Events for 01/24/2022 from all calendars

Colloquium - Wanlin Li

Time: 11:30AM - 12:30PM

Location: ZOOM

Speaker: Wanlin Li, CRM-ISM

Description:
Title: Algebraic/Arithmetic properties of curves and Galois cohomology
Abstract: A lot of the algebraic and arithmetic information of a curve is contained in its interaction with the Galois group. This draws inspiration from topology, where given a family of curves over a base B, the fundamental group of B acts on the cohomology of the fiber. As an arithmetic analogue, given an algebraic curve C defined over a non-algebraically closed field K, the absolute Galois group of K acts on the etale cohomology of the geometric fiber and this action gives rise to various Galois cohomology classes. In this talk, we discuss how to use these classes to detect algebraic/arithmetic properties of the curve, such as the rational points (following Grothendieck's section conjecture), whether the curve is hyperelliptic, and the set of ``supersingular'' primes.

Colloquium - Nataliya Goncharuk

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Nataliya Goncharuk, University of Toronto, Canada

Description:
Title: Complex rotation numbers and renormalization
Abstract: The complex rotation number (suggested by V.Arnold) is an invariant related to the dynamics of an analytic circle diffeomorphism f. Complex rotation numbers give rise to a nice fractal set ``bubbles'' analogous to classical Arnold's tongues.
I will give a survey on complex rotation numbers and list open problems. Also, I will explain how the renormalization operator makes the ``bubbles'' self-similar and controls their sizes.