Events - October 2022

Luke MacLean, Department of Pure Mathematics, University of Waterloo

"Relations enumerable from positive information"

Yash Singh, Department of Pure Mathematics, University of Waterloo

"Properties of horospherical varieties"

We study when a given horospherical variety is affine. Additionally, we study G-orbits of horospherical varieties and their correspondence with colored cones.

This seminar will be held jointly online and in person:

Gian Cordana Sanjaya, Department of Pure Mathematics, University of Waterloo

"On the squarefree values of $a^4 + b^3$"

Robert Harris, Department of Pure Mathematics, University of Waterloo

"Abelian Covers and Line Arrangements in CP^2"

Ross Willard, Department of Pure Mathematics, University of Waterloo

"Finite axiomatizability problems for finite algebras"

Nicole Kitt, Department of Pure Mathematics, University of Waterloo

"Morphisms of horospherical varieties"

In this talk, we define and look at examples of morphisms of horospherical varieties. Additionally, we will see how morphisms of horospherical varieties are related to maps of the coloured fans.

This seminar will be held jointly online and in person:

Amanda Petcu, Department of Pure Mathematics, University of Waterloo

"An Introduction to Calibrated Geometry"

Owen Sharpe, Department of Pure Mathematics, University of Waterloo

"Primality Testing and Integer Factorization"

Primality testing and integer factorization are mathematical problems which have occupied number theorists throughout the centuries. They have become very important in the field of cryptography over the last fifty years. We give a brief history of primality testing and integer factorization algorithms, from the sieve of Eratosthenes to the AKS test, and from trial division to Shor's algorithm.

Leo Jimenez, Department of Pure Math, University of Waterloo

"Expansions of the group of integers"

Sean Monahan, Department of Pure Mathematics, University of Waterloo

“Combinatorics of horospherical varieties”

In this talk we finish our brief introduction of horospherical varieties by examining their
combinatorial interpretation. In the case of toric varieties, we have a combinatorial interpretation
using fans; in the case of horospherical varieties, we use so-called “coloured fans” which
account for the colours that we discussed in the last talk.
This seminar will be held jointly online and in person:

Xuemiao Chen, Department of Pure Mathematics, University of Waterloo

“Restriction of slope semi-stable bundles”

Given a slope semi-stable bundle over a projective manifold, a classical theorem by Mehta
and Ramanathan states that its restriction to a generic high degree hyper-surface is still slope
semi-stable. This plays a key role in Donaldson’s proof for the existence of Hermitian-Einstein
metrics for stable vector bundles over projective manifolds. We will discuss Flenner’s proof of