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Texas A&M University
Mathematics

Events for 01/16/2019 from all calendars

Noncommutative Geometry Seminar

iCal  iCal

Time: 2:00PM - 3:00PM

Location: BLOC 628

Speaker: Jianchao Wu, Pennsylvania State University

Title: The Novikov conjecture, the group of volume preserving diffeomorphisms, and Hilbert-Hadamard spaces

Abstract: The Novikov conjecture is a central problem in manifold topology. Noncommutative geometry provides a potent approach to tackle this conjecture. Using C*-algebraic and K-theoretic tools, we prove that the Novikov conjecture holds for any discrete group admitting an isometric and metrically proper action on an admissible Hilbert-Hadamard space, which is an infinite-dimensional analogue of complete simply connected nonpositively curved Riemannian manifolds. In particular, these groups include geometrically discrete subgroups of the group of volume preserving diffeomorphisms of a compact smooth manifold with a fixed volume form. This is joint work with Sherry Gong and Guoliang Yu.


Colloquium - Florent Baudier

iCal  iCal

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Florent Baudier, Texas A&M University

Description:
Title: Faithful embeddability of metric spaces and graphs into Banach spaces.
Abstract: Faithful embeddability of metric spaces into Banach spaces is pivotal to research areas as diverse as: -the design of approximation algorithms in theoretical computer science (sparsest cut problem, multi-commodity flows, approximate nearest neighbor search, sketching...), -topology (Novikov conjecture), -noncommutative geometry (coarse Baum-Connes conjecture), -geometric group theory (Von Neumann's amenability, Gromov's program). This non-exhaustive list can be stretched at will since metric spaces, with a wide variety of features, arise in nearly all areas of mathematics. In this talk, I will focus on bi-Lipschitz and coarse embeddings of graphs (finite and infinite) into Banach spaces with some desirable geometric properties. I will discuss fundamental geometric problems of either local or asymptotic nature, in particular purely metric characterizations of "linear" properties of Banach spaces in the spirit of the Ribe program. One of the main goal of the talk is to present some fundamental ideas and techniques, as well as to convey the geometric intuition behind them.

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