SATURDAY, APRIL 27, 2024, IUPUI, INDIANAPOLIS, IN
There will be a Colloquium Talk at IUPUI by Keith Burns on Friday 3:30pm, April 26.
Location: LD 229 in the Science Building
(Tea at 3pm in the Math Department Lounge LD 259)
Speakers:
Vitaly Bergelson (OSU)
Keith Burns (Northwestern)
Daniel Mitsutani (UChicago)
Wouter van Limbeek (UIC)
Schedule:
Times below are given in Eastern Time.
10:00-10:30 Registration and Refreshments
10:30-11:20 Vitaly Bergelson
11:30-11:45 Coffee Break
11:45-12:35 Wouter van Limbeek
12:45-2:30 Lunch Break
2:30-3:20 Daniel Mitsutani
3:30-4:00 Coffee Break
4:00-4:50 Keith Burns
5:00 farewells
Parking and Local Info:
Parking is available in the Gateway Garage, 525 N Blackford St.
(enter and we will supply a prepaid ticket to exit)
All activities will take place in the LD building, 402 N. Blackford St.
(entrance directly across from the end of W. Vermont St.)
Talks are in LD 136.
Registration and Refreshments are in Math Faculty Lounge LD 259.
Organizers:
Lvzhou Chen (Purdue)
Marlies Gerber (IUB)
Bruce Kitchens (IUPUI)
Nick Salter (Notre Dame)
Support:
This GGD workshop is funded with the support of the IU Mathematics Journal, IUPUI and its School of Science.
Titles and Abstracts
Vitaly Bergelson
Title: The Prime Number Theorem via Ergodic Theory
Abstract: We will discuss a new type of ergodic theorem which has among its corollaries numerous classical results from multiplicative number theory, including the Prime Number Theorem, a theorem of Pillai-Selberg and a theorem of Erdős-Delange. This ergodic approach leads to a new dynamical framework for a general form of Sarnak’s Möbius disjointness conjecture which focuses on the "joint independence" of actions of (N,+) and (N,×).
The talk is based on joint work with Florian Richter.
Keith Burns
Title: The effect of Ricci flow on surfaces with no conjugate points
Abstract: This talk will describe joint work with Solly Coles and Dong Chen. We want to show that it is possible for conjugate points to appear when a surface with no conjugate points evolves under Ricci flow. This gives a negative answer to a question asked by Manning in a 2004 paper.
Daniel Mitsutani
Title: Symmetries of Geodesic Flows on covers and rigidity
Abstract: An old result of Bochner proves that closed Riemannian manifolds of negative Ricci curvature admit only finitely many isometries. On the other hand, work beginning with Eberlein, and later extended by Farb and Weinberger, shows that rigidity in the presence of too many isometries still occurs provided one looks at covers of a closed manifold of negative sectional curvature to find “hidden symmetries”: Eberlein proves that a closed Riemannian manifold of negative sectional curvatures admitting infinitely many isometries of its universal cover must be locally symmetric.
From the dynamical perspective, hyperbolic dynamical systems also display such a phenomenon: if the centralizer group of a hyperbolic dynamical system is too large often it is conjugate to an algebraic one. In this talk we will consider hidden symmetries of the hyperbolic dynamical system given by the geodesic flow of a manifold of negative sectional curvatures. We will introduce an appropriate notion of a centralizer for the geodesic flow on the universal cover, and prove that when it is not discrete the metric must be locally symmetric.
Wouter van Limbeek
Title: Rigidity of commensurators and its applications
Abstract: I will discuss a question raised independently by Greenberg and Shalom: Can an infinite discrete subgroup of a simple Lie group have dense commensurator and not be a lattice? I will explain the surprising connections between this question and other long-standing open problems, and discuss recent progress on special cases of the question. This is joint work with (subsets of) Brody, Fisher, and Mj.