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Xiao Zhong, Department of Pure Mathematics, University of Waterloo

"Capacity Theory, equilibrium distribution and potential functions"

This is a continuation of the series of talks from the last semester.  This talk will basically follow Chapter 6 of Baker-Rumely's Book: "Potential Theory and Dynamics on the Berkovich Projective Line". We will introduce the Capacity Theory and equilibrium distribution. Then we will study the potential function attached to the equilibrium distribution.

MC 5417

Uri Bader, The Weizmann Institute

"Cohomology of Arithmetic Groups, Higher Property T and Spectral Gap"

Groups of matrices with integer entries, aka arithmetic groups, are prominent objects of mathematics. From a geometric point of view, they appear as the fundamental groups of locally symmetric space. Topological invariants of such spaces could be seen as group invariants and vice versa. In my talk I will relate this useful link between topology and arithmetics with the theory of unitary representations. More precisely, I will focus on the cohomology of arithmetic groups with unitary coefficients, presenting a recent joint work with Roman Sauer which completely clarifies the theory in small degrees. By the end of the talk I will discuss the relation of the above with the phenomenon of spectral gap and state various related conjectures. I will make an effort to present the subject to a general audience.

MC 5501

Adi Glücksam, Northwestern University

"Multi-fractal spectrum of planar harmonic measure"

In this talk, I will define various notions of the multi-fractal spectrum of harmonic measures and discuss finer features of the relationship between them and properties of the corresponding conformal maps. Furthermore, I will describe the role of multifractal formalism and dynamics in the universal counterparts. This talk is based on a joint work with I. Binder.

MC 5501

Lawrence Mouillé, Syracuse University

"Positive intermediate Ricci curvature with maximal symmetry rank"

The Grove-Searle Maximal Symmetry Rank Theorem (MSRT) is a foundational result in the study of manifolds with positive sectional curvature and large isometry groups. It provides a classification of closed, positively curved manifolds that admit isometric actions by tori of large rank. In this talk, I will present progress towards extending the MSRT to positive intermediate Ricci curvature, a condition that interpolates between positive sectional curvature and positive Ricci curvature. Grove and Searle were able to employ concavity of distance functions to establish their MSRT, but this feature is not available for positive intermediate Ricci curvature. I will discuss how we can overcome this barrier using a strengthening of Wilking's Connectedness Lemma. A portion of this talk is from joint work with Lee Kennard.

MC 5417

Organisational Meeting

We will discuss the format of the seminar and determine the first set of speakers. If you would like to speak or otherwise participate in the meeting and are unable to attend, please contact AJ Fong.

MC 5417

An organizational meeting for the Differential Geometry Working Seminar will be held at 2:30pm on January 9, 2024.

M3 4206

Niclas Technau, Max Plank Institute

"Counting Rational Points Near Manifolds"

Choose your favourite, compact manifold M. How many rational points, with denominator of bounded size, are near M? We report on joint work with Damaris Schindler and Rajula Srivastava addressing this question. Our new method reveals an intriguing interplay between number theory, harmonic analysis, and homogeneous dynamics.

MC 5501

Jesse Peterson, Vanderbilt University

"Amenability and von Neumann algebras"

Amenability for groups is a notion that was first introduced by von Neumann in 1929 in order to provide a conceptual explanation for the Banach-Tarski paradox. The notion has since been exported to many different areas of mathematics and continues to hold a distinguished position in fields such as group theory, ergodic theory, and operator algebras. For von Neumann algebras the notion plays a fundamental role, with the classification of amenable von Neumann algebras by Connes and Haagerup being considered a touchstone of the area. In this talk, I will give a survey of amenability and von Neumann algebras, emphasizing my own contributions related to von Neumann algebras associated with lattices in Lie groups.

MC 5501

Lucas Mason-Brown, University of Oxford

"Unitary representations of semisimple Lie groups and conical symplectic singularities"

One of the most fundamental unsolved problems in representation theory is to classify the set of irreducible unitary representations of a semisimple Lie group. In this talk, I will define a class of such representations coming from filtered quantizations of certain graded Poisson varieties. The representations I construct are expected to form the "building blocks" of all unitary representations.

MC 5501

We will be streaming the last two lectures of Alain Connes’ Lecture Series titled “From rings of operators to noncommutative geometry” given at the Fields Institute. The lecture series details the origin and impact of non-commutative geometry to various areas in mathematics and will end with recent advances in the program of the operator theoretic approach to the Riemann Hypothesis. Everyone is welcome to join us for a joint viewing experience. For more information and the Zoom link for the first part of the Lecture Series see: http://www.fields.utoronto.ca/activities/23-24/Alain-Connes

MC 5479