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Colloquium. Academic Year 20-21

Thursdays 4:10pm on Zoom, unless otherwise noted

Colloquium Chair (2020-2021): Doug Hardin



September 17, 2020 (Thursday), 4:10 pm

Quantitative measure equivalence

Romain Tessera, Institut de Mathématiques de Jussieu-Paris
Virtual Talk via Zoom
Zoom Meeting ID: 998 6775 5871
Email mathcolloquium@vanderbilt.edu to request pass code

Measure equivalence is an equivalence relation between countable groups that has been introduced by Gromov. A fundamental instance are lattices in a same locally compact group. According to a famous result of Ornstein Weiss, all countable amenable groups are measure equivalent, meaning that geometry is completely rubbed out by this equivalence relation. Recently a more restrictive notion has been investigated called integrable measure equivalence, where the associated cocycles are assumed to be integrable. By contrast, a lot of surprising rigidity results have been proved: for instance Bowen has shown that the volume growth is invariant under integrable measure equivalence, and Austin proved that nilpotent groups that are integrable measure equivalent have bi-Lipschitz asymptotic cones. I will present a work whose goal is to understand more systematically how the geometry survives through measure equivalence when some (possibly very weak) integrability condition is imposed on the cocycles. We shall put the emphasis on amenable groups, for which we will present new rigidity results, and the first flexibility results known in this context.

September 24, 2020 (Thursday), 11:10 am

Equivariant homotopy commutativity, trees and chicken feet

Constanze Roitheim, University of Kent
Zoom Meeting ID: 998 6775 5871
Email mathcolloquium@vanderbilt.edu to request pass code

Commutativity up to homotopy can be daunting, and it becomes even more difficult to track when group actions get introduced. In the case of a finite group, however, the options for equivariant homotopy commutativity can be encoded using simple combinatorics, and we will show some examples.

*Talk will be offered live at 11:10a and replayed at 4:10pm*

October 1, 2020 (Thursday), 4:10 pm

Ramanujan: A Century Of Inspiration

Bruce C. Berndt, University of Illinois
Zoom Meeting ID: 998 6775 5871
Email mathcolloquium@vanderbilt.edu to request pass code

Srinivasa Ramanujan is perhaps the most enigmatic mathematician in the history of our subject. First, an account of Ramanujan’s life will be given. Second, the history of Ramanujan’s (earlier) notebooks and “lost” notebook will be provided. Third, the speaker will describe how he became fascinated with Ramanujan’s work, beginning with proving a few claims from his notebooks in February, 1974, and then since May, 1977, devoting all of his research efforts to proving the claims in Ramanujan’s earlier notebooks, lost notebook, and published papers. Fourth, some examples from Ramanujan’s notebooks and lost notebook will be given. This lecture will be aimed at a general audience.

October 8, 2020 (Thursday), 4:10 pm

The Navier-Stokes, Euler and Other Related Equations

Edriss S. Titi, Texas A&M University, University of Cambridge, Weizmann Institute of Science
Zoom Meeting ID: 998 6775 5871
Email mathcolloquium@vanderbilt.edu to request pass code

In this talk I will present the most recent advances concerning the questions of global regularity
of solutions to the three-dimensional Navier-Stokes and Euler equations of incompressible fluids. Furthermore, I will also present recent global regularity (and finite time blow-up) results concerning certain three-dimensional geophysical flows, including the three-dimensional viscous (non-viscous) “primitive equations” of oceanic and atmospheric dynamics.

» Past Colloquia