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 COVID19 Information website for information on our response to the pandemic.
Please note: The University of Waterloo is closed for all events until further notice.
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Andrej Vukovic, Department of Pure Mathematics, University of Waterloo
"Homotopy Type Theory and Univalent Foundations"
An organizational meeting for the Model Theory Seminar will be held on Thursday, September 6 at 3:30 pm in MC 5403.
Andrew Nicas, McMaster University
"Metric transforms yielding Gromov hyperbolic spaces"
Tyrone Ghaswala, University of Manitoba
"Amalgamated free products of circularly ordered groups"
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
John Dykes, Department of Pure Mathematics, University of Waterloo
"Homotopy Type Theory and Univalent Foundations: Lecture 2"
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
Tyrone Ghaswala, University of Manitoba
"Mapping class groups, coverings, braids and groupoids"
Given a finitesheeted, 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 BirmanHilden theorem, the Burau representation and new embeddings of the braid group in mapping class groups.
Eli Shamovich, Department of Pure Mathematics, University of Waterloo
"Fixed points of selfmaps of the free ball"
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
Tristan Freiberg, Department of Pure Mathematics, University of Waterloo
"Biases in the distribution of primes in intervals"
Gurbir Dhillon, Stanford University
"Double cosets, character formulas, and the Virasoro algebra"
Eli Shamovich, Department of Pure Mathematics, University of Waterloo
"Topologies and the DifferenceDifferential Operator"
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 Homfunctors. 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.
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
Christopher Hawthorne, Department of Pure Mathematics, University of Waterloo
"Pseudofinite sets and dimensions, Part 1"
We take a first look at the pseudofinite setting. We recall some basics of ultraproducts; we see how cardinality and counting measures can be lifted to the pseudofinite setting; and we use this machinery to give pseudofinite versions of the Szemerédi regularity lemma.
McMaster University, Hamilton Hall, Room 401
Yulan Qing, University of Toronto
"Loops with Large Twist Get Short Along Quasigeodesics in Out(F_n)"
Robert T.W. Martin, University of Cape Town
"(Multivariable) Operator Theory, (Noncommutative) Function Theory and the Free Hardy space"
Simon Crawford, Department of Pure Mathematics, University of Waterloo
"Deformations of Quantum Kleinian Singularities"
Eli Shamovich, Department of Pure Mathematics, University of Waterloo
"Analytic nc functions"
In this talk, we will discuss higherorder 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 multilinear coefficients, the socalled TaylorTaylor series.
MC 5479
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
Adam Humeniuk, Department of Pure Mathematics, University of Waterloo
"A Primer on Topological Data Analysis"
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 MartinLof type theory in a homotopytheoretic 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
Rémi 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}.
Jesse Kass, University of South Carolina
"How to count lines on a cubic surface arithmetically"
Douglas Farenick, University of Regina
"Lowdimensional operator systems, equivalence, and free convexity"
Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca