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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

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

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

Ila Varma, University of Toronto

"Counting number fields and predicting asymptotic"

A guiding question in number theory, specifically in arithmetic statistics, is: Fix a degree n and a Galois group G in S_n. How does the count of number fields of degree n whose normal closure has Galois group G grow as their discriminants tend to infinity? In this talk, we will discuss the history of this question and take a closer look at the story in the case that n = 4, i.e. the counts of quartic fields.

MC 5501

Christine Eagles, Department of Pure Mathematics, University of Waterloo

"NIP"

We continue to read through Pierre Simon's "A Guide to NIP theories". 

MC 5403

Michael Albanese, Department of Pure Mathematics, University of Waterloo

"Blowups and examples!"

We will discuss blowups and prove that the blowups of S^2 bundles over S^2 are diffeomorphic. We will use the remaining time to discuss other examples.

MC 5403

Yash Singh, Department of Pure Mathematics, University of Waterloo

"Lines and surfaces in P^3"

We use our understanding of Grassmannians so far to study the geometry of lines and surfaces in P^3.

This seminar will be held both online and in person:

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

Jing Zhang, University of Toronto

"Compactness and incompactness in higher dimensional combinatorics"

We describe an organizing framework to study higher dimensional infinitary combinatorics based on \v{C}ech cohomology, originating from works by Barry Mitchell, Barbara Osofsky and others. A central combinatorial notion is $n$-dimensional coherence sequences, generalizing the 1-dimensional ones studied extensively by Todorcevic using the method of minimal walks. We will discuss ZFC results suggesting $\aleph_n$ is not "compact for $(n+1)$-dimensional combinatorics" and consistency results that any regular cardinal greater or equal to $\aleph_{\omega+1}$ can be "compact for $n$-dimensional combinatorics for all $n$". The talk will be purely combinatorial. Joint work with Jeffrey Bergfalk and Chris Lambie-Hanson.

MC 5479