Student Seminar
Speaker: Samiun Ali Molla, IIT Bombay
Host: Suman Kumar Sahoo
Title: Free Boundary methods and scattering phenomena
Time, day and date: 2:00:00 PM – 3:00:00 PM, Wednesday, April 15
Venue: Ramanujan Hall
Abstract: We study Schrödinger-type equations with potentials supported in a bounded domain and investigate the existence of nontrivial solutions. The problem is reformulated as a free boundary problem, allowing the use of tools such as unique continuation and approximation techniques. We present the main existence results and highlight the connection with free boundary theory. This talk is based on one of fundamental result of Mikko Salo and Henrik Shahgholian.

Mathematics Colloquium
Speaker: Kévin Le Balc'h, Jacques-Louis Lions Laboratory, Sorbonne Université à Paris
Host: Debanjana Mitra
Title: Control of the Heat Equation
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, April 15
Venue: Ramanujan Hall
Abstract: The study of controllability and observability for the heat equation is a central topic in the control theory of parabolic partial differential equations, at the crossroads of spectral analysis, functional analysis, and geometry. This talk presents an overview of null-controllability for the heat equation, beginning with the seminal work of Fattorini and Russell (1971), who established the one-dimensional case via moment methods, and continuing with the multidimensional breakthroughs of Lebeau–Robbiano and Fursikov–Imanuvilov (1995–1996), which rely on Carleman estimates to obtain observability from arbitrary nonempty open subsets. Building on these foundational results, I will discuss more recent developments concerning the characterization of the reachable space for the controlled heat equation, as well as the minimal size or “dimension” of observable sets.