Events for 04/02/2025 from all calendars

Noncommutative Geometry Seminar

Time: 2:00PM - 3:00PM

Location: BLOC 302

Speaker: Jun Yang, Harvard University

Title: The Atiyah-Schmid formula for Jacquet-Langlands correspondence

Abstract: We extend the Atiyah-Schmid formula from semi-simple groups to reductive groups. Based on the extended formula, we show that the dimension over arithmetic groups is an invariant under the Jacquet-Langlands correspondence.

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Ricky Martua Simon Simanjuntak, Indiana University Bloomington

Title: Understanding the Boundary of the Cubic Main Hyperbolic Component

Abstract: Milnor in 2014 outlined a program to understand the boundary of hyperbolic component, with computational evidence indicating in a family with two free critical points, they are not locally connected. We focus on H_3 the cubic main hyperbolic component. Our approach is to use model space X with a homeomorphism \beta: H_3 -> X, compactify X and study the extension property of \beta to navigate the boundary of H_3.
The model space of our choosing is Blaschke product, and the compactification is through measure outlined by McMullen. Our conclusions are the following:
(1) Following Petersen-Tan Lei, divide \partial H_3 into “tame” = multiplier of fixed point in disk, and “wild” = multiplier in circle.
(2) The tame part is homeomorphic to solid torus (in progress).
(3) The wild part is a fractal fibered over Mobius strip, with blow-up at every rational point.
(4) The main parabolic component is contained in the wild part.
We also present a new result in the theory of Blaschke product: complete understanding the topology of parameter space of Blaschke product. This work is under the supervision of Kevin Pilgrim.

Committee P Meeting

Time: 4:00PM - 5:00PM

Location: Blocker Room 117