Edgar Shaghoulian- University of Pennsylvania

Abstract- TBD

Matt Kennedy- University of Waterloo

Since the work of von Neumann, the theory of operator algebras has been inextricably linked to the theory of groups. On the one hand, operator algebras constructed from groups provide an important source of examples and insight. On the other hand, many problems about the groups are most naturally studied within an operator-algebraic framework. In this talk I will give an overview of some problems relating the structure of a group to the structure of a corresponding operator algebra, and describe some recent developments.

Shi-Zhuo Looi, University of Kentucky

In this talk, I will give a survey of recent and upcoming results on various linear, semilinear and quasilinear wave equations on a wide class of dynamical spacetimes in various even and odd spatial dimensions. These results include asymptotics for a wide range of nonlinearities. For many of these results, the spacetimes under consideration have only weak asymptotic flatness conditions and are allowed to be large perturbations of the Minkowski spacetime, provided that an integrated local energy decay estimate holds. We explain the dichotomy between even- and odd-dimensional wave behaviour. Part of this work is joint with Mihai Tohaneanu and Jared Wunsch.

Romain Tessera- Institut de Mathematiques de Jussieu-Paris Rive Gauche

Geometric group theory considers finitely generated groups as metric objects, and classically studies them up to quasi-isometries. This line of research has led to impressive classification results, notably for lattices in semi-simple Lie groups. Beyond quasi-isometries, another natural family of maps is formed by coarse embeddings. For instance, subgroup inclusion is a coarse embedding. These maps also arise in pseudo-Riemannian geometry: for example, Gromov observed in the eighties that the isometry group of a closed Lorentz (n+1)-manifold coarsely embeds into the real hyperbolic space of dimension n. In this talk, I will expose recent developments in the study of coarse embeddings, comprising the following result: an amenable group coarsely embeds in a hyperbolic group if and only if it is virtually nilpotent.

Christy Hazel, UCLA

Given a space X we can consider the configuration space of n distinct points from X. When X is a Euclidean space, the singular (co)homology of these configuration spaces has rich structure. If we instead consider configurations of points in G-representations where G is a finite group, then the configuration space inherits an action of the group G. We can thus investigate the structure of the equivariant (co)homology of these configuration spaces. In this talk we’ll review some of the classical computations by Arnold and Cohen to compute the singular cohomology, and then discuss new techniques used to compute the Bredon G-equivariant cohomology computations. This is joint work with Dan Dugger.

Lili He- Johns Hopkins University

Abstract- TBA

Charles Gale- McGill University

Abstract- TBD

Mark Trodden- University of Pennsylvania

Abstract- TBD

Frans Pretorius- Princeton University

Abstract- TBD