Algebraic Geometry Seminar Fall 2015

The seminar meets on Fridays at 2:25 pm in Van Vleck B223.

The schedule for the previous semester is here.

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Fall 2015 Schedule

date	speaker	title	host(s)
September 18	Eric Riedl (UIC)	Rational Curves on Hypersurfaces	Jordan
September 25	David Zureick-Brown (Emory)	Hilbert schemes of canonically embedded curves of low genus	Jordan
October 2	Vasily Dolgushev (Temple)	A manifestation of the Grothendieck-Teichmueller group in geometry	Andrei
October 9	Laurentiu Maxim (Madison)	TBA	local
October 23	Jesse Kass (South Carolina)	How to count zeros arithmetically?	Melanie
November 13	Jake Levinson (Michigan)	TBA	Daniel

Abstracts

Eric Riedl

Rational Curves on Hypersurfaces

One way to understand the geometry of a variety is to understand its rational curves. Even for some relatively simple varieties, little is known about their spaces of rational curves. Many people have made previous progress on these questions, but there remain many open cases. In joint work with David Yang, we investigate the dimensions of the spaces of rational curves on very general hypersurfaces, and prove that for n > d+1 or d > (3n+1)/2, the spaces of rational curves have the expected dimension, as conjectured (in various cases) by several people, including Coskun, Harris and Starr, and Voisin. In this talk, we focus our attention particularly on the Fano case and try to motivate some of the ideas used to attack this problem.

David Zureick-Brown

Hilbert schemes of canonically embedded curves of low genus

I'll discuss new work (joint with Aaron Landesman) on smoothability of low genus curves.

Jess Kass

How to count zeros arithmetically?

A celebrated result of Eisenbud--Kimshaishvili--Levine computes the local Brouwer degree of a real polynomial function at an isolated zero as the signature of a quadratic form. I will discuss a parallel result in A1-homotopy theory, and time permitting, explain how to study a singularity by applying these results to the gradient of a defining equation. This is joint work with Kirsten Wickelgren.

Vasily Dolgushev

A manifestation of the Grothendieck-Teichmueller group in geometry

Inspired by Grothendieck’s lego-game, Vladimir Drinfeld introduced, in 1990, the Grothendieck-Teichmueller group GRT. This group has interesting links to the absolute Galois group of rationals, moduli of algebraic curves, solutions of the Kashiwara-Vergne problem, and theory of motives. My talk will be devoted to the manifestation of GRT in the extended moduli of algebraic varieties, which was conjectured by Maxim Kontsevich in 1999. My talk is partially based on the joint paper with Chris Rogers and Thomas Willwacher: http://arxiv.org/abs/1211.4230.