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Spencer Gao, Department of Pure Mathematics, University of Waterloo

"Representation of General Linear Group over Finite Field"

This talk aims at discussing the techniques used in finding all the irreducible representations of general linear groups over finite fields. A brief overview of representation theory is also provided, but no such overview is provided for group theory and field theory.

Aidan Patterson, Department of Pure Mathematics, University of Waterloo

"Local Normal Forms for Hamiltonian Actions of Poisson-Lie Groups"

Daniel Perales Anaya, Department of Pure Mathematics, University of Waterloo

"On the anti-commutator of two free random variables"

David McKinnon, Department of Pure Mathematics, University of Waterloo

"Arithmetic Geometry Learning Seminar organisational meeting"

We’re going to study something related to the proof of Fermat’s Last Theorem, having to do with solving Diophantine equations.  Come to the first meeting to help us figure out exactly what that will be!

Place: Zoom

Ruxandra Moraru, Department of Pure Mathematics, University of Waterloo

"Divisors and line bundles"

In this talk, we will discuss the relationship between divisors and line bundles on complex varieties. We will, in particular,  compare the divisor class group $Cl(X)$ and the Picard group $Pic(X)$ of a complex variety $X$, which classify divisors and line bundles up to equivalence, respectively. We will also give explicit examples and, time permitting, describe $Div(X)$ and $Pic(X)$ in the case where $X$ is a toric variety.

Shengda Hu, Wilfrid Laurier University

"Curvature of generalized holomorphic bundles"

We continue with the discussion on generalized connections on a Riemannian manifold. We will discuss properties of curvatures on generalized holomorphic vector bundles over a generalized Kahler manifold and generalized analogues of classical notions.

Zoom link: https://us02web.zoom.us/j/84677935521?pwd=WTdsV0ExQXNKRGUxclJvRWhTQXlUZz09

Ping Zhong, University of Wyoming

The meetings of this learning seminar will continue on Tuesday afternoons, 2:30-4 pm, on Zoom. The plan for the next meeting is to wrap-up the discussion about the Fuglede-Kadison determinant and to move on towards the definition of the Brown spectral measure associated to an element of a W*-probability space.

The seminar will meet on Zoom.

• Meeting ID: 913 2631 2873
• Passcode: 581735

Shengda Hu, Wilfrid Laurier University

"Curvature for connections in generalized geometry"

We continue with the discussion on generalized connections on a Riemannian manifold, discuss the curvature identities and generalize holomorphic bundle over a generalized Kahler manifold.

Zoom meeting:

• Meeting ID: 958 7361 8652
• Passcode: 577854

Sean Monahan, Department of Pure Mathematics, University of Waterloo

"An introduction to toric varieties"

Toric varieties are a special kind of variety equipped with a group action from an algebraic torus. These varieties are very nice to work with because they have a combinatorial interpretation involving polyhedral geometry. I will (very quickly) introduce toric varieties and focus on some concrete examples.

The seminar will meet on Zoom.
Meeting ID: 811 2094 8164
Passcode: 033003

Ping Zhong, University of Wyoming

The Brown measure was introduced by L.G. Brown in 1983. It is a generalized notion of spectral measure which applies to non-normal operators living in a suitable non-commutative probability framework -- the framework of a so-called W*-probability space. The purpose of this learning seminar is to provide an accessible entry point to the notion of Brown measure, with an eye towards becoming able to do calculations of Brown measures in examples which come from free probability.