris Shaw
10:00am|Simonyi 101

Abstract: This talk asks which tropicalisations of subvarieties of the torus know the cohomology of the original variety. A motivating example are linear embeddings of complements of hyperplane arrangements. 

We can prove that the tropicalisation...