MenuEvents for 03/28/2024 from all calendars
Noncommutative Geometry Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 628
Speaker: Liang Guo, East China Normal University
Title: Hilbert-Hadamard spaces and the equivariant coarse Novikov conjecture
Abstract: The equivariant coarse Novikov conjecture synthesizes all the Novikov-type conjectures, including the strong Novikov conjecture for groups and the coarse Novikov conjecture for metric spaces. In a recent work of Sherry Gong, Jianchao Wu, and Guoliang Yu, a notion of Hilbert-Hadamard space is introduced to study the Novikov conjecture for specific groups. To generalize their idea to the equivariant coarse Novikov conjecture, in this talk, we will study the equivariant coarse Novikov conjecture for a dynamic system which admits an equivariant coarse embedding into an admissible Hilbert-Hadamard space. This is joint work with Qin Wang, Jianchao Wu, and Guoliang Yu.
Departmental Colloquia
Time: 4:00PM - 5:00PM
Location: BLOC 117
Speaker: Persi Diaconis, Stanford University
Title: Hyperplane walks
Abstract: Picture a collection of hyperplanes in d-dimensional Euclidean space. These divided space into chambers (points not on any of the hyperplanes) and faces (points on some hyperplanes). The geometry and combinatorics of such arrangements is a world of its own, with applications in topology,algebraic geometry and every kind of algebra. I'll supplement this by introducing a simple family of random walks on the chambers. These include classical walks (Ehrenfest urn, card shuffling, dynamic storage allocation) but also lots of fresh examples(walks on parking functions!). Strangely, in more or less complete generality, there is a complete theory (all eigenvalues of the associated transition operators and sharp rates of convergence to stationarity--known). Naturally, there are open problems-- Understanding the stationary distribution of these walks involves the classical problem of sampling from an urn without replacement in various guises and there is a lot we don't know. I'll try to explain all this to a non-specialist audience.
