Events for 04/28/2021 from all calendars

Probability Seminar

Time: 10:30AM - 11:30AM

Location: BLOC 627

Speaker: Pierre Patie, Cornell University

Title: Interweaving relations

Abstract: In this talk, we introduce the concept of interweaving relations as a strengthening of usual intertwining relations between Markov semigroups. We proceed by providing some interesting applications of this new idea which includes the spectral decomposition, the characterization of ergodic constants and hypercontractivity estimates for non-self-adjoint and non-local semigroups. We illustrate these results by presenting several examples that have emerged from the recent literature: discrete-to-continuous interacting particle models, degenerate hypoelliptic Ornstein-Uhlenbeck processes, and diffusion-to-jump Jacobi processes.

Groups and Dynamics Seminar

Time: 12:00PM - 1:00PM

Location: online

Speaker: Andy Zucker, UCSD

Title: Topological Furstenberg boundaries of C*-simple groups.

Abstract: Given a group G, a boundary action of G is an action of G on a compact space which is minimal and strongly proximal. The topological Furstenberg boundary of a group G, denoted \Pi_s(G), is the largest boundary action it admits. It is non-trivial if and only if G is non-amenable. More recently, Kalantar and Kennedy have shown that a countable discrete group G is C*-simple if and only if G acts freely on \Pi_s(G). However, in the setting of abstract topological dynamics, one can ask much more precise questions about the size of \Pi_s(G), even knowing that it is free. At one extreme, perhaps there is a C*-simple group G where \Pi_s(G) is "almost metrizable," i.e. a highly proximal extension of some metrizable boundary action. For other C*-simple groups, perhaps one can find a continuum-sized family of "mutually disjoint" free boundary actions, which in some sense means that \Pi_s(G) is as large as possible. This talk will discuss the open question of whether every C*-simple group falls into the latter category; while the talk will have more questions than answers, we will discuss joint work in progress with Tianyi Zheng giving an affirmative answer for free groups.

Topology Seminar

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Aleksander Doan, Columbia University

Title: The Gopakumar-Vafa finiteness conjecture

Abstract: The Gopakumar-Vafa conjecture concerns the Gromov-Witten invariants of symplectic manifolds of dimension six. The first part of the conjecture, the integrality conjecture, which was proved recently by Ionel and Parker, asserts that the Gromov-Witten invariants can be expressed in terms of simpler, integer invariants called the BPS numbers. The second part of the conjecture, the finiteness conjecture, predicts that only finitely many of the BPS numbers are nonzero for every homology class. In this talk, based on joint work with E. Ionel and T. Walpuski, I will discuss a proof of the second part of conjecture. The proof combines ideas from the theory of pseudo-holomorphic curves, including Ionel and Parker's proof of the integrality conjecture, and methods of geometric measure theory, especially Allard's regularity theorem for currents with bounded mean curvature.