Lecture 1: (Commutative Algebra/Algebraic Geometry seminar)

Speaker : Nitin Nitsure

Title: Zariski's Main Theorem

Time, Day, Date, Venue : Monday, 6th Jan, 11:30 am, Ramanujan Hall

Abstract : This lecture will discuss the algebraic formulation, and sketch
its proof by Peskine.

Speaker: Peter Sarnak, IAS Princeton 

Date & Time: Monday, 06 January 2025, 4 pm

Venue: Seminar Room 2, Ground Floor, VMCC

Title: Bass Note Spectra of Locally Uniform Geometries

Abstract: We formulate and report on the problem of the bass note spectrum of an invariant operator as one varies over locally uniform geometries. In the Euclidean setting this recasts classical problems of Mahler from the geometry of numbers in a new light. For certain operators, homogeneous dynamics can be used decisively. In the non-Euclidean setting of hyperbolic manifolds we review some recent developments using the conformal bootstrap method and random covers to study the bass note spectra. We highlight the theme and impact of rigidity.