Events

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

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

Kieran Mastel, University of Waterloo

Analysis Seminar: 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

Ababacar Sadikhe Djité, Université Cheikh Anta Diop de Dankar & University of Waterloo

Shape Stability of a quadrature surface problem in infinite Riemannian manifolds

In this talk, we revisit a quadrature surface problem in shape optimization. With tools from infinite-dimensional Riemannian geometry, we give simple control over how an optimal shape can be characterized. The framework of the infinite-dimensional Riemannian manifold is essential in the control of optimal geometric shape. The covariant derivative plays a key role in calculating and analyzing the qualitative properties of the shape hessian. Control only depends on the mean curvature of the domain, which is a minimum or a critical point. In the two-dimensional case, Gauss-Bonnet's theorem gives a control within the framework of the algorithm for the minimum.

MC 5417