# Steven Sam (UCSD)

January 21, 2021 at Northeastern (virtual)

Title: Polynomials of bounded degree

Abstract: Ananyan and Hochster proved the existence of “small

subalgebras” for collections of polynomials with a priori bounded

degrees. Roughly speaking, this means that arbitrary polynomials can be

written as polynomial expressions of a fixed number of more basic

polynomials with good properties. I’ll discuss some motivations for this

coming from finding uniform bounds for numerical invariants of ideals

and discuss ideas (ultraproducts, GL-noetherianity) related to new

proofs of their result.

# Greg Lawler (Chicago)

April 1, 2021 at Northeastern (virtual)

Title: Loop-erased random walk—a random fractal

Abstract: Many models in equilibrium statistical physics produce random fractal curves “at criticality.” I will discuss one particular model, the loop-erased random walk, which is closely related to uniform spanning trees and Laplacian motion, and survey what is known today including some more recent results. I will also discuss some of the important open problems and explain why the problem is hardest in exactly three dimensions. This talk is intended for a general mathematics audience and does not assume the audience knows the terms in the previous sentence.

# Melody Chan (Brown)

April 15, 2021 at Northeastern (virtual)

Title: On the cohomology of moduli of abelian varieties

Abstract: I’ll discuss recent work using tropical techniques to find new

rational cohomology classes in moduli spaces A_g of abelian varieties,

building on previous joint work with Galatius and Payne on M_g. I will

try to take a broad view. Joint work with Madeline Brandt, Juliette

Bruce, Margarida Melo, Gwyneth Moreland, and Corey Wolfe.

The colloquium meets virtually on Thursdays at 4:30 PM Eastern and is organized by Joël Bellaïche at Brandeis; by Fabian Gundlach and Arnav Tripathy at Harvard; by Scott Sheffield at MIT; and by Matthew Hogancamp, Ben Knudsen, Gapor Lippner, Alina Marian, and Jonathan Weitsman at Northeastern. This website is maintained by Ben Knudsen. The image of Boston is the property of Wikimedia user King of Hearts and is reproduced here under Creative Commons license CC BY-SA 4.0. Images of speakers are their own property and are reproduced here with permission.