Events - September 2022

Izar Alonso Lorenzo, Oxford University

"Balanced SU(3)-structures and coclosed $G_2$-structures in cohomogeneity one manifolds"

Jerry Wang, Department of Pure Mathematics, University of Waterloo

"An improvement to the Schmidt bound"

Counting number fields of fixed degree and bounded discriminant is a classical question in arithmetic statistics. The problem is known in degrees at most 5. In this talk, we will talk about an improvement to Schmidt's upper bound for general degree n, which beats existing improvements for n up to 94. This is joint work with Manjul Bhargava and Arul Shankar.

This seminar will be held jointly online and in person:

Xiao Zhong, Department of Pure Mathematics, University of Waterloo

"$p$-Adic interpolation of orbits under rational maps"

Rivera-Letelier’s characterization of possible analytic uniformizations of $p$-adic analytic maps has played an important role within arithmetic dynamics over the past fifteen years. The characterization is given by a trichotomy of indifferent, attracting and superattracting cases near a fixed point of a map.

Sean Monahan, Department of Pure Mathematics, University of Waterloo

"Introduction to horospherical varieties"

We will begin the seminar with an introduction to horospherical varieties. In this talk we will define horospherical varieties, and we will (at least start to) discuss their “colours”.

This seminar will be held jointly online and in person:

Paul Cusson, Department of Pure Mathematics, University of Waterloo

"Infinite Flag Manifolds and Vector Bundle Filtrations"

Xingchi Ruan, Department of Pure Mathematics, University of Waterloo

"On the Solubility of Diophantine Systems"

Kevin Hare, Department of Pure Mathematics, University of Waterloo

"Matrix based number system"

Most number systems are of the form $a_k d^k + a_{k-1} d^{k-1} + … + a_0$ where the $a_i$ are taken from a finite set of digits, and $d$ is the base of the number system.

In this talk we will discuss what happens if $d$ is taken to be a $n \times n$ Jordan block and $a_i$ are taken to be vectors.

Claude LeBrun, Stony Brook University

"Four-Manifolds, Conformal Curvature, and Differential Topology"