# Events - January 2023

Tuesday, January 31, 2023 — 3:30 PM EST

## Number Theory Seminar

David McKinnon, Department of Pure Mathematics, University of Waterloo

"Gaussian integers and gcds"

Tuesday, January 31, 2023 — 2:30 PM EST

## Differential Geometry Working Seminar

Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo

"Nearly Kahler 6-manifolds have SU(3)-structures"

Tuesday, January 31, 2023 — 2:30 PM EST

## Logic Seminar

Elliot Kaplan, McMaster University

"Hilbert polynomials for finitary matroids"

Tuesday, January 31, 2023 — 10:00 AM EST

## Student Number Theory Seminar

Jeremy Champagne, Department of Pure Mathematics, University of Waterloo

"Geometry of numbers as a tool for Diophantine approximation"

Anybody who has taken a course on algebraic number theory, has probably seen Minkowski's convex body theorem as a mean to prove the finiteness of class groups. However, less people know about Minkowski's second convex body theorem, which gives much more insight into this problem of finding integer points with certain properties.

Monday, January 30, 2023 — 2:30 PM EST

## Colloquium

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

Thursday, January 26, 2023 — 4:00 PM EST

## Analysis Seminar

Erik Seguin, Department of Pure Mathematics, University of Waterloo

"Amenability and stability for discrete groups"

Thursday, January 26, 2023 — 2:30 PM EST

## Computability Theory Learning Seminar

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

Thursday, January 26, 2023 — 10:00 AM EST

## Learning Seminar on Elliptic Curves

The intent of this seminar is to cover some of the basic theory of elliptic curves. Our first objective is to cover chapters 2, 3 and 6 from Joseph Silverman’s book (The Arithmetic of Elliptic Curves). Later in the semester, we will switch our focus towards more specific topics in the theory of elliptic curves.

This week's presenter is Yash Singh, Department of Pure Mathematics, University of Waterloo.

MC 5403

Wednesday, January 25, 2023 — 2:00 PM EST

## Algebraic Geometry Working Seminar

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:

Wednesday, January 25, 2023 — 1:00 PM EST

## Model Theory Working Seminar

Leo Jimenez, Department of Pure Mathematics, University of Waterloo

"Not pfaffian"

James Freitag has shown that the j-function is not Pfaffian using the model theory of differentially closed fields. We will work though his paper, entitled "Not pfaffian".

MC 5417

Wednesday, January 25, 2023 — 11:00 AM EST

## Horospherical MMP Seminar

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:

Tuesday, January 24, 2023 — 3:30 PM EST

## Number Theory Seminar

Debanjana Kundu, University of Toronto

"Heuristics for  anti-cyclotomic $\mathbb{Z}_p$-extensions"

For an imaginary quadratic field, there are two natural $\mathbb{Z}_p$-extensions, the cyclotomic and the anticyclotomic. We'll start with a brief description of Iwasawa theory for the cyclotomic extensions, and then describe some computations for anticyclotomic  $\mathbb{Z}_p$ extensions, especially the fields and their class numbers. This is joint work with LC Washington.

This seminar will be held both online and in person

Tuesday, January 24, 2023 — 2:30 PM EST

## Differential Geometry Working Seminar

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

Tuesday, January 24, 2023 — 2:30 PM EST

## Logic Seminar

Gianluca Basso, Université Lyon 1

"Kaleidoscopic groups and the generic point property"

Tuesday, January 24, 2023 — 10:00 AM EST

## Student Number Theory Seminar

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:

Monday, January 23, 2023 — 2:30 PM EST

## Colloquium

Dmitry Ryabogin, Kent State University

"On bodies floating in equilibrium in every orientation"

We give a negative answer to Ulam's Problem 19 from the Scottish Book asking is a solid of uniform density which will float in water in every position a sphere? Assuming that the density of water is 1, we show that there exists a strictly convex body of revolution K\subset {\mathbb R^3} of uniform density \frac{1}{2}, which is not a Euclidean ball, yet floats in equilibrium in every orientation.

MC 5501

Friday, January 20, 2023 — 1:30 PM EST

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.

Thursday, January 19, 2023 — 4:00 PM EST

## Analysis Seminar

Jeremy Hume, University of Glasgow

"The K-theory of a rational function"

Thursday, January 19, 2023 — 2:30 PM EST

## Computability Theory Learning Seminar

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

"Effectively closed sets -- Part II"

Thursday, January 19, 2023 — 10:00 AM EST

## Learning Seminar on Elliptic Curves

Sourabhashis Das, Department of Pure Mathematics, University of Waterloo

"Chapter 2 – Algebraic curves"

In this first talk of the learning seminar, we will introduce algebraic curves and present basic facts about these curves which are essential in the study of elliptic curves. In particular, we will talk about the divisor group associated to such curves and discuss certain important results such as the Riemann-Roch theorem.

This seminar will be held both online and in person:

Tuesday, January 17, 2023 — 2:30 PM EST

## Differential Geometry Working Seminar

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

Tuesday, January 17, 2023 — 2:30 PM EST

## Logic Seminar

"Regular solutions of systems of E-polynomials"

Tuesday, January 17, 2023 — 11:30 AM EST

## Number Theory Seminar

**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"

Tuesday, January 17, 2023 — 10:00 AM EST

## Student Number Theory Seminar

Owen Sharpe, Department of Pure Mathematics, University of Waterloo

"Vinogradov's Mean Value Theorem and Bourgain's Discrete Restriction Conjecture"

Monday, January 16, 2023 — 2:30 PM EST

## Colloquium

David Kribs, University of Guelph

"Quantum error correction and operator algebras"

Quantum error correction is a central topic in quantum information science. Its origins as an independent field of study go back more than a quarter century, and it now arises in almost every part of the subject, including in recent years as a key area of focus in the development of new quantum technologies.

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