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.