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: 11:00:00 AM – 12:00:00 PM, Monday, February 02
Venue: Ramanujan Hall
Abstract: n this seminar, we will introduce a notion of weak solution for the time-harmonic Maxwell's equations. We will demonstarte that the associated weak formulation is well posed. Thereafter we will establish a regularity result proving Holder continuity of solutions.

Liquid Crystals
Speaker: Prof. Apala Majumdar, FRSE, FIMA, Department of Mathematics, University of Manchester, UK
Host: Parthanil Roy
Title: The Mathematics of Liquid Crystals - Theory and Applications
Time, day and date: 12:00:00 PM – 1:00:00 PM, Monday, February 02
Venue: Ramanujan Hall
Online: https://us06web.zoom.us/j/6950684207?pwd=VkNmYzFBd0c0QWx3azhJODJ0QUp1Zz09&omn=83584890072 (Meeting ID: 695 068 4207 Passcode: 802747)
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.

Number theory seminar
Speaker: Devadatta Hegde, School of Mathematics, TIFR, Mumbai
Host: Ravi Raghunathan
Title: Poles and Residues of Eisenstein Series:
Time, day and date: 4:00:00 PM - 5:00:00 PM, Monday, February 02
Venue: Ramanujan Hall
Abstract: Just as the Fourier transform involves the exponential function, the continuous spectrum of automorphic forms is expressed in terms of Eisenstein series. These series are meromorphic functions of one or several complex variables with values in the space of automorphic forms. Two fundamental questions concern the location of their poles and the contribution of their residues to the discrete spectrum. This talk presents our investigation into these problems.

Finite Geometry and Coding Theory Seminar
Speaker: Subrata Manna, IIT Hyderabad
Host: Sudhir R. Ghorpade
Title: Cubic Sections of Hermitian Varieties and Edoukou-Type Conjectures
Time, day and date: 4:00:00 PM - 5:00:00 PM, Monday, February 02
Venue: Online (https://meet.google.com/rpe-qyxv-jvy)
Abstract: Please see the file attached. (https://drive.google.com/open?id=1-WV0anL9Z2VJtgE3i61p6Hnlna8dETRt)

Monge-Ampere equation
Speaker: Sooraj AP, IIT Bombay
Host: Harsha Hutridurga
Title: On the Monge-Ampere equation
Time, day and date: 11:15:00 AM – 12:30:00 PM, Tuesday, February 03
Venue: Room 215
Abstract: We shall talk about some basic properties of the Monge-Ampère measure, and use these to show the uniqueness of solutions to the Dirichlet problem in the Alexandrov weak formulation of the Monge-Ampère equation. We shall also show some stability results for the weak solutions which will play a major role in our study of the existence of Alexandrov solutions.

Number Theory and Random Geometry Seminar
Speaker: Nihar Gargava, Institut de Mathématiques d'Orsay, Université Paris-Saclay,
Host: Sudhir R. Ghorpade
Title: Random lattices that are modules over the ring of integers
Day, Date and Time: Wednesday, 4th February 2026 at 4 pm
Venue: Ramanujan Hall, Dept. of Mathematics
Abstract: We investigate the average number of lattice points within a ball where the lattice is chosen at random from the set of unit determinant ideals or modules lattices of some cyclotomic number field. The goal is to consider the space of such lattices as a probabilistic space and then study the distribution of lattice point counts. This is inspired by the connections of this problem to lattice-based cryptography and sphere packings in a high dimensional Euclidean space. Based on joint work with Vlad Serban, Maryna Viazovska, Ilaria Viglino.

Real Algebraic Geometry and Combinatorial Optimization Seminar
Speaker: Luca Wellmeier, UiT - The Arctic University of Norway
Host: Sudhir R. Ghorpade
Title: Hierarchies in Polynomial Optimization
Day, Date and Time: Wednesday, 4th February 2026 at 5.15 pm
Venue: Ramanujan Hall, Dept. of Mathematics
Abstract: In the first part, we explored polynomial optimization through the lens of the sum-of-squares hierarchy. By relaxing the question of non-negativity of a given polynomial by whether it is a sum-of-squares (SOS) or not, we were able to derive a tractable way for solving polynomial optimization problems: a series of semidefinite convex optimization problems that provide increasingly tight, certified bounds on the true solution. A recap can be found at https://lcwllmr.github.io/momsos/. The second talk will focus on the dual viewpoint. As we will see, the conic dual of the SOS cone is closely related to moment sequences of probability measures. We will end up with a second hierarchy of optimization problems that will turn out to be mostly equivalent to the SOS hierarchy. It allows for new insights into the original problem. As an application we will see how to use the moment perspective to extract concrete minimizers on top of just bounds.

Student Seminar
Speaker: Satya Sai Aditya Duggaraju, IIT Bombay
Host: Suman Kumar Sahoo
Title: A proof of the Kolmogorov Extension theorem
Time, day and date: 2:00:00 PM – 3:00:00 PM, Thursday, February 05
Venue: Room 215 
Abstract: We give a proof of the Kolmogorov's extension theorem and, as an application, derive the Ionescu-Tuleca theorem. The talk only assumes familiarity with basic measure and probability theory.

Commutative Algebra seminar
Speaker: Sayed Sadiqul Islam, IIT Bombay
Host: Tony Puthenpurakal
Title: F^e-modules with applications to D-modules
Time, day and date: 3:00:00 PM - 4:00:00 PM, Thursday, February 05
Venue: Ramanujan Hall
Abstract: In this talk, I will present the theory of F^e-modules, a natural extension of Lyubeznik’s F-module theory using higher powers of the Frobenius map. I will discuss a recent result by Wenliang Zhang, which extends properties of the Matlis dual of F-finite F-modules to D-submodules of F^e-finite F^e-modules. Finally, I will explain how these results are applied to the Lyubeznik–Yildirim conjecture in mixed characteristic.

IPDF Seminar
Speaker: Arnab Pal, IISc Bangalore
Host: Neela Nataraj
Title: Adaptive Finite Element Methods for PDE-Constrained Optimization: Error Analysis and Quasi-optimality
Time, day and date: 3:30:00 PM - 4:30:00 PM, Thursday, February 05
Venue: Online (https://us06web.zoom.us/j/85975402584?pwd=Aaab5EKV8eZOTYRUbDYjlb235cPw6e.1 Meeting ID: 859 7540 2584 Passcode: 460208)
Abstract: Attached (https://drive.google.com/open?id=1BQoLjghh5bh5g8NUxMZbabilrSB-D78z)

Algebraic groups seminar
Speaker: Dipendra Prasad, IIT Bombay
Host: Shripad Garge
Title: Representations of GL(n, F_q)
Time, day and date: 4:00:00 PM - 5:30:00 PM, Thursday, February 05
Venue: Room 215
Abstract: We will discuss Greeen's work on the complex irreducible representations of the general linear group over a finite field.

Mathematics Colloquium I
Speaker: Frederic Herau, Universite de Nantes
Host: Harsha Hutridurga
Title: What is hypocoercivity?
Time, day and date: 2:15:00 PM – 3:15:00 PM, Friday, February 06
Venue: Ramanujan Hall
Abstract: Twenty years ago, the notion of hypocoercivity appeared into the mathematical community. This neologism stands for time evolving physical systems that have a natural convergence property towards an equilibrium. Beginning with very simple examples, we shall try to present this notion, some parts of its history, some natural applications in statistical and fluid mechanics and, if enough time, some recent developments.

Mathematics Colloquium II
Speaker: Alessandra Sarti, Universite de Poitiers
Host: Harsha Hutridurga
Title: From K3 surfaces to Enriques manifolds
Time, day and date: 3:30:00 PM – 4:30:00 PM, Friday, February 06
Venue: Ramanujan Hall
Abstract: K3 surfaces occuy a remarkable place in the classification of complex algebraic surfaces, the most easy example is the quartic Fermat surface in complex projective three space. Because of their beautiful properties, A. Weil in 1958 named them in honour of the three famous mathematicians Kummer, Kähler and Kodaira and of the K2 mountain in Cachemire. From K3 surfaces one can construct others remarkables algebraic surfaces that are the Enriques surfaces.  After giving several examples and exmplaining basic properties  of K3 and Enriques surfaces, I will show how these notions can be generalized to manifolds in higher dimensions and in particular I will introduce Enriques manifolds. Time permitting I will show recent developpements and in particular I will explain how one can consider all these manifolds in the singular setting.

APS
Speaker: Niladri Sekhar Patra, IIT Bombay
Host: Manoj Kumar Keshari
Title: Descent problem for certificate of non-negativity on semi-algebraic sets.
Time, day and date: 5:15:00 PM – 6:15:00 PM, Monday, February 09
Venue: Ramanujan Hall
Abstract: Let R[X] (resp. Q[X]) denote the polynomial ring in n variables with real (resp. rational) coefficients. Given a finite set S in Q[X], if the quadratic module M generated by S is archimedean in R[X], then we show that the quadratic module M generated by S is Archimedean in Q[X] when Q[X]/Supp(M) is 0 dimensional, giving a partial answer to Powers' question. I will also discuss some result on saturation. This is joint work with M.K. Keshari and Debapriya Ojha.

APS
Speaker: Aratrika Pandey, IIT Bombay
Host: Ravi Raghunathan
Title: Simultaneous Khintchine theorem in local field of positive characteristic
Time, day and date: 11:45:00 AM – 12:45:00 PM, Wednesday, February 11
Venue: Ramanujan Hall
Abstract: In this talk, we focus on the convergence case of Khintchine's theorem for analytic nonplanar manifolds over local fields of positive characteristic, allowing general approximation functions $\psi$ that are not necessarily monotonic. Our approach is based on the method of counting rational points near manifolds developed by Beresnevich and Yang \cite{BY}. To address the scenario in which $\psi$ is not monotonic, we extend the function field by adjoining an appropriate root. Additionally, in the course of the proof, we establish several new results in the geometry of numbers over function fields, which we believe are of independent interest. If time permits, we will also briefly discuss the divergence case, which deals with lower bounds for counting rational points

Student Seminar
Speaker: Aditya Khambete, IIT Bombay
Host: Suman Kumar Sahoo
Title: Dependence modelling using copulas, and the extension to discrete random vectors.
Time, day and date: 2:00:00 PM – 3:00:00 PM, Wednesday, February 11
Venue: Room 215
Abstract: In this talk we will introduce the notion of copulas to model the dependence in multivariate distributions, discuss how the classical notion fails for discrete multivariate distributions, and then use ideas from Geenens (2020) to extend the idea to multivariate discrete distributions.

Mathematics Colloquium
Speaker: Girish Aras, IIT Bombay (Visiting Faculty)
Host: Radhendushka Srivastava
Title: Introduction to Causal Inference
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, February 11
Venue: Ramanujan Hall
Abstract: I will start with a few examples where confounders disrupt classical inference paradigm and motivate why a causal approach is needed. I will review the basic formalism and central ideas of causal inference such as Neyman’s potential outcomes (counterfactuals) and Don Rubin’s foundational assumptions under which causal inference is possible.

The presentation, though rigorous, should be accessible with minimal knowledge of statistics and probability theory.
 

Monge-Ampere equation
Speaker: Sooraj A P, IIT Bombay
Host: Harsha Hutridurga
Title: On the Monge-Ampere equation
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, February 12
Venue: Room 215
Abstract: We shall see a proof of the existence of solutions to the zero-boundary Dirichlet problem for the Alexandrov formulation of the Monge-Ampère equation. Later, we shall look at extensions of this to the case where the boundary data is an arbitrary continuous function.

Commutative algebra seminar
Speaker: Sayed Sadiqul Islam, IIT Bombay
Host: Tony J P
Title: F^e-modules with applications to D-modules-2
Time, day and date: 3:00:00 PM – 4:00:00 PM, Thursday, February 12
Venue: Ramanujan Hall
Abstract: In this talk, I will present the theory of F^e-modules, a natural extension of Lyubeznik’s F-module theory using higher powers of the Frobenius map. I will discuss a recent result by Wenliang Zhang, which extends properties of the Matlis dual of F-finite F modules to D-submodules of F^e-finite F^e-modules. Finally, I will explain how these results are applied to the Lyubeznik–Yildirim conjecture in mixed characteristic.

Algebraic groups seminar
Speaker: Shripad M. Garge, IIT Bombay
Title: Basic results on algebraic groups. I
Time, day and date: 4:00:00 PM - 5:30:00 PM, Thursday, February 12
Venue: Room No .215
Abstract: We begin with the first chapter of Digne-Michel, Representations of finite groups of Lie type.

Deep Learning Methods in Mathematical Physics
Speaker: Prof. Ovidiu Calin, Department of Mathematics & Statistics, Eastern Michigan University
Host: S Baskar
Title: Review of Feed-Forward Neural Networks
Time, day and date: 10:00:00 AM – 11:00:00 AM, Monday, February 16
Venue: Ramanujan Hall
Abstract: This lecture presents an introduction to feed-forward neural networks, emphasizing their mathematical structure and relevance to modern problems in physics. We discuss how neural networks are trained, why they are effec.ve function approximators, and how they can be used to model physical systems governed by differential equations. The lecture serves as a foundation for a lecture series on deep learning methods in mathematical and computational physics