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.

Topology seminar
Speaker: Bittu Singh, IIT Bombay
Host: Rekha Santhanam
Title: Rational Homotopy theory
Time, day and date: 11:45:00 AM – 1:00:00 PM, Thursday, April 16
Venue: Room 215
Abstract: Dennis Sullivan introduced a framework in which the rational homotopy type of a topological space is encoded by commutative differential graded algebras (CDGAs). Earlier, Daniel Quillen established an equivalence between the rational homotopy category and an algebraic category, although this equivalence arises through a sequence of intermediate categorical constructions. In their paper "On PL De Rham Theory and Rational Homotopy Type", A. K. Bousfield and Victor K. A. M. Guggenheim gave a precise formulation of Sullivan's equivalence using the language of model category theory.

In this talk, we outline this approach and discuss the relationship between topological spaces and CDGAs in rational homotopy theory.

Commutative algebra seminar
Speaker: Aditya Diwedi, IIT Bombay
Host: Tony Puthenpurakal
Title: Deformation of F-injectivity and other F-singularities
Time, day and date: 3:00:00 PM – 4:00:00 PM, Thursday, April 16
Venue: Ramanujan Hall
Abstract: In positive characteristic, the question of whether F-singularities deform remains a central problem. While the deformation of F-injectivity is known in special cases, it remains open in general. This problem is particularly interesting due to its implications for local cohomology.

It is well-known that F-injectivity deforms if the ring is Cohen-Macaulay, a result later generalized by Horiuchi, Miller, and Shimomoto to generalized Cohen-Macaulay rings. In this talk, we present the work of Ma and Quy on F-full and F-anti-nilpotent singularities. We prove that F-injectivity deforms for these classes of rings, providing a generalisation to Horiuchi,Miller and Shimomoto's work.

Algebraic groups seminar
Speaker: Patrick Polo, IIT Bombay, Mumbai
Host: Shripad Garge
Title: Harish-Chandra series (cont.) and Deligne-Lusztig induction
Time, day and date: 4:00:00 PM - 5:30:00 PM, Wednesday, April 16
Venue: Room No .215
Abstract: We complete the chapter on HC induction by proving that the HC series form a partition of the irreducible representations. This shows the importance of cuspidal representations. We then define Deligne-Lusztig induction, which allows to get a large number of cuspidal representations as we will see in the next lectures.

Seminar
Speaker: Dr Hariom Sharma, IIT Bombay
Host: Dipendra Prasad
Title: Global Jacquet-Langlands Correspondence
Time, day and date: 5:30:00 PM – 6:45:00 PM, Thursday, April 16
Venue: Room 105
Abstract: In this talk, we discuss the work of Alexandru Ioan Bădulescu on the extension of the Jacquet–Langlands correspondence to a broader setting. We begin with a brief overview of the classical local correspondence between representations of general linear groups and their inner forms. We then present its generalization to all irreducible unitary representations. The main focus of the talk is the global Jacquet–Langlands correspondence in characteristic zero, which establishes a precise relationship between automorphic representations of GL(n) and those of its inner forms. As important consequences of this correspondence, we obtain the multiplicity one and strong multiplicity one theorems for inner forms of GL(n).

Graphicality of prime gap graphs
Speaker: Ms. Annesha Das, IIT Bombay
Host: Keshav Aggarwal
Title: An explicit upper bound for logarithmic derivative of zeta at negative real part
Time, day and date: 5:30:00 PM – 6:00:00 PM, Thursday, April 16
Venue: Room 113
Abstract: We present an explicit bound of logarithmic strength for the logarithmic derivative of the Riemann zeta function at negative real part.

Graphicality of prime gap graphs
Speaker: Mr. Divye Goyal, IIT Bombay
Host: Keshav Aggarwal
Title: Bounds towards the first moment of Large prime gaps
Time, day and date: 6:00:00 PM – 6:30:00 PM, Thursday, April 16
Venue: Room 113
Abstract: We do not expect the gaps between primes to be too big. Therefore, the first moment of large prime gaps is expected to be small. Using asymptotic expansion of the Chebyshev function, the problem is transformed into bounding an integral. We present the bounds on this integral.

Algebraic groups seminar
Speaker: Patrick Polo, IIT Bombay, Mumbai
Host: Shripad Garge
Title: Galois cohomology and/of algebraic groups
Time, day and date: 11:00:00 AM - 12:30:00 PM, Friday, April 17
Venue: Room No .215
Abstract: This will be an informal discussion around Galois cohomology and algebraic groups. This is meant especially for students. They will be allowed to ask questions on the topic and get their doubts cleared which will help them follow the seminar on "Finite Groups of Lie Type".