## 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

Tuesday, March 3, 2020 — 2:00 PM EST

Luke MacLean, Department of Pure Mathematics, University of Waterloo

"Kleene's $\mathcal{O}$"

Kleene's $\mathcal{O}$ is a system for ordinal notation used in computability theory that relates the concepts of constructive and computable ordinals. This notation allows one to unambiguously perform transfinite induction on ordinals by ensuring that there is a unique representation for each ordinal.

We will prove some properties about the notation system and show that there are ordinals which are not computable.

MC 5413

Tuesday, March 3, 2020 — 1:30 PM EST

**Sacha Mangarel, Centre de Recherches Mathématiques**

"On Low Discrepancy Multiplicative Sequences"

Tuesday, March 3, 2020 — 10:30 AM EST

**Wilson Poulter, Department of Pure Mathematics, University of Waterloo**

"NIP XIII"

We continue section 4.1 of Simon's Guide to NIP theories.

MC 5479

Tuesday, March 3, 2020 — 10:00 AM EST

**Hongdi Huang, Department of Pure Mathematics, University of Waterloo**

In the half part, we will complete the leftover on the generators and relations. Then we will setup for Frobenius algebras. Finally, we will go-ahead to the algebra structure.

MC 5417

Monday, March 2, 2020 — 4:00 PM EST

**Ilan Hirshberg, Ben Gurion University of the Negev**

"Mean dimension and radius of comparison"

Friday, February 28, 2020 — 3:30 PM EST

**Alex Rutar, Department of Pure Mathematics, University of Waterloo**

"Geometric and Combinatorial Separation Conditions for Iterated Function Systems"

Friday, February 28, 2020 — 3:00 PM EST

**Michael Klug, University of California Berkeley**

"Concordance of homotopic spheres in 4-manifolds"

Wednesday, February 26, 2020 — 3:30 PM EST

**Wilson Poulter, Department of Pure Mathematics, University of Waterloo**

"Ultraproducts, Hyperreals, and Pseudofinite Graphs"

An ultraproduct is a construction used in mathematical logic to construct limits of first-order structures. Due to a result of Jerzy Los, the first-order properties of these limits is very well understood, allowing one to construct counter-examples as well as structures that are interesting in and of themselves.

Wednesday, February 26, 2020 — 2:30 PM EST

**Brett Nasserden, Department of Pure Mathematics, University of Waterloo**

"An introduction to the Laplacian operator on a metrized graph: Part 2"

We will continue our discussion of harmonic analysis on a finite metrized graph. The goal is to finish the introduction to the theory and go over some explicit examples.

MC 5403

Tuesday, February 25, 2020 — 2:30 PM EST

**Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo**

"Return Sets on Algebraic Varieties"

Tuesday, February 25, 2020 — 2:00 PM EST

**Dino Rossegger, Department of Pure Mathematics, University of Waterloo**

"Iterated Reflection principles and Feferman's Completeness Theorem"

Tuesday, February 25, 2020 — 11:00 AM EST

**Andrew Staal, Department of Pure Mathematics, University of Waterloo**

"Reducibility of Varieties of Commuting Matrices"

We will present some well-known results on reducibility of the varieties C(k,n) of commuting k-tuples of nxn-matrices. In particular, we will discuss the Motzkin—Taussky Theorem proving irreducibility of C(2,n) and Guralnick’s Theorem, which shows that C(3,n) is reducible when n ≥ 29.

MC 5413

Tuesday, February 25, 2020 — 10:30 AM EST

**Alexi Taylor Block Gorman, University of Illinois at Urbana-Champaign**

"Continuous Regular Functions: where automata theory meets metric geometry"

Tuesday, February 25, 2020 — 10:00 AM EST

**Hongdi Huang, Department of Pure Mathematics, University of Waterloo**

This week, we will further talk about the generators and relations for 2Cob.

MC 5417

Monday, February 24, 2020 — 4:00 PM EST

**Zhouli Xu, MIT**

"In and around stable homotopy groups of spheres"

Tuesday, February 18, 2020 — 1:30 PM EST

**Angelos Koutsianas, University of British Columbia**

"Solving generalized Fermat equations with Frey hyperelliptic curves"

In this talk, I will talk about Darmon's program and the resolution of the generalized Fermat equation of signature (p,p,5) using Frey hyperelliptic curves. This is joint work with Imin Chen (Simon Fraser University).

MC 5417

Tuesday, February 18, 2020 — 11:00 AM EST

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

"Bryant-Salamon G2 manifolds and coassociative fibrations"

Tuesday, February 18, 2020 — 10:00 AM EST

**Patrick Naylor, Department of Pure Mathematics, University of Waterloo**

"The category of cobordisms (Part III)"

We specialize to the 2-cobordism category, and work towards developing a set of generators and relations.

MC 5417

Friday, February 14, 2020 — 3:30 PM EST

**Kathryn Hare, Department of Pure Mathematics, University of Waterloo**

"The size of complementary sets"

Wednesday, February 12, 2020 — 2:30 PM EST

**Brett Nasserden, Department of Pure Mathematics, University of Waterloo**

"An introduction to the Laplacian operator on a metrized graph"

In this presentation we shall attempt to give a self contained introduction to finite metrized graphs. Following this introduction we shall discuss how to define a Laplacian operator on a finite metrized graph and discuss its basic properties.

MC 5403

Tuesday, February 11, 2020 — 1:30 PM EST

**Jerry Wang, Department of Pure Mathematics, University of Waterloo**

"Density of polynomials with squarefree discriminant II"

In this talk, we will discuss the squarefree sieve for discriminants of arbitrary polynomials. We will find that there are striking differences between odd and even degree polynomials, where additional techniques of counting on varieties will be required for the latter. This is joint work with Manjul Bhargava and Arul Shankar.

MC 5417

Tuesday, February 11, 2020 — 10:30 AM EST

**Jinhe Ye, University of Notre Dame**

"A model theoretic adic space"

Tuesday, February 11, 2020 — 10:00 AM EST

**Patrick Naylor, Department of Pure Mathematics, University of Waterloo**

"The category of cobordisms (Part II)"

We will continue to discuss the category of cobordisms, along with more examples.

MC 5417

Monday, February 10, 2020 — 4:00 PM EST

**Marco Gualtieri, University of Toronto **

"From generalized Kahler geometry to noncommutative algebra"

Friday, February 7, 2020 — 3:30 PM EST

**Adam Humeniuk, Department of Pure Mathematics, University of Waterloo**

"On C*-Envelopes of Semicrossed Products"

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.