Maxwell's equations
Speaker: Kshitij Sinha, IIT Bombay
Host: Harsha Hutridurga
Title: Time-Harmonic Maxwell's equations - Regularity theory and related topics
Time, day and date: 11:15:00 AM – 12:30:00 PM, Monday, January 19
Venue: Ramanujan Hall
Abstract: -

Thesis Defence
Speaker: Sakshi, IIT Bombay
Host: Sudhir R. Ghorpade
Title: Structure and Symmetries of Affine Cartesian Codes and Constructions of Convolutional Codes
Time, day and date: 2:30:00 PM - 3:30:00 PM, Monday, January 19
Venue: Ramanujan Hall
Abstract: We give a presentation of the PhD thesis which focuses mainly on two topics in algebraic coding theory, namely affine Cartesian codes and convolutional codes. For affine Cartesian codes, we investigate the minimum weight codewords and automorphism groups. For convolutional codes, we develop new constructions of Maximum Distance Profile (MDP).

Book Reading
Speaker: Prof. Chandrashekhar Khare, Dept of Maths, UCLA
Host: S. Krishnan
Title: Chasing a Conjecture
Time, day and date: 3:30:00 PM – 5:00:00 PM, Monday, January 19
Venue: Ramanujan Hall
Abstract: The speaker, Chandrashekhar Khare is a Professor at the Dept of Maths, UCLA and recently authored a book "Chasing a Conjecture" on which he will speak. Excerpts from the book will be read. The event is a public lecture on a Conjecture in Number Theory but does not expect mathematical maturity from the audience.

Pre-synopsis Seminar
Speaker: Chayan Karmakar, IIT Bombay
Host: Ravi Raghunathan
Title: Character Values at Special Elements in Complex Classical Groups
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, January 19
Venue: Room 215
Abstract: -

Stefan Problem
Speaker: Neeraj Rawat, IIT Bombay
Host: Harsha Hutridurga
Title: Stefan problem - A free boundary problem
Time, day and date: 11:15:00 AM – 12:30:00 PM, Tuesday, January 20
Venue: Ramanujan Hall
Abstract: -

Coagulation-Fragmentation equations
Speaker: Ram Gopal Jaiswal, IIT Bombay
Host: Harsha Hutridurga
Title: A first course on the Coagulation-Fragmentation equations.
Time, day and date: 9:30:00 AM – 11:00:00 AM, Wednesday, January 21
Venue: Ramanujan Hall
Abstract: -

Talk
Speaker: Mohmedmunavvar Mubarak Bapu, IIT Kanpur
Host: Debanjana Mitra
Title: Controllability results for two systems of nonlinear partial differential equations
Time, day and date: 2:30:00 PM – 3:30:00 PM, Wednesday, January 21
Venue: Online
Link: https://us06web.zoom.us/j/87110001554?pwd=8Hys9A00FlTb9gmOd1ZfALkwAE120T.1
(Meeting ID: 871 1000 1554 Passcode: 464604)
Abstract: In this talk, we study controllability results for two nonlinear partial differential equation systems. The first one is the Grey–Scott reaction–diffusion system, and the second one is a fourth-order pseudo-parabolic equation with a source term.
For both systems, we first study the null controllability of the corresponding linearized problems. In the case of the Gray–Scott system, the equation is linearized around a positive trajectory. Using Carleman inequalities, we obtain an observability inequality, whichleads to the null controllability of the linearized system. The nonlinear controllability result is then obtained by applying Kakutani’s fixed-point theorem, giving local controllability to a trajectory.
For the pseudo-parabolic equation, we first rewrite the fourth-order equation as a coupled parabolic-elliptic system of second order. We then show that null controllability of the parabolic part is equivalent to null controllability of the original pseudo-parabolic equation. Using Carleman estimates, we obtain the null controllability result for the linear parabolic equation. Finally, the controllability of the nonlinear system is obtained by using the source term method together with the Banach fixed-point theorem.

Mathematics Colloquium
Speaker: Prof. Joachim Rosenthal, University of Zurich, Switzerland
Host: Sudhir R. Ghorpade
Title: The Standardization Process to Post-Quantum Cryptography
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, January 21
Venue: Ramanujan Hall
Abstract: Public key cryptography has been at the center of modern cryptography. It is not only used for the exchange of secret keys but also for the authentication of entities on the Internet, for digital signatures and for the construction of digital currencies.
Until a few years ago most public key systems were based on the hardness of factoring integers or on the hardness of the discrete logarithm problem in an elliptic curve.
With the realization that a quantum computer would make many practically used public key cryptographic systems obsolete it became an important research topic to design public key systems which are expected to be secure even if a powerful quantum computer would exist.
This new area of research is called post-quantum cryptography and there has been in the last couple of years a lot of efforts to come up with new standards to be used in everyday applications.
The lecture will overview the currently used systems and the current ongoing standardization process. We will also explain the underlying mathematical problems.

Commutative Algebra seminar
Speaker: Tony Puthenpurakal, IIT Bombay
Title: Modular invariant theory and Steenrod operators
Time, day and date: 3:00:00 PM - 4:00:00 PM, Thursday, January 2
Venue: Ramanujan Hall
Abstract: We study modular invariant theory. We investigate applications of Steenrod operators on i

Algebraic groups seminar
Speaker: Dipendra Prasad, IIT Bombay
Host: Shripad Garge
Title: Finite Groups of Lie Type
Time, day and date: 4:00:00 PM – 5:00:00 PM, Thursday, January 22
Venue: Room 215
Abstract: General introduction to the whole subject as well as to the seminar series. The seminar will be based on the book "Representations of finite groups of Lie type" by Digne and Michel, 2nd edition (2020).

Liquid Crystals
Speaker: Prof. Apala Majumdar, FRSE, FIMA, Department of Mathematics, University of Manchester, UK
Host: Prof. Neela Nataraj
Title: The Mathematics of Liquid Crystals - Theory and Applications
Time, day and date: 12:00:00 PM – 1:00:00 PM, Friday, January 23
Venue: Ramanujan Hall
Abstract: This mini-course will comprise four lectures on the mathematics of liquid crystals and modelling of liquid crystal applications. Liquid crystals are complex materials that combine fluidity with the ordering of solids and consequently, have fascinating physical, mechanical and rheological properties. Liquid crystals are best known as the working material of choice for the multi-billion dollar display industry. We will give a non-technical introduction to liquid crystals - their history, physics and applications, followed by an overview of the main mathematical theories for liquid crystals. We will conclude the lecture course with examples of mathematical modelling of real-life liquid crystal systems.

Commutative Algebra Seminar
Speaker: Prof J. K. Verma
Host: Tony J P
Title: Lipman's conjecture about adjoints of ideals in regular local rings
Time, day and date: 12:00:00 PM – 1:00:00 PM, Friday, January 23
Venue: Room 215
Abstract: Joseph Lipman introduced adjoints of ideals in regular local rings in 1994 for improving the Briancon-Skoda theorem for integral closure of ideals.
He conjectured that for any ideals I in a regular local ring of dimension $d$ $adj(I^{n+1})= I adj(I^n)$ for all $n\geq s(I)-1$ where $s(I)$ is the dimension of the closed fibre when Spec R is blown at the closed set $V(I).$
There is also the conjecture about subadditivity: adj(IJ)\subset ad(I) adj(J)$ for all ideals in regular local rings. Both these conjectures are open. Howald, Cutkosky-Lipman and Takagi Watanabe proved these in some cases using convex geometry and certain vanishing theorems for sheaf cohomology modules.
I will present a new solution to these conjectures for complete ideals in regular local rings of dimension two, using Zariski's theory of complete ideals, a formula of Hoskin-Deligne and mixed multiplicities of ideals.