Events for 11/04/2020 from all calendars

Groups and Dynamics Seminar

Time: 12:00PM - 1:00PM

Location: online

Speaker: George Willis, The University of Newcastle, Australia

Title: Scale Groups

Abstract: Scale groups are closed, vertex-transitive groups of automorphisms of a regular tree that fix an end of the tree. These concrete groups emerge from the structure theory of abstract totally disconnected, locally compact groups. There is also a very close correspondence between scale groups and closed self-replicating groups, which are groups of automorphisms of a rooted tree. The role of scale groups in the study of general totally disconnected, locally compact groups and their connection with self-replicating groups will be explained in the talk.

Noncommutative Geometry Seminar

Time: 1:00PM - 2:00PM

Location: Zoom 942810031

Speaker: Rudy Rodsphon, Northeastern University

Title: A KK-theoretical perspective on quantization commutes with reduction

Abstract: We propose a reframing of Paradan--Vergne's approach to the quantization commutes with reduction problem in KK-theory, more especially the index theoretic part that leads to their "Witten non-abelian localization formula". While our method is similar to theirs at least in spirit, interesting conceptual simplifications occur, and it makes the relationship to Ma--Tian--Zhang's analytic methods quite apparent. Time permitting, I'll also sketch another possible way to derive this localization formula, which is purely functorial.

URL: Event link

Probability Seminar

Time: 2:00PM - 3:00PM

Location: Zoom

Speaker: Maria Gordina, University of Connecticut

Title: Ergodicity for Langevin dynamics with singular potential

Abstract: We discuss Langevin dynamics of N particles on R^d interacting through a singular repulsive potential, such as the Lennard-Jones potential, and show that the system converges to the unique invariant Gibbs measure exponentially fast in a weighted Sobolev norm. The proof relies on an explicit construction of a Lyapunov function using a modified Gamma calculus. In contrast to previous results for such systems, our results imply geometric convergence to equilibrium starting from an essentially optimal family of initial distributions. This is based on the joint work with F. Baudoin and D. Herzog.

Topology Seminar

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Sanjay Kumar, Michigan State University

Title: Fundamental shadow links realized as links in the 3-sphere

Abstract: In this talk, I will discuss two conjectures which relate quantum topology and hyperbolic geometry. Chen and Yang conjectured that the asymptotics of the Turaev-Viro invariants determine the hyperbolic volume of the 3-manifold, and Andersen, Masbaum, and Ueno (AMU) conjectured for a surface that the asymptotics of the quantum representations reflect certain geometric properties of the mapping class group. For a manifold M(f) constructed as the mapping tori of an element f in the mapping class group, Detcherry and Kalfagianni showed that M(f) satisfying the Turaev-Viro invariant volume conjecture implies that f satisfies the AMU conjecture. Using techniques from Turaev's shadow theory, I construct infinite families of links in the 3-sphere with complement homeomorphic to the complement of fundamental shadow links which are a class of links in connected sums of S^2 times S^1 that satisfy the Turaev-Viro invariant volume conjecture. Through homeomorphisms, these link complements in S^3 can be realized as the mapping tori for explicit elements in the mapping class group providing families that satisfy the AMU conjecture. Video recording is available at https://tamu.zoom.us/rec/share/NVDt4tmOzD6DyGdOfO8XTjBCMBG0d_BK4grFJPN35hrSa7b-N_0rD1MS_OfLEOWK.OV72bu9Mc4g3cwyL (Access Password: 13TuT+XF)

Student/Postdoc Working Geometry Seminar

Time: 11:00PM - 12:00PM

Location: zoom

Speaker: R. Geng, TAMU

Title: The variety of commuting matrices and geometric rank