Events

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 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.

Eli Shamovich, Department of Pure Mathematics, University of Waterloo

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

Christian Rosendal, University of Illinois at Chicago

"Geometries of topological groups"

Gurbir Dhillon, Stanford University

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

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 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

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