Events - January 2023

Elliot Kaplan, McMaster University

"Hilbert polynomials for finitary matroids"

Ian Hambleton, McMaster University

"Euler Characteristics and 4-manifolds"

The topology and total curvature of a Riemann surface is determined by a single integer, the Euler characteristic (Leonhard Euler, 1707-1783). In dimension four and higher, the Euler characteristic gives an interesting invariant for finitely presented groups. The talk will survey some recent joint work with Alejandro Adem on this theme.

MC 5501

Joey Lakerdas-Gayle, Department of Pure Mathematics, University of Waterloo

"Effectively closed sets - Part III"

An effectively closed set (or $\Pi^0_1$ class) in Baire space $\omega^\omega$ is the set $[T]$ of infinite branches through a computable tree $T$. This semester in the computability seminar, we will be studying $\Pi^0_1$ classes from Cenzer \& Remmel's textbook. This week, we will conclude chapter 2 by discussing some applications of $\Pi^0_1$ classes in computability theory.

MC 5403

Francisco Villacis, Department of Pure Mathematics, University of Waterloo

"Integrable systems on smooth projective toric varieties"

Let X be a smooth projective toric variety of complex dimension n. We can endow X with a symplectic form coming from the Fubini-Study form on projective space. We will show that we have an action of a real n-torus on X which is Hamiltonian and gives rise to an integrable system on X.

This seminar will be held both online and in person:

Changho Han, Department of Pure Mathematics, University of Waterloo

"Brief Introduction to General MMP"

Before we dive into the less ventured area of horospherical MMP, it would be nice to first understand how the general MMP works in order to prove MMP results in horospherical settings. In that regard, I will present some motivations behind the definition of MMP singularities, and give a general overview of the general MMP.

This seminar will be held jointly online and in person:

Hanming Liu, Department of Pure Mathematics, University of Waterloo

"Heegaard Floer Homology"

This will be an introduction to Heegaard Floer homology. We will aim to present its definition and state some topological applications.

MC 5403

Owen Sharpe, Department of Pure Mathematics, University of Waterloo

"Diophantine Techniques in Bourgain's Discrete Restriction Conjecture"

We continue the last talk about Bourgain's discrete restriction conjecture, and explain the Diophantine techniques used in the recent progress on the conjecture by Hughes and Wooley.

This seminar will be held both online and in person:

This semester there will be a reading seminar on Riemann Surfaces. We'll be using Simon Donaldson's book as a reference. 

These seminars are pretty accessible as the only hard pre-requisite is some Complex Analysis. Donaldson's exposition is also especially good as he gives a lot of focus on intuition and examples.

The aim of the seminar is to go through the whole book. One chapter each week. Though, we will slow down if we need to. 

Joey Lakerdas-Gayle, Department of Pure Mathematics, University of Waterloo

"Effectively closed sets -- Part II"

Xuemiao Chen, Department of Pure Mathematics, University of Waterloo

"Bogomolov inequality"

After introducing some necessary basics, we will present Miyaoka's elegant proof of the Bogomolov inequality for slope semistable bundles over projective smooth surfaces.

MC 5403

**Note this seminar will not be held at the usual time**

Yu-Ru Liu, Department of Pure Mathematics, University of Waterloo

"On the multidimensional Hilbert-Kamke problem"