## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Thursday, June 29, 2017 — 4:00 PM EDT

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

"The Pisano Period"

Thursday, June 29, 2017 — 11:00 AM EDT

**Sam Harris, Department of Pure Mathematics, University of Waterloo**

"Connes' Embedding Problem & Kirchberg's Conjecture (continued)"

Wednesday, June 28, 2017 — 11:00 AM EDT

**Sam Harris, Department of Pure Mathematics, University of Waterloo**

"Connes' Embedding Problem & Kirchberg's Conjecture"

Tuesday, June 27, 2017 — 2:30 PM EDT

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

"A new construction of compact $G_2$ manifolds by glueing Eguchi-Hanson spaces, Part IV: The Correction Theorem"

We give the details of the "correction theorem" that allow us to produce the closed pair $(\tilde \varphi, \tilde \psi)$ on the Eguchi-Hanson bundle with sufficiently small torsion. The proof involves several steps, including the Lockhart-McOwen theory of elliptic operators on weighted Sobolev spaces in the asymptotically locally Euclidean category.

MC 5479

Tuesday, June 27, 2017 — 12:00 PM EDT

**Adam Morgan, Department of Applied Mathematics, University of Waterloo**

"Classical Field Theory from the Hamiltonian Viewpoint"

Tuesday, June 27, 2017 — 9:00 AM EDT

**Sam Harris, Department of Pure Mathematics, University of Waterloo**

"Hyperlinear Groups"

Today we look at the class of hyperlinear groups. We will show that every sofic group is hyperlinear, and we will summarize some of the closure properties of sofic/hyperlinear groups. If time allows, we will look at how sofic groups can address a weaker form of Connes' embedding problem.

MC 5403

Monday, June 26, 2017 — 10:00 AM EDT

**Ertan Elma, Department of Pure Mathematics, University of Waterloo**

"The Large Sieve"

We will prove the large sieve inequality and then construct the large sieve. We will also mention some applications of this important technique in analytic number theory.

MC 5403

Monday, June 26, 2017 — 9:00 AM EDT

**Sam Harris, Department of Pure Mathematics, University of Waterloo**

"Sofic Groups"

Today we will give a brief introduction to Connes' embedding problem. We will then introduce invariant length groups and what it means for a countable discrete group to be sofic.

MC 5403

Thursday, June 22, 2017 — 2:30 PM EDT

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

"A new construction of compact $G_2$ manifolds by glueing Eguchi-Hanson spaces, Part III.c: Constructing the closed pair on the Eguchi-Hanson bundle"

Wednesday, June 21, 2017 — 5:00 PM EDT

**Ertan Elma, Department of Pure Mathematics, University of Waterloo**

"Selberg's Sieve II"

We will finish the proof of the main theorem of Selberg's sieve and prove the Brun-Titchmarsh theorem as an application.

MC 5403

Tuesday, June 20, 2017 — 3:30 PM EDT

**Jonny Stephenson, Department of Pure Mathematics, University of Waterloo**

"Effective bi-interpretability and Graphs II"

Last time we saw that every structure is effectively bi-interpretable with a structure over a simple language consisting of a unary predicate U and a symmetric binary predicate E. This week, we will show that any structure over this language is effectively bi-interpretable with a graph. This will complete the proof that every structure is effectively bi-interpretable with a graph.

MC 5403

Tuesday, June 20, 2017 — 2:30 PM EDT

**Panagiotis Gianniotis, Department of Pure Mathematics, University of Waterloo**

"The Michael-Simon Sobolev inequality"

I will talk about the paper of Michael and Simon "Sobolev and Mean-Value inequalities on Generalized Submanifolds of R^n". In this paper, Michael-Simon use an elegant argument to prove a general Sobolev inequality for functions on subsets of the Euclidean space, which in particular is quite useful in the study of submanifolds.

MC 5479

Monday, June 19, 2017 — 2:30 PM EDT

**Tyrone Ghaswala, Department of Pure Mathematics, University of Waterloo**

"The liftable mapping class group"

Monday, June 19, 2017 — 10:00 AM EDT

**Letian Chen, University of Waterloo**

"Applications of the Riemann-Roch Theorem"

We will continue from last time and state the Riemann-Roch theorem after recalling some key definitions and results. We will then use the Riemann-Roch theorem to give a characterization of function fields of genus 0 and show the finiteness of the class group.

MC 5403

Wednesday, June 14, 2017 — 5:00 PM EDT

**Ertan Elma, Department of Pure Mathematics, University of Waterloo**

"Selberg's Sieve"

We will start reading Chapter 7 of the book *An Introduction to Sieve Methods and Their Applications*, by R. Murty, C. Cojocaru.

MC 5403

Tuesday, June 13, 2017 — 3:30 PM EDT

**Jonny Stephenson, Department of Pure Mathematics, University of Waterloo**

"Effective Bi-interpretability with Graphs"

Monday, June 12, 2017 — 10:00 AM EDT

**David Urbanik, University of Waterloo**

"Motivating the Riemann-Roch Theorem"

We attempt to motivate the Riemann-Roch Theorem for compact Riemannian surfaces by considering the concrete cases of the Riemann sphere and complex tori.

MC 5403

Thursday, June 8, 2017 — 4:00 PM EDT

**Anthony McCormick, Department of Pure Mathematics, University of Waterloo**

"Physics for Mathematicians"

Thursday, June 8, 2017 — 2:30 PM EDT

**Nickolas Rollick, Department of Pure Mathematics, University of Waterloo**

"Scheming with my associates"

Wednesday, June 7, 2017 — 10:30 AM EDT

**Blake Madill, Department of Pure Mathematics, University of Waterloo**

"Contributions to the Theory of Radicals for Noncommutative Rings"

We consider several radical classes of noncommutative rings. In particular, we provide new results regarding the radical theory of semigroup-graded rings, monomial algebras, and Ore extensions of derivation type.

Tuesday, June 6, 2017 — 3:30 PM EDT

**Michael Deveau, Department of Pure Mathematics, University of Waterloo**

"Effective Bi-interpretability -- Part 2"

We continue exploring the properties of effective bi-interpretability introduced last time. We shall see that two structures being effectively bi-interpetable requires that they have very similar properties in terms of many of the notions discussed thus far.

MC 5403

Tuesday, June 6, 2017 — 2:30 PM EDT

**Anthony McCormick, Department of Pure Mathematics, University of Waterloo**

"Ricci Flow and Renormalization"

Many of us have heard that there is some sort of relationship between Ricci flow and renormalization group flow in QFT. The goal of this talk/discussion will be to try and understand this relationship.

MC 5479

Monday, June 5, 2017 — 1:30 PM EDT

**Pantelis Eleftheriou, University of Konstanz**

"Small sets in dense pairs"

Monday, June 5, 2017 — 10:00 AM EDT

**David Tweedle, The University of the West Indies**

"Artin's conjecture on primitive roots and function field analogues"

Recall Artin's primitive root conjecture, which states that if *a* is not -1 or a square then the reduction of *a* modulo *p* generates the multiplicative group of the integers modulo *p* for infinitely many primes *p*. We will examine the similarities and differences between Artin's conjecture and some natural analogues for elliptic curves and function fields.

MC 5403

Thursday, June 1, 2017 — 2:30 PM EDT

**Anton Mosunov, Department of Pure Mathematics, University of Waterloo**

"Normality and Factoriality"

We will define normal schemes and factorial schemes, see several examples of them, and prove that factoriality of a scheme implies its normality.

MC 5403

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

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