Deep Learning Methods in Mathematical Physics
Speaker: Prof. Ovidiu Calin, Department of Mathematics & Statistics, Eastern Michigan University
Host: S Baskar
Title: Conservation Laws
Time, day and date: 11:30:00 AM – 12:30:00 PM, Monday, February 23
Venue: Ramanujan Hall
Abstract: This lecture focuses on conservation laws and their role as structural constraints in machine-learning models for dynamical systems. We discuss how conservation principles can be incorporated through soft regularization, hard architectural constraints, and integral formulations. The lecture also explores the identification of conserved quantities via functional invariance and Noether’s theorem, highlighting connections between symmetry, Lagrangian and Hamiltonian formulations, and structure-preserving learning.

Seminar
Speaker: Dr. Sanjay Chaudhuri, Department of Statistics, University of Nebraska-Lincoln, USA
Host: Koushik Saha
Title: On an Empirical Likelihood-Based Solution to the Approximate Bayesian Computation Problem
Time, day and date: 10:00:00 AM - 11:00:00 AM, Tuesday, February 24
Venue: Online (TBA)
Abstract: For many complex models studied in natural, engineering, and environmental sciences, it is nearly impossible to specify a likelihood for the observed data.  Approximate Bayesian Computation (ABC) methods try to estimate such model parameters only by comparing the given observation and some replicates generated from the model for various input parameter values. No explicit relationship between the parameters and the data is postulated.  In this article, we propose an empirical likelihood (EL) based solution to the ABC problem. By construction, our method is based on an interpretable likelihood (i.e., the EL) which is computed using estimating equations completely specified by the observed and the replicated data and a few well-chosen summary statistics.  The proposed method can be justified through information projections on a specified class of densities.  We further show that the posterior is consistent and discuss several of its favourable large sample and large replication properties.  Illustrative examples from various real-life applications will also be presented.        

This work is joint with Subhroshekhar Ghosh and Pham Thi Kim Cuc, all from the National University of Singapore.

Keywords: ABC; Empirical likelihood; Data-dependent estimating equations; Modified empirical likelihood.

Deep Learning Methods in Mathematical Physics
Speaker: Prof. Ovidiu Calin, Department of Mathematics & Statistics, Eastern Michigan University
Host: S Baskar
Title: Hamilton-Jacobi Theory
Time, day and date: 11:30:00 AM – 12:30:00 PM, Tuesday, February 24
Venue: Ramanujan Hall
Abstract: This lecture presents the Hamilton–Jacobi theory from a neural-network perspective. We study how neural networks can be used to solve the Hamilton–Jacobi equation and recover system dynamics, with applications to the eikonal equation and distance computation. The lecture highlights neural-network-based approaches to solving first-order nonlinear PDEs and demonstrates how Riemannian distances and optimal trajectories can be computed in a data-driven framework.

Pre-synopsis
Speaker: Saikat Maji, IIT Bombay
Host: Mayukh Mukherjee
Title: Perturbative Nodal Geometry: Stability of Nodal Sets and Applications to Dumbbells
Time, day and date: 2:00:00 PM – 3:00:00 PM, Tuesday, February 24
Venue: Room 114
Abstract: -

Statistics and Probability seminar
Speaker: Arnab Chowdhury, TIFR Centre For Applicable Mathematics
Host: Parthanil Roy
Title: Invariant Measures of Branching Brownian Motion
Time, day and date: 3:00:00 PM - 4:00:00 PM, Tuesday, February 24
Venue: Room 113
Abstract: We will discuss the fixed points of one-dimensional, binary branching Brownian motion (BBM). The recent work of Chen, Garban, and Shekhar (PTRF, 2023) classified the fixed points of BBM with the critical drift under the assumption that the fixed points have a top particle almost surely. A related result for supercritical drifts was obtained by Kabluchko (J. Appl. Prob., 2012), but under the more restrictive assumption of a locally finite intensity measure. We study the BBM with both critical and supercritical drifts and obtain a complete characterization of the fixed points without any additional assumptions, thereby removing the top particle hypothesis in the critical drift case. (This talk is based on a joint work with Xinxin Chen, Atul Shekhar, and Shuo Zhu.)

APS
Speaker: Prerna Gupta, IIT Bombay
Host: Prachi Mahajan
Title: Geometry and Analysis in Several Complex Variables
Time, day and date: 3:00:00 PM – 4:00:00 PM, Tuesday, Friday 24
Venue: Ramanujan Hall
Abstract: -

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: -

Monge-Ampere equation
Speaker: Sooraj A P, IIT Bombay
Host: Harsha Hutridurga
Title: On the Monge-Ampere equation
Time, day and date: 10:30:00 AM – 11:30:00 AM, Thursday, February 26
Venue: Room 215
Abstract: We shall show the existence and Hölder regularity of classical solutions to the Monge-Ampère equation using tools from elliptic regularity theory.

APS
Speaker: Annu, IIT Bombay
Host: Saurav Bhaumik
Title: Tensor algebra, Symmetric algebra, Alternating algebra
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, February 26
Venue: Room 215
Abstract: -

Deep Learning Methods in Mathematical Physics
Speaker: Prof. Ovidiu Calin, Department of Mathematics & Statistics, Eastern Michigan University
Host: S Baskar
Title: Classical PDEs of Mathematical Physics
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, February 26
Venue: Ramanujan Hall
Abstract: This lecture presents neural-network-based methods for solving classical partial differential equations arising in mathematical physics. We consider elliptic, parabolic, and hyperbolic equations, including Poisson and Dirichlet problems, the heat and Schrödinger equations, and wave equations with various boundary conditions. Neural network solutions are compared with classical analytical solutions, highlighting their effectiveness as flexible solvers and their potential for high-dimensional and complex boundary-value problems.

APS
Speaker: Saibur Alom, IIT Bombay
Host: Manas Rachh
Title: Approximation of Fredholm equations using collectively compact operators
Time, day and date: 1:00:00 PM - 2:00:00 PM, Thursday, February 26
Venue: Ramanujan Hall
Online: https://meet.google.com/yym-cjgs-hhj
Abstract: This presentation focuses on the approximation of operator equations involving compact linear operators on Banach spaces using collectively compact operator sequences. Assuming that A is compact and that I − A is invertible, we analyze approximation schemes based on sequences of collectively compact operators (Aₙ) that converge pointwise to A. Under suitable conditions, we show that the approximate equations ϕₙ − Aₙϕₙ = f are uniquely solvable for sufficiently large n. Moreover, we establish stability results and derive explicit error estimates that describe the convergence of the approximate solutions ϕₙ to the exact solution ϕ.

Pre-Synopsis Seminar
Speaker: Rishi Das, IIT Bombay
Host: Harsha Hutridurga
Title: Mathematical analysis and Numerical methods for multi-physics problems in diffusion and viscoelasticity.
Time, day and date: 2:00:00 PM – 3:00:00 PM, Thursday, February 26
Venue: Ramanujan Hall
Online: https://monash.zoom.us/my/rishidasmeeting33071187?pwd=c8s1VRSlqcsfwT23hIj3P68vSFRMBL.1&omn=89130451355 (ID. 252 917 5562 Passcode: 382315)
Abstract: -

Algebraic groups seminar
Speaker: Shripad M. Garge, IIT Bombay, Mumbai
Title: Basic results on algebraic groups. III
Time, day and date: 4:00:00 PM - 5:30:00 PM, Thursday, February 26
Venue: Room No .215
Abstract: We study root systems, Weyl groups, simple groups, etc. in this talk, culminating in the structure of reductive groups.

APS
Speaker: Swapnamoy Sikder, IIT Bombay
Host: Siuli Mukhopadhyay
Title: Estimation of Model Parameters under Network Structure
Time, day and date: 4:30:00 PM – 5:00:00 PM, Thursday, February 26
Venue: Online https://meet.google.com/qfh-rnny-coi
Abstract: Water quality monitoring systems are increasingly designed as networks of spatially distributed observation units, where responses of one location may be highly influenced by the responses of the neighbouring locations. Thus, to estimate the water quality across locations, one needs not only to consider the dependencies among the locations, but also to reduce the no. of parameters in order to estimate accurately. In this work, two estimation procedures have been discussed to estimate the water quality across this multi-station framework, one using LASSO, and the other using a spatial autoregressive model.

APS
Speaker: Vinay Kumar Sharma, IIT Bombay
Host: Siuli Mukhopadhyay
Title: Spatial Sampling Designs
Time, day and date: 5:00:00 PM - 5:30:00 PM, Thursday, February 26
Venue: Online https://meet.google.com/qfh-rnny-coi
Abstract: In this work, we study how different spatial sampling plans influence the predictor \hat{Y}(x_0) at unsampled locations within a simple kriging framework, assuming all model parameters are known. We examine the theoretical properties of the predictor and investigate its behavior through simulation studies. In particular, we compare the unconditional and conditional predictive distributions and observe distinct patterns under different combinations of sample size n and covariance parameter \theta.

Pre-Synposis
Speaker: Mayukh Choudhury, IIT Bombay
Host: Debraj Das
Title: Asymptotic Theory of Bootstrap in Generalized Linear Models
Time, day and date: 4:00:00 PM – 5:00:00 PM, Friday, February 27
Venue: Ramanujan Hall
Abstract: Generalized Linear Models (GLMs) are central to modern statistical analysis, but classical inference methods often become challenging in the presence of regularization, high dimensionality, and data-driven model selection. This talk develops a unified theoretical framework for Bootstrap-based inference in GLMs addressing structurally regularized models, addressing challenges arising from sparsity, growing dimensionality, cross validated tuning, and low-rank constraints. The first part establishes the validity of Bootstrap methods for Lasso estimators in generalized linear models, where traditional asymptotic approximations fail due to penalization bias. The second part develops high-dimensional distributional approximations of the GLM estimator based on Bootstrap when the dimension may grow exponentially with sample size. The third part provides rigorous asymptotic analysis of usual Lasso estimators tuned via K-fold cross-validation, clarifying the inferential impact of data-dependent penalty selection. The final part extends the theory developed in the first part to the matrix linear model setting. In this part, a valid Bootstrap method is developed for low-rank parameter matrix estimation under nuclear-norm penalization. Together, these results provide theoretical foundations and practical tools for reliable inference in modern high-dimensional statistical models.