## 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

Visit our **COVID-19 Information website** for information on our response to the pandemic.

Please note: The University of Waterloo is closed for all events until further notice.

Friday, September 28, 2018 — 3:00 PM EDT

**Douglas Farenick, University of Regina**

"Low-dimensional operator systems, equivalence, and free convexity"

Friday, September 28, 2018 — 1:30 PM EDT

**Jesse Kass, University of South Carolina**

"How to count lines on a cubic surface arithmetically"

Thursday, September 27, 2018 — 3:30 PM EDT

**Ré****mi**** Jaoui, Department of Pure Mathematics, University of Waterloo**

"Disintegration phenomena for planar algebraic vector fields"

In my talk, I will discuss some disintegration phenomena in the specific case of complex polynomial vector fields on the affine plane \mathbb{A}^2_\mathbb{C}.

Thursday, September 27, 2018 — 3:00 PM EDT

**John Dykes, Department of Pure Mathematics, University of Waterloo**

"Putting the "Homotopy" in Homotopy Type Theory"

In this week's meeting of the Homotopy Type Theory Seminar, we begin by reviewing path induction. We then interpret Martin-Lof type theory in a homotopy-theoretic manner, viewing types as higher groupoids and functions as functors. We also discuss in detail how the notion of a homotopy between paths is related to identity types. Those who did not attend previous meetings are still encouraged to come!

MC 5413

Wednesday, September 26, 2018 — 4:30 PM EDT

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

"A Primer on Topological Data Analysis"

Wednesday, September 26, 2018 — 3:30 PM EDT

**Ross Willard, Department of Pure Mathematics, University of Waterloo**

"Stone duality revisited: hom functors"

Let B be a Boolean algebra and X a Stone space. Today I’ll show how Hom(B,2) naturally has the structure of a Stone space and Hom(X,2) naturally has the structure of a Boolean space. In particular, Hom(Hom(B,2),2) is isomorphic to B.

MC 5403

Wednesday, September 26, 2018 — 2:00 PM EDT

**Eli Shamovich, Department of Pure Mathematics, University of Waterloo**

"Analytic nc functions"

In this talk, we will discuss higher-order nc functions and in particular, derivatives of arbitrary order. We will show that every locally bounded nc functions is analytic and can locally be expressed as “power series" with multi-linear coefficients, the so-called Taylor-Taylor series.

MC 5479

Tuesday, September 25, 2018 — 2:30 PM EDT

**Simon Crawford, Department of Pure Mathematics, University of Waterloo**

"Deformations of Quantum Kleinian Singularities"

Friday, September 21, 2018 — 3:00 PM EDT

**Robert T.W. Martin, University of Cape Town**

"(Multi-variable) Operator Theory, (Non-commutative) Function Theory and the Free Hardy space"

Friday, September 21, 2018 — 1:30 PM EDT

**Yulan Qing, University of Toronto**

"Loops with Large Twist Get Short Along Quasi-geodesics in Out(F_n)"

Thursday, September 20, 2018 — 3:30 PM EDT

**Christopher Hawthorne, Department of Pure Mathematics, University of Waterloo**

"Pseudo-finite sets and dimensions, Part 1"

We take a first look at the pseudo-finite setting. We recall some basics of ultraproducts; we see how cardinality and counting measures can be lifted to the pseudo-finite setting; and we use this machinery to give pseudo-finite versions of the Szemerédi regularity lemma.

McMaster University, Hamilton Hall, Room 401

Thursday, September 20, 2018 — 3:00 PM EDT

**Andrej Vukovic, Department of Pure Mathematics, University of Waterloo**

"Recursion and Induction"

In this week's meeting of the Homotopy Type Theory Seminar, we begin with a review of dependent types. We discuss certain examples of types that arise "in nature" and introduce recursion and path induction. We also examine propositional logic from the point of view of homotopy type theory. Those who did not attend previous meetings are still encouraged to come!

MC 5413

Wednesday, September 19, 2018 — 3:30 PM EDT

**Ross Willard, Department of Pure Mathematics, University of Waterloo**

"Stone duality revisited"

Last winter the seminar included some lectures on Boolean algebras and Stone duality. In this introductory lecture to the fall term I will quickly summarize that presentation of Stone duality, and then show how to recast it using Hom-functors. This will prepare us for future lectures in which a reasonably general context for building dualities between certain categories of algebras and categories of structured topological spaces will be explored.

Wednesday, September 19, 2018 — 2:00 PM EDT

**Eli Shamovich, Department of Pure Mathematics, University of Waterloo**

"Topologies and the Difference-Differential Operator"

Tuesday, September 18, 2018 — 2:30 PM EDT

**Gurbir Dhillon, Stanford University**

"Double cosets, character formulas, and the Virasoro algebra"

Tuesday, September 18, 2018 — 1:30 PM EDT

**Tristan Freiberg, Department of Pure Mathematics, University of Waterloo**

"Biases in the distribution of primes in intervals"

Monday, September 17, 2018 — 4:00 PM EDT

**Christian Rosendal, University of Illinois at Chicago**

"Geometries of topological groups"

We will discuss how topological groups (of which Banach spaces are a particular example) come equipped with inherent geometries at both the large and small scale. In the context of Banach spaces, the ensuing study is part of geometric nonlinear analysis and we shall present various results and fundamental concepts dealing both with Banach spaces and more general topological groups appearing in analysis, dynamics and topology.

MC 5501

Friday, September 14, 2018 — 3:00 PM EDT

**Eli Shamovich, Department of Pure Mathematics, University of Waterloo**

"Fixed points of self-maps of the free ball"

Friday, September 14, 2018 — 1:30 PM EDT

**Tyrone Ghaswala, University of Manitoba**

"Mapping class groups, coverings, braids and groupoids"

Given a finite-sheeted, possibly branched covering space between surfaces, it's natural to ask how the mapping class group of the covering surface relates to the mapping class group of the base surface. In this talk, we will take a journey through this question for surfaces with boundary. It will feature appearances from the fundamental groupoid, the Birman-Hilden theorem, the Burau representation and new embeddings of the braid group in mapping class groups.

Thursday, September 13, 2018 — 3:30 PM EDT

**Levon Haykazyan, Department of Pure Mathematics, University of Waterloo**

"Sheaves of Structures and Positive Model Theory"

Can we relax the assumptions on Łoś's theorem if we only care about positive formulas? The answer to this question will lead us to rediscover sheaves of structures and generalised ultraproducts.

MC 5403

Thursday, September 13, 2018 — 3:00 PM EDT

**John Dykes, Department of Pure Mathematics, University of Waterloo**

"Homotopy Type Theory and Univalent Foundations: Lecture 2"

Wednesday, September 12, 2018 — 2:00 PM EDT

**Eli Shamovich, Department of Pure Mathematics, University of Waterloo**

"Background and basics"

The study of free analysis --- a quantized version of complex analysis was initiated by Taylor and Voiculescu. Free analysis is the study of functions of several noncommuting complex variables. This is the introductory talk of the seminar. I will cover the origins of free analysis in the works of Taylor and Voiculescu. We will define noncommutative (nc) sets and functions and provide basic examples.

MC 5479

Tuesday, September 11, 2018 — 2:30 PM EDT

**Tyrone Ghaswala, University of Manitoba**

"Amalgamated free products of circularly ordered groups"

Friday, September 7, 2018 — 1:30 PM EDT

**Andrew Nicas, McMaster University**

"Metric transforms yielding Gromov hyperbolic spaces"

Thursday, September 6, 2018 — 3:30 PM EDT

An organizational meeting for the Model Theory Seminar will be held on Thursday, September 6 at 3:30 pm in 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