Events

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

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

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

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

Xuemiao Chen, University of Waterloo

The Sphere

I will make a long story regarding the two dimensional sphere.

MC 5403

Joaco Prandi, University of Waterloo

Bounding the Local Dimension of the Convolution of Measures

Let mu be a finite measure on a metric space X. Then the local dimension of the measure mu at the point x in the support of mu is given by

dim_{loc}mu(x)=lim_r ln(B(x,r))}\ln(r)

In a sense, dim_{loc}mu(x) represents how much mass there is around the point x. The bigger the local dimension, the less mass there is. In this talk, we will explore how the local dimension of the convolution of two measures mu and nu can be bounded by the local dimension of one of the measures. This is based on joint work with Kevin Hare.

MC5417

Laura DeMarco, Harvard University

The (algebraic) geometry of the Mandelbrot set

One of the most famous -- and still not fully understood -- objects in mathematics is the Mandelbrot set. By definition, it is the set of complex numbers c for which the recursive sequence defined by x_1 = c and x_{n+1} = (x_n)^2+c is bounded. This set turns out to be rich and complicated and related to many different areas of mathematics. I will present an overview of what's known and what's not known about the Mandelbrot set, and I'll describe recent work that (perhaps surprisingly) employs tools from number theory and algebraic geometry.

MC 5501

Kaleb Domenico Ruscitti, University of Waterloo

Organization Meeting

We will be scheduling talks for the term, please join us!

MC 5403