Seminars and Colloquia by Series

Rescaling limits were first introduced by Jan Kiwi to study degenerations of rational maps of degree at least two. Building on the work of Luo and Favre–Gong, we explain how rescaling limits can serve as a substitute for a good compactification of $Rat_d$, the moduli space of degree d rational maps. In particular, this framework allows one to promote pointwise results to uniform statements in a systematic way.

Chromatic polynomials and moduli of curves

Series: Algebra Seminar
Time: Monday, February 2, 2026 - 13:00 for 1 hour (actually 50 minutes)
Location: Skiles 005
Speaker: Rob Silversmith – Emory University

Please Note: There will be a pre-seminar 10:55-11:25 in Skiles 005.

The chromatic polynomial of a graph, which counts colorings of the graph, has a habit of showing up in unexpected places in geometry, e.g. in the theory of hyperplane arrangements. This sometimes has interesting purely combinatorial consequences, such as Huh's proof of Hoggar/Read's conjecture on coefficients of chromatic polynomials.

I'll discuss a new incarnation of chromatic polynomials. To a graph G, we can naturally associate a sequence of intersection numbers on moduli spaces of stable curves. Surprisingly, we prove that these recover values of the chromatic polynomial of G at negative integers.

I'll also discuss how this leads to new algebraic invariants of directed graphs.

(Joint with Bernhard Reinke)

Entrywise positivity preservers and sign preservers

Series: Algebra Seminar
Time: Monday, January 26, 2026 - 13:00 for 1 hour (actually 50 minutes)
Location: Skiles 005
Speaker: Chi Hoi (Kyle) Yip – Georgia Institute of Technology

Please Note: The talk will be held in a hybrid format. ( https://gatech.zoom.us/j/95766668962?pwd=uXNAdqzq8IpL1T2bQONQhUg77iCQyP.1 / Meeting ID: 957 6666 8962 / PW: 232065 )

Let $A = (a_{ij})$ be an $n \times n$ matrix with entries in a field $\mathbb{F}$ and let $f$ be a function defined on $\mathbb{F}$. The function naturally induces an entrywise transformation of $A$ via $f[A] := (f(a_{ij}))$. The study of such entrywise transforms that preserve various forms of matrix positivity has a rich and long history since the seminal work of Schoenberg. In this talk, I will discuss recent developments in the setting that the underlying field $\mathbb{F}$ is the real field, the complex field, and finite fields. I will also highlight some interesting connections between these problems with arithmetic combinatorics, finite geometry, and graph theory. Joint work with Dominique Guillot, Himanshu Gupta, and Prateek Kumar Vishwakarma.

Georgia Institute of Technology College of Sciences

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