Events

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

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

Enric Solé-Farré, University College London

The Hitchin and Einstein indices of cohomogeneity one nearly Kahler manifolds

Nearly Kähler manifolds are Riemannian 6-manifolds admitting real Killing spinors. They are the cross-sections of Riemannian cones with holonomy G2. Like the Einstein equation, the nearly Kähler condition has a variational interpretation in terms of volume functionals, first introduced by Hitchin in 2001.

The existence problem for nearly Kähler manifolds is poorly understood, and the only currently known inhomogeneous examples were found in 2017 by Foscolo and Haskins using cohomogeneity one methods. For one of their examples, we establish non-trivial bounds on the coindex of the Hitchin-type and Einstein functionals. We do this by analysing the eigenvalue problem for the Laplacian on coclosed primitive (1,1)-forms under a cohomogeneity-one symmetry assumption.

MC 5417