Events

Félix Baril Boudreau, University of Lethbridge

"Arithmetic rank bounds for abelian varieties over function fields"

It is known since the works of Ogg (1962) and Shafarevich (1961) (under tameness assumptions), followed by Grothendieck (1968), that the rank of a given abelian variety over the function field of a curve is bounded by a quantity which depends on the genus of the base curve and on reduction data. This bound is "geometric" in nature. In particular, it holds if we replace the constant field by its algebraic closure.

Ulmer asked in 2004 if, for an elliptic curve, there was an arithmetic bound that could improve on the geometric one. This question recently obtained a positive answer (Gillibert and Levin, 2022).

In this talk, we present a similar arithmetic refinement of the geometric bound for higher-dimensional abelian varieties. When specialized to elliptic curves, we improve on Gillibert-Levin's bound. Time permitting, we will discuss some consequences of our result.

This is joint work with Jean Gillibert and Aaron Levin.

MC 5501

Victor Liao, Department of Pure Mathematics, University of Waterloo

"Properly proximal groups and their von Neumann algebras"

In this talk, I will be presenting the first part of the 2018 paper by Boutonnet, Ioana, and Peterson titled "Properly proximal groups and their von Neumann algebras". I will aim to cover the main motivation of the paper and introduce notions like proximal/boundary pieces of discrete groups, as well as properly proximal groups.

MC 5417

Xiao Zhong, Department of Pure Mathematics, University of Waterloo

"Continuous Functions on the Berkovich Projective Line and Measures"

We will look at the space of continuous functions on the Berkovich projective line and coherent system of measures. If time permits, we will introduce Laplacian on this space. This talk will basically follows Chapter 5 of Baker-Rumely's Book: "Potential Theory and Dynamics on the Berkovich Projective Line".

MC 5479

Rachael Alvir, Department of Pure Mathematics, University of Waterloo

"Effective Descriptive Set Theory 5"

We will continue to introduce effective descriptive set theory following Andrew Marks's notes.

MC 5479

Christine Eagles, Department of Pure Mathematics, University of Waterloo

"Domination equivalence and fibers"

In stable theories we may understand types of finite rank in terms of a finite collection of minimal types. One such method is a domination decomposition. This talk will serve as an exposition on domination in stable theories, particularly in how it relates to images of a type under a function. In particular, we show that when the fibers of a map f from a type p to another type are almost internal to a minimal type r, then we have that p is domination equivalent to a Morley product of the image of f and some copies of r. This is joint work with Léo Jimenez. 

MC 5479

Sean Monahan, Department of Pure Mathematics, University of Waterloo

"Approximating rational points on horospherical varieties"

I will discuss a recent paper that I wrote with Matt Satriano, the title of which is conveniently the title of this talk (arXiv 2308.11847). David McKinnon has a conjecture known as the “curve of best approximation (COBA)” conjecture, which says that among the sequences which approximate a given rational point on a projective variety, the ones that do their job the best must lie on a rational curve inside the variety. To probe this conjecture, Matt and I explored the case where the variety is horospherical so that we could use the tractable combinatorial theory which these varieties possess. Unfortunately, the stars did not align since this talk will not take place in MC 5417, which is roughly the centre point between the offices of Matt, David, and myself.

QNC 1502

Junsheng Zhang, University of California Berkeley

"On complete Calabi-Yau manifolds asymptotic to cones"

We proved a "no semistability at infinity" result for complete Calabi-Yau metrics asymptotic to cones, by eliminating the possible appearance of an intermediate K-semistable cone in the 2-step degeneration theory developed by Donaldson-Sun. As a consequence, a classification result for complete Calabi-Yau manifolds with Euclidean volume growth and quadratic curvature decay is given. Moreover a byproduct of the proof is a polynomial convergence rate to the asymptotic cone for such manifolds. Joint work with Song Sun.

QNC 2501

Laindon Burnett, Department of Pure Mathematics, University of Waterloo

"Honest Definitions in NIP"

We cover the idea of Honest Definitions from Pierre Simon's "A Guide to NIP Theories". In particular, we show that in an NIP theory, even if a particular type is not definable over a given set (and hence there is a bad formula which prevents it from being so), we may instead define this formula with parameters from an elementary extension, and this new defining formula is captured inside of the bad formula when we loosen ourselves and allow for object variables to come from the extension.

MC 5403

Benjamin Anderson-Sackaney, University of Saskatchewan

"Amenability of Fusion Modules and Coideals"

The coideals of a quantum group offer a quantum analogue of a subgroup of a group. For certain classes of coideals there is an obvious quantum analogue of a quasi-regular representation. For a larger class of coideals recently introduced by De Commer and Dzokou Talla, namely, the so-called $g$-integral coideals, we will introduce a notion of a $g$-quasi-regular representation. We will then define a notion of $g$-coamenability that generalizes the notion of a coamenable inclusion of groups. We will also introduce a notion of amenability of a fusion module equipped with a dimension function that is compatible with a dimension function on the given fusion algebra. This notion gives a characterization of $g$-coamenability at the tensor categorical level.

This seminar will be held both online and in person:

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

Brady Ali Medina, Department of Pure Mathematics, University of Waterloo

"Schubert Cycles"

I will introduce Schubert cycles and explain some facts about them. This corresponds to section 4.1 of 3264 & All That by Eisenbud and Harris.

This seminar will be held both online and in person:

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