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Annie Lafrance, University of Waterloo

Introduction to p-approximation property for locally compact groups

We will introduce the p-approximation property and show that if G has the p-approximation property, then the algebra of convoluters is the algebra of pseudomeasures.

MC 5403

Spiro Karigiannis, University of Waterloo

Organizational Meeting

We will plan out the DG working seminar for the May to August summer period. The plan is to have two talks per week, from 1:00pm to 2:15pm and from 2:30pm to 3:34pm.

MC 5403

Elizabeth Cai, University of Waterloo

Mirror Symmetry Seminar: Isomorphism Between Small Analytical Neighborhoods of Points on (n − s − 1)-dim Stratum, Open Ball and Affine Toric Variety

In Batryrev's construction on dual polyhedra and mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties, when he introduces regularity conditions for hypersurfaces, he proposes a theory implied by the definition of ∆-regular, in which sugguests that there exists an analytical isomorphism from small analytical neighbourhoods of points on a (n − s − 1)-dimensional stratum Zf,σ ⊂ Zf,Σ to products of a (s − 1)-dimensional open ball and a small analytical neighbourhood of the point pσ on the (n − s)-dimensional affine toric variety Aσ,N(σ). This theory and its corollaries help obtain a simultanious resolution of all members of the family F(∆). 

MC 2017

Soham Chakraborty, École Normale Supérieure

Measured groupoids and the Choquet-Deny property

A countable discrete group is called Choquet-Deny if for every non-degenerate probability measure on the group, the corresponding space of bounded harmonic functions is trivial. Recently a complete characterization of Choquet-Deny groups was obtained by Frisch, Hartman, Tamuz and Ferdowsi. In this talk, we will look at the extension of the Choquet-Deny property to the framework of discrete measured groupoids. Our main result gives a complete characterisation of this property in terms of the associated measured equivalence relation and the isotropy groups of the groupoid. This talk is based on a joint work with Tey Berendschot, Milan Donvil, Mario Klisse and Se-Jin Kim.

MC 5417 or Join on Zoom

Jashan Bal, University of Waterloo

Veech's theorem

We present Veech's theorem which states that for every nontrivial locally compact group there exists a compact Hausdorff space on which it acts continuously and freely. As a consequence, we obtain that no nontrivial locally compact group is extremely amenable.

MC 5403

Kieran Mastel, University of Waterloo

The weighted algebra approach to constraint system games

Entanglement allows for correlations between spatially separated experiments that are not possible classically. One way to study the computational power of entanglement is via nonlocal games. I will discuss my recent works with Eric Culf and William Slofstra on constraint system games. Different types of perfect entangled strategies for these games can be understood as representations of the algebra of the underlying constraint system. The weighted algebra formalism, introduced by Slofstra and me, extends this to non-perfect strategies. Using this formalism we can show that classical reductions between constraint systems are sound against quantum provers, which allows us to prove the RE-completeness of some constraint system games and to show that MIP* admits two prover perfect zero knowledge proofs.

MC 5417

Kira Bruschke, University of Watelroo, Centre for Career Development

Career Decision

The Career Talks seminar series aims to provide valuable advice and guidance for current graduate students. In this final seminar, a career advisor from the Centre for Career Development will provide a framework for career-decision making and resources for identifying career options.

MC 5417

Aleksa Vujicic, University of Waterloo

The Spine of a Fourier Algebra

Given a locally compact group G, one can define the Fourier and Fourier-Stieltjes algebras A(G) and B(G), which in the abelian case, are isomorphic to L1(G^) and M(G^) respectively. The Fourier algebra A(G) is typically more tractable than B(G), and often easier to describe. A notable exception is when B(G) = A(G), which occurs precisely when G is compact.
The spine of a Fourier Algebra A*(G), introduced by M. Ilie and N. Spronk, is a subalgebra of B(G) which contains all A(H)∘η  where η : G → H is a continuous homomorphism.
It has been shown that for G = Qp ⋊ Op*, that B(G) = A*(G), despite not being compact.
We also explore G = Qp^2 ⋊ Op*, where we have shown that although B(G) is strictly larger than A*(G), they are close to being similar.

MC 5417

Joey Lakerdas-Gayle, University of Waterloo

Infinitary Continuous Logic II

We will prove a continuous analog of Scott's Isomorphism Theorem using the Scott analysis for metric structures developed by Ben Yaacov, Doucha, Nies, and Tsankov.

MC 5479

Rahim Moosa, University of Waterloo

Model theory and the birational geometry of algebraic vector fields

I will try to illustrate how and why model theory (itself a branch of mathematical logic) can sometimes have something to say about algebraic geometry. I will focus on some results of mine (along with Jim Freitag and Remi Jaoui), from the last few years, on the birational geometry of algebraic vector fields.

MC 5479