Hi all,

This is a reminder that GradSWANTAG IX will be held this Saturday, June 2nd.

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

9:30-10 Light breakfast
10-11 Zonglin
11-12 Thanakorn
1-2 Gabriel
2-3 Peter

Zonglin Jiang
Title: Quantum Computation Meets Number Theory

Abstract: It has long been known that quantum computation is a powerful tool for (computational) number theory, as demonstrated by Shor's algorithm. Relatively recently, it has been discovered that number theory can help design quantum circuits. In this talk, we will give a brief introduction to quantum computation, and its connection with number theory, featuring a letter written by Peter Sarnak in 2015, and a pre-print of Jesus Lacalle & Laura N. Gatti in May 2018.

Thanakorn Prinyasart
Title: On Some Methods to Prove Effective Equidistribution on Homogeneous Spaces

Abstract: In this talk, we will talk about the study of homogeneous dynamics, how it
has been developed in the past few decades, and some of its applications.
After that, we will focus on the concept of equidistribution, and discuss
some methods that are normally used to obtain the rate of
equidistribution.

Gabriel Dorfsman-Hopkins
Title: Using analysis to find projective modules.

Abstract: We prove the Quillen-Suslin theorem for the perfectoid Tate algebra, which states that all vector bundles on the perfectoid unit disk are trivial.  To do so, we will reduce to the case of the rigid unit disk, which in turn can be reduced to the classical case of affine space over a field.  We will focus on the first reduction, arguing that every vector bundle on the perfectoid disk is the base extension of a classical vector bundle.  We adapt a nifty argument of Kedlaya and Liu which uses Newton approximation on the space of matrices to produce an idempotent matrix whose image will be the projective module corresponding to the vector bundle we are looking for.

Peter Wear
Title: Uniformization of abelian varieties over the complex and p-adic numbers

Abstract: Over the complex numbers, abelian varieties are all complex tori. Over a non-archimedean field such as Q_p, this is no longer the case. The goal of this talk is to explain why this happens. We will begin with an overview of the story over the complex numbers. We will explain how to reduce questions about moduli spaces of complex abelian varieties to linear algebra. We will then explore what happens when we try to replicate this construction over a non-archimedean field. 

Hope to see you there,
Peter and Francois