Hi all,

This is a reminder that GradSWANTAG X will be held this Sunday, December 9th. 

All talks will be held in APM 7421. See below for the schedule and abstracts.

9:30-10 Light breakfast
10-11 Samir
11-12 Pieter
12-1 Lunch break
1-2 Zach
2-3 Peter

Samir Canning
Title: Lines on Fano Complete Intersections

Abstract: For a general hypersurface X of degree d in n-dimensional projective space, the dimension of the Hilbert scheme of lines on X is 2n-d-3. We call this number the expected dimension. It is conjectured by Debarre and de Jong that for any smooth Fano hypersurface the dimension of the Hilbert scheme of lines is as expected. Beheshti has proven this conjecture for d<9. In this talk, I will state a version of the Debarre-de Jong conjecture for smooth Fano complete intersections and prove some low degree cases by following the ideas of Beheshti.

Pieter Spaas
Title: Doing algebra by not (only) doing algebra

Abstract: We consider some (open) problems in algebra, for instance Kaplansky's direct finiteness conjecture for group rings, and Gottschalk's surjunctivity conjecture for shift actions of groups, and survey some of the (partial) solutions that have been obtained. Perhaps surprisingly, these involve a range of techniques coming from several areas of math, not only algebra. The intention is that this talk is interesting to everyone.

Zach Higgins
Title: Explicit class field theory for global function fields using Drinfeld modules

Abstract:  We will introduce Drinfeld modules, give some basic properties, and discuss some applications.  As an example of one such application, we will describe the class field theory of F_q(t) explicitly.  We will then indicate how these techniques generalize to give explicit class field theory of an arbitrary global function field.

Peter Wear
Title: Tilting perfectoid covers of abelian varieties

Abstract: We will first talk about abelian varieties, then perfectoid spaces, then perfectoid spaces living over abelian varieties, and then the tilts of these perfectoid spaces. The emphasis will be on examples and intuition.

Hope to see you there,
Peter, Francois, and Thomas