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Colloquium: Dr. Alex Furman
November 5, 2021 @ 2:00 pm - 3:00 pm
This event will be held both online via. Microsoft Teams. To view Dr. Furman’s talk virtually, enter his Online chatroom via. Microsoft Teams— it will open at 2:00pm on Friday, November 5th, 2021.
Hyperbolic manifolds: recent updates on the interplay between geometry and number theory
Dr. Alex Furman
Distinguished Professor of Mathematics
University of Illinois-Chicago
“Hyperbolic manifolds, i.e. Riemannian manifolds of constant sectional curvature -1, are important objects of study in Geometry, Dynamics, Number theory etc. We have a fairly good grasp on these objects in dimensions 2 and 3, but our understanding seems to decrease in higher dimensions.
In the talk I will discuss some ways of constructing hyperbolic manifolds, relation to Number Theory, and Margulis’ arithmeticity criterion, and will conclude with the recent proof by Bader-Fisher-Miller-Stover of a conjecture of McMullen and Reid that hyperbolic manifolds with infinitely many totally geodesic submanifolds of maximal dimension are arithmetic.”