Lecture series on algebraic stacks

Monday, 06 Nov 2023, 11:30 am

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Host: Sudarshan Gurjar

Venue: Ramanujan Hall

Speaker: Nitin Nitsure

Title: Schematic loci of algebraic spaces.

Abstract: Michael Artin showed that any algebraic space has a unique largest open subscheme which is dense in it. In this talk, we will give a proof. The ingredients of the proof are of even more general interest: the chief one is Grothendieck's form of Zariski's main theorem. The other inputs are the Grothendieck-Gabriel quotient theorem and a typical use of generic points of schemes. The lecture will focus on conceptual explanations, relegating the detailed proof to notes in the form of a handout for the participants.

Geometric analysis seminar

Monday 6 Nov, 2023, 5:30 - 6:30 pm

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Host: Saikat Mazumdar

Venue: Ramanujan Hall, Zoom meet, Link TBA

Speaker: Ayush Khaitan

Affiliation: Rutgers University

Title: Conformal Geometry and Ricci flow 

Abstract: We study a surprising duality between conformal geometry and Ricci flow. Using a classical construction called the Fefferman-Graham ambient space, we construct an infinite family of fully nonlinear analogs of Perelman's F and W functionals and study their monotonicity under several natural conditions.