Topology and Related Topics Seminar
Speaker: Omkar Ramdas, IIT Bombay
Host: Rekha Santhanam
Title: An introduction to Lawvere theory and their applications
Time, day and date: 11:00:00 AM – 12:00:00 PM, Friday, October 31
Venue: Room 105
Abstract: Lawvere theory is a unique categorical framework which unifies the ideas of algebraic structures like groups, rings, etc into one category using their "logical signatures". I am planning to give two talks on this.
In this first talk, I'll cover the logical prerequisites needed and then we'll go on to define what Lawvere theories are. This talk will be very basic and accessible to all.

Analysis seminar
Speaker: Prof. S. Thangavelu
Host: Sanjoy Pusti
Title: On Hardy's inequality for fractional powers of the sublaplacian
Time, day and date: 4:00:00 PM – 5:15:00 PM, Friday, October 31
Venue: Ramanujan Hall
Abstract: In these lectures we plan to give an introduction to Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group. We will recall the case of the standard Laplacian on $ \R^n $ and give a proof of Hardy's inequality for $ (-Delta)^s $ using extension problem and trace Hardy inequality. We will then develop necessary background for studying the modified extension problem for the sublaplacian, establish an analogue of trace Hardy inequality and deduce Hardy's inequality.