Kathryn Mann (Cornell)

Math & Stats Department Colloquium

Friday, February 9th, 2023

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Kathryn Mann (Cornell)

Title: Anosov flows on 3-manifolds

Abstract: Anosov flows are a beautiful class of dynamical systems, generalizing and including geodesic flows on manifolds of negative curvature. These systems exhibit "local chaos but global stability" - individual orbits diverge wildly, but the systems as a whole are stable under perturbation. This stability means there is some hope to classify them by discrete, algebraic invariants. Even on 3-dimensional spaces, this is an interesting and challenging problem. In this talk, I will describe some of the history and motivation for classification (dating back to work of Anosov, Smale and others in the 60s), connections with low-dimensional geometric topology, and will describe recent joint work with Barthelmé, Bowden, Frankel and Fenley (in various combinations) answering one thread of the classification problem in dimension 3.

Bio: Professor Kathryn Mann received her PhD from the University of Chicago in 2014, she then held positions at MSRI, UC Berkeley, the Institut de math´ematiques de Jussieu and Brown University. In 2019, she joined Cornell University where she is now an Associate Professor and Rosevear Faculty Leadership Fellow. Prof. Mann was an invited speaker at the 2022 ICM, she also received a Sloan Fellowship, an NSF Career Award, the AWM-Birman Research Prize in Topology and Geometry, the Kamil Duszenko Award and the Mary Ellen Rudin young researcher award.