Events

Jack Jia, University of Waterloo

Categories of representations of groups are well-behaved: They are abelian (behave like module categories), symmetric monoidal (have tensor products), every object has a dual and is semi-simple, to name a few. A natural question to ask is whether every category that exhibits similar behaviour is a representation category. Deligne proved a remarkable theorem that shows every symmetric tensor category with some imposed growth condition is in fact a category of representations. Moreover, he constructed some symmetric tensor categories with faster-than-exponential growth-these are so-called Deligne categories, which can be interpreted as complex rank analogs of classical representation categories. In this talk, I will introduce the notion of symmetric tensor categories, state Deligne's Theorem, and construct some of the Deligne categories. 

MC 5403

Mainak Poddar, IISER Pune

Equivaraint principal bundles over toric DM stacks

We extend the classification of torus equivariant framed principal bundles over toric varieties using Tits buildings by Kaveh, Mannon, and Huang to such bundles over toric Deligne-Mumford stacks. A corollary is that any such bundle over a stacky projective line splits. This is a joint work with Chandranandan Gangopadhyay and Ramandeep Singh Arora.

MC 5479

Beining Mu, University of Waterloo

Degree of categoricity and treeable degrees

In this seminar, we will discuss treeable degrees and degree of categoricity. We will introduce past results on which degrees can or cannot be a degree of categoricity and when degrees of categoricity coincide with treeable degrees. We will also introduce a notion of \(\Pi^0_1\) singletons as an example of treeable degrees and their relation to degree of categoricity.

MC 5403

Julius Frizzell, University of Waterloo

Factors of Measure Preserving Systems

We will discuss the basic idea of homomorphisms of measure spaces and measure preserving systems and what it means for a measure preserving system to be a factor of another measure preserving system.

MC 5417

Facundo Camano, University of Waterloo

Classifying ALF Gravitational Instantons of Cyclic Type

I will go over the paper ”Rigidity for Multi-Taub-NUT Metrics” by Vincent Minerbe.

MC 5417

Benoit Charbonneau, University of Waterloo

The Dirac operator on homogeneous manifolds

MC 5417

Joey Lakerdas-Gayle, University of Waterloo

Dominant functions and high sets

We prove Martin's theorem that \(A'\geq_T\emptyset''\) if and only if $A$ computes a function that bounds every total computable function almost everywhere. Then we will begin discussing the infinite injury priority tree construction of Sacks' theorem that there exists a high incomplete c.e. set.

MC 5403

Julius Frizzell, University of Waterloo

Examples of Factors and Conditional expectation

We will discuss examples of factors of measure preserving systems arising from products and skew-products. We will also briefly define regular and separable extensions. We will then introduce the concept of Conditional expectation and prove some of its basic properties.

MC 5417

Joey Lakerdas-Gayle, University of Waterloo

High incomplete c.e. set

We use an infinite injury priority tree construction to prove Sacks' theorem that there exists a high incomplete c.e. set.

MC 5403

Erik Séguin, University of Waterloo

Ulam Stability for Quantum Groups and Noncommutative Dynamics

In this talk, we discuss various "noncommutative" extensions of classical commutative phenomena. We focus on two particular cases of this: representation stability for locally compact quantum groups (extending representation stability for classical locally compact groups) and minimality for C*-dynamical systems (extending minimality for topological flows). In the first part of the talk, we discuss the question of Ulam stability for approximate representations of locally compact quantum groups. We show that compact quantum groups and amenable discrete quantum groups are representation stable. In the process, we establish a partial stability result for general amenable locally compact quantum groups, showing that if one imposes additional constraints on the approximate representation in question then the assumption of compactness or discreteness can be dispensed with. In the second part of the talk, we discuss the notion of minimality for C*-dynamical systems. We show that the accepted definition is somewhat unsatisfactory as an extension of its commutative counterpart from both a topological dynamical and an operator algebraic perspective and present an alternative notion of an extension which rectifies these issues. We demonstrate that this alternate notion also encodes operator algebraic structure which does not appear to have a direct dynamical connection, further motivating its study. We outline various characterizations and extension properties for this notion and discuss its consequences.

MC 2009