Events

Changho Han, Department of Pure Mathematics, University of Waterloo

"Aspects of genus 4 curves"

If you know several different ways to characterize a given projective variety, then you can gain knowledge of the properties of this object by interconnecting methods involved in different viewpoints. For example, one can interconnect both algebraic and analytic methods to study complex elliptic curves, which could be viewed as either plane cubic curves or lattice quotients of a complex plane. Motivated by this principle, we will explore various different ways to characterize a general genus 4 curve, and then see how those viewpoints can be extended to special genus 4 curves as well. In particular, I will show that general genus 4 curves can alternatively be characterized by trigonal maps to projective line, bidegree (3,3)-curves in a smooth quadric surface, or particular kinds of K3 surfaces. If time remains, then I will explain how those viewpoints induce birational maps between corresponding moduli spaces. This talk is based on a pictorial portion of joint works in progress with Valery Alexeev, Anand Deopurkar, and Philip Engel.

MC 5417

Robert Harris, Department of Pure Mathematics, University of Waterloo

"Kirby diagrams cont. - what manifold is this?"

We will continue our discussion on Kirby diagrams. In particular we will look at the Kirby diagrams for some well known 4-manifolds and see some of the techniques used for determining what a Kirby diagram for a given manifold should look like.

MC 5403

Lukas Mueller, Perimeter Institute for Theoretical Physics

"Quantum representations of handlebody groups"

Nicolas Chavarria Gomez, Department of Pure Mathematics, University of Waterloo

"NIP"

We will continue learning about the basics on NIP theories guided by Pierre Simon's A Guide to NIP Theories.

MC 5403

Arthur Troupel, Université Paris Cité

"Free wreath product quantum groups as fundamental C*-algebras of graphs"

The free wreath product of a compact quantum group by the quantum permutation group $S_N^+$ has been introduced by Bichon in order to give a quantum counterpart of the classical wreath product. The representation theory of such groups is well-known, but some results about their operator algebras were still open, for example stability of Haagerup property, of $K$-amenability or factoriality of the von Neumann algebra. I will present a joint work with Pierre Fima in which we identify these algebras with the fundamental C*-algebras of certain graphs of C*-algebras, and we deduce these properties from these constructions.

This seminar will be held both online and in person:

• Room: MC 5479
• Zoom link: https://uwaterloo.zoom.us/j/94186354814?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT09

AJ Fong, Department of Pure Mathematics, University of Waterloo

"Curves on Surfaces"

This week, we will introduce the genus formula for smooth curves on surfaces. Then we will review the theory of blow-ups of a point on a surface $S,$ and then completely describe the Chow group of the blow-up in terms of the Chow group of $S.$ If time permits, we will also derive the genus formula for possibly singular curves on surfaces.

This seminar will be held both online and in person:

• MC 5417
• Zoom link:https://uwaterloo.zoom.us/j/93801243240?pwd=blpUMVJ1dExUYVlEMkJVWjlscUNqZz09

Liam Orovec, Department of Pure Mathematics, University of Waterloo

"Solving the Rubic’s Cube (Group)"

Everyone has seen a Rubik's Cube, maybe some of you have solved it once or twice. But if there was some sort of omnipotent being what is the most amount of moves they would take to solve it. This concept is known as God's Number, we will go over the basic ideas proof as well as the history in the best known results leading up to the proof. We will also go over some other math related facts about the cube and other related puzzles. Puzzles will be provided to play with if you rather do that then listen to the talk.

MC 5417

Dror Bar-Natan, University of Toronto

"Cars, Interchanges, Traffic Counters, and some Pretty Darned Good Knot Invariants"

Reporting on joint work with Roland van der Veen, I'll tell you some stories about ρ1, an easy to define, strong, fast to compute, homomorphic, and well-connected knot invariant. ρ1 was first studied by Rozansky and Overbay, it is dominated by the coloured Jones polynomial (but it isn't lesser!), it has far-reaching generalizations, and I wish I understood it. Further information can be found at this link: http://drorbn.net/wat23

MC 5501

Nicolo Fellini, Queen's University

"Variations of a conjecture of Ankeny-Artin-Chowla"

A famous conjecture of Ankeny, Artin and Chowla relates the class number of a real quadratic field $\mathbb{Q}(\sqrt{p})$ with $p$ a prime congruent to $1\bmod{4}$,  with its fundamental unit $\epsilon = (t+u\sqrt{p})/2$ via a $\bmod{p}$ congruence. In particular, the Ankeny--Artin--Chowla (AAC) conjecture states that $u$ is not divisible by $p$. The significance of their conjecture lies in the fact that it provides an arithmetic way of computing the class number of $\mathbb{Q}(\sqrt{p})$ for $p$ a prime congruent to $1\bmod{4}$. I will discuss the history and techniques of their work as well as show that there are further connections with Fermat quotients and Wieferich style congruences. This is joint work with M. Ram Murty.

MC 5501

Xiao Zhong, Department of Pure Mathematics, University of Waterloo

"Metrized Graphs and Laplacians"

This will be a continuation of previous Berkovich space talk where we established the tree structure of Berkovich space. Now, we look at how to put metric on it, study various function spaces on graphs and Laplacians on those function spaces. This talk basically follows Chapter 3 of Baker-Rumely's Book: "Potential Theory and Dynamics on the Berkovich Projective Line".

MC 5479