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Mikael De La Salle, Université de Lyon

"Variations around the Hilbert transform"

The Hilbert transform is the operator of convolution by the distribution 1/t. It is an emblematic example of a Fourier multiplier. I will present variants on other spaces than the real line, such as matrices, manifolds and groups, and applications to operator algebras, representation theory. I will present more or less recent results obtained in collaboration with Vincent Lafforgue, Tim de Laat, Javier Parcet and Eduardo Tablate.

MC 5501

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

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

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

Nathan Grieve, Acadia University

"On Schmidt's Subspace Theorem, Vojta's height inequalities and algebraic points in projective varieties: recent developments and progress"

I will report on a collection of recent results and ongoing work that surround extensions and applications of Schmidt's Subspace Theorem and Vojta's height inequalities.  As two examples: (i) It is of interest to understand the qualitative features of Diophantine exceptional sets; (ii) It is of interest to understand the extent to which algebraic points of a given bounded degree in a given general type projective variety are not-Zariski dense.  As I will explain, there are several logically equivalent points of departure for these results.  They build on a collection of my past contributions in addition to work of many others.

Online talk: https://uwaterloo.zoom.us/j/98950813087?pwd=SEl1NlNqNHl0QzlYNGJzeDVla204QT09

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

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

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

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

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