Program Title:  Advances in High Dimensional Statistical Learning Conference
Date: 15-16 Dec 2024
Venue: Ramanujan Hall, Department of Mathematics
Program Brochure: Attached
Program Webpage: Under Construction

Thesis Defence
Speaker: PMS Sai Krishna (IIT Bombay)
Title: Exponential maps and their applications
Time, day and date: 11:30:00 AM - 12:39:00 PM, Monday, December 16
Venue: Room 216

Abstract
Exponential maps of k-domains generalize locally nilpotent derivations, and they coincide when k is of zero characteristic. They have proven to be a useful tool in approaching problems in Affine Algebraic Geometry. In the first part of the talk, we will look at some results related to locally nilpotent derivations. Next, we introduce exponential maps and define some related invariants, using which we give an algebraic characterization of the affine plane and affine three-space. The second part of the talk will be about some results related to the rigidity and triangularity of exponential maps. The last part of the talk will be about the rigidity problem, which is about the existence of a non-trivial exponential map of a k-domain. We will see some results related to the rigidity of the ring of invariants of an exponential map, and we provide a sufficient condition under which the ring of invariants of an exponential map of k^[3] is k^[2].