APS
Speaker: Soumyadeb Samanta, IIT Bombay
Host: Bata Krishna Das
Title: Lipschitz Harmonic Functions and Coarse Harmonic Coordinates on Groups
Time, day and date: 11:30:00 AM – 12:30:00 PM, Wednesday, February 25
Venue: Room 215
Abstract: -

APS
Speaker: Siyad Rahman M, IIT Bombay
Host: Neela Nataraj
Title: A mixed finite element method for a fourth-order / second-order Poisson--Fermi interfacial problem
Time, day and date: 1:00:00 PM – 2:00:00 PM, Wednesday, February 25
Venue: Online (https://us06web.zoom.us/j/86267046558?pwd=zAbVSdWqxdEm2usw1ngFnVOoVOQoTk.1 Meeting ID: 862 6704 6558 Passcode: 802747)
Abstract: We study a mixed finite element method for a fourth-order / second-order Poisson-Fermi interface problem arising from the Bazant--Storey--Kornyshev (BSK) theory. The BSK theory leads to an interface problem between the fourth-order and the second-order problem in the interface of solvent and solute region. We formulate the fourth-order equation in mixed form by introducing the electric field and electric displacement field as new independent variables. For the numerical approximation, we employ Raviart--Thomas elements for the vector fields and piecewise polynomial elements for the scalar variables, providing a stable and efficient discretization suitable for the interface problem. We establish the stability and well-posedness of the mixed formulation under suitable assumptions, and derive optimal a priori error estimates. Numerical experiments are presented to confirm the theoretical convergence rates and to demonstrate the robustness of the proposed method with respect to complex geometries.

Deep Learning Methods in Mathematical Physics
Speaker: Prof. Ovidiu Calin, Department of Mathematics & Statistics, Eastern Michigan University
Host: S Baskar
Title: Free-boundary Value Problems
Time, day and date: 3:00:00 PM – 4:00:00 PM, Wednesday, February 25
Venue: Ramanujan Hall
Abstract: This lecture explores the use of neural networks for solving free-boundary value problems, with emphasis on classical examples such as the Stefan problem, the Muskat problem, and the punctured membrane problem. We discuss how neural-network-based methods can handle moving boundaries and unknown interfaces, particularly in situations where analytic solutions are unavailable. The lecture highlights the effectiveness of deep learning for modeling complex free-boundary phenomena arising in physics and applied mathematics.

Mathematics Colloquium
Speaker: Mohan Swaminathan, Tata Institute of Fundamental Research
Host: Ravi Raghunathan
Title: Obstructions to Smoothing Maps from Nodal Curves
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, February 25
Venue: Ramanujan Hall
Abstract: Fix integers g, n, d and consider the space of all degree d maps from smooth projective curves of genus g to projective n-space. A theorem of Gromov and Kontsevich says that, in order to compactify this space, it suffices to allow the domains of our maps to be at-worst-nodal projective curves of arithmetic genus g. After recalling this theorem, I will discuss some results in the converse direction (obtained in joint work with Fatemeh Rezaee), i.e., given a map from a nodal curve, how can we tell if it actually arises as the limit of a sequence of maps from smooth curves?

APS
Speaker: Advaith Nair, IIT Bombay
Host: Saurav Bhaumik
Title: De Rham isomorphism theorem
Time, day and date: 5:15:00 PM – 6:15:00 PM, Wednesday, February 25
Venue: Room 215
Abstract: -