Upcoming Events

This talk will be a guided tour of some very distinct, but highly interconnected areas of combinatorics, algebraic geometry and number theory. 

Graph complexes were introduced by Kontsevich and encode the contraction of edges in a graph. Despite the elementary definition, their homology…

The weight 0 compactly supported Euler characteristic of moduli spaces of marked hyperelliptic curves

Joint work with Madeline Brandt and Siddarth Kannan.  We use moduli spaces of G-admissible covers and tropical geometry to give a sum-over-graphs formula for the weight-0…

We'll explore some applications of the Aityah-Singer index theorem (Applications to be determined).

I will begin by illustrating on a simple example how the value
of the L-function of an elliptic curve at the point 2 may be interpreted
as a period integral associated to a simple extension, in accordance
with Beilinson’s conjecture. However, this extension involves an
additional…

Abstract

tba

Given any elliptic curve $E$ over the rationals, we show that $50\%$ of the quadratic twists of $E$ have $2^{\infty}$-Selmer corank $0$ and $50\%$ have $2^{\infty}$-Selmer corank $1$. As a result, we show that Goldfeld's conjecture follows from the Birch and Swinnerton--Dyer conjecture.

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Gaussian elimination with partial pivoting is a standard method of solving systems of linear equations. I will discuss some problems on the singular spectrum of structured random matrices which are related to average-case analysis of stability of the algorithm.

This is based on joint…

I will discuss a two-dimensional stochastic heat equation with a nonlinear noise strength, and consider a limit in which the correlation length of the noise is taken to 0 but the noise is attenuated by a logarithmic factor. The limiting pointwise statistics can be related to a stochastic…

Using tools from lattice homology, we calculate the Seiberg-Witten Floer spectra of Seifert fibered spaces. We also discuss some speculative connections with algebraic geometry. This is joint work with Hirofumi Sasahira and Matthew Stoffregen.