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.