## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

**Returning to in-person experiences in February:** Visit the COVID-19 website for more information.

Wednesday, June 30, 2021 — 11:00 AM EDT

**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.

Tuesday, June 29, 2021 — 2:30 PM EDT

**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

Monday, June 28, 2021 — 1:30 PM EDT

**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

Monday, June 28, 2021 — 11:00 AM EDT

**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.

Wednesday, June 23, 2021 — 12:00 PM EDT

**Sean Fitzpatrick, University of Lethbridge**

"How using OER made me a better teacher"

I began working with open educational resources (OER) not long after my arrival at the University of Lethbridge. There were two immediate appeals: affordability (I could provide a textbook to students at no cost) and adaptability (I could edit the source to get the textbook I wanted). When the only commercial textbook we could find for a new course was over $300, I knew it was time to consider OER.

Wednesday, June 23, 2021 — 11:00 AM EDT

**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

Wednesday, June 23, 2021 — 9:00 AM EDT

**Nolan Pyott, Department of Pure Mathematics, University of Waterloo**

"Counting Irreducible Polynomials with the Turán Sieve"

Monday, June 21, 2021 — 2:30 PM EDT

**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.

Monday, June 21, 2021 — 11:00 AM EDT

**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

Thursday, June 17, 2021 — 1:30 PM EDT

**Katarina Spasojevic, USRA, Department of Pure Mathematics, University of Waterloo**

Wednesday, June 16, 2021 — 11:00 AM EDT

**Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo**

Last time we reviewed the classical decomposition of the Riemann curvature tensor into scalar, traceless Ricci, and Weyl curvature. This time we will examine special features in dimensions 3 and 4. Then I will consider the more general case of a metric compatible connection with torsion, and see how this decomposition generalizes.

Thursday, June 10, 2021 — 4:00 PM EDT

**Shayla Redlin, Department of Combinatorics & Optimization, University of Waterloo**

"Counting Antichains in the Boolean Lattice"

Wednesday, June 9, 2021 — 12:00 PM EDT

**Jason Siefken, University of Toronto**

"Onboarding Instructors to an Active Learning Class"

Wednesday, June 9, 2021 — 9:00 AM EDT

**Shuo Gao, Department of Pure Mathematics, University of Waterloo**

"Introduction to Elementary Sieve"

This talk aims at introducing sieve theory in an elementary way. Sieve problem and two elementary sieves - larger sieve and square sieve - will be discussed in detail, as well as their applications and a broad overview of the historical development of sieve theory. Some standard results including the Mobius inversion formula will also be covered in this talk to make the proof self-contained.

Wednesday, June 2, 2021 — 11:00 AM EDT

**Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo**

"Decomposition of curvature tensor for metrics with torsion"

I will first review the classical decomposition of the Riemann curvature tensor into scalar, traceless Ricci, and Weyl curvature, with an emphasis on special features in dimensions 3 and 4. Then I will consider the more general case of a metric compatible connection with torsion, and see how this decomposition generalizes.

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.