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.

Student APS
Speaker: Pradyumna Poduri, IIT Bombay
Host: S. Krishnan
Title: On 4PC related matrices of complete bipartite graphs
Time, day and date: 10:00:00 AM – 10:40:00 AM, Monday, February 16
Venue: Room 113 
Online: https://meet.google.com/hui-ztpc-khr 
Abstract: In this presentation,  we focus on the $2$-Steiner distance matrix  of the complete bipartite graph $K_{m,n}$. This is  a matrix whose rows and columns are indexed by a 2-sized subset of vertices. The entry indexed by a row 2-sized subset and column 2-sized subset is the minimum number of edges in a connected subgraph that contains the union of the vertices in the row 2-sized subset and the column 2-sized subset.   For $K_{m,n}$, we get a complete set of eigenvectors and eigenvalues of its 2-Steiner distance. Along the way, we consider the $\Max$, $\Min$ and $\Mid$ matrices of $K_{m,n}$ and determine a complete set of eigenvectors for these matrices. We outline a common procedure for generating these eigenbasis. 

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

Student APS
Speaker: Kaushik Khamari, IIT Bombay
Host: Ananthnarayan Hariharan
Title: Intermediate extensions of the S_2-ification and connectedness
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, February 16
Venue: Ramanujan Hall
Abstract: In 1994, Hochster and Huneke defined the S_2-ification of a noetherian local ring and established its relation with a connectedness condition on the spectrum. 
In this talk, we will define certain intermediate extensions of the S_2-ification and present a generalization of their connectedness result

Deep Learning Methods in Mathematical Physics
Speaker: Prof. Ovidiu Calin, Department of Mathematics & Statistics, Eastern Michigan University
Host: S Baskar
Title: Deep Learning for Solving Equations
Time, day and date: 11:30:00 AM – 12:30:00 PM, Monday, February 17
Venue: Ramanujan Hall
Abstract: This lecture presents how deep learning can be used to solve a broad class of mathematical equations, including algebraic, functional, integral, and differential equations. We discuss neural-network-based formulations for direct and inverse problems, illustrate solution strategies for ordinary and partial differential equations, and highlight modern techniques such as multiphase resolution and equation discovery. The lecture emphasizes how neural networks provide a unified framework for solving diverse equation types arising in applied mathematics and physics.
The details of the lectures in this series are given in the following PDF document:
https://drive.google.com/file/d/1MyJ-QN_VswUaRcuaztPdG2TgWbvXybhW/view?usp=sharing

Student APS
Speaker: Bhawani Singh, IIT Bombay
Host: Sutanu Roy
Title: Different Perspectives of Quantum Graphs
Time, day and date: 4:00:00 PM – 5:00:00 PM, Tuesday, February 17
Venue: Ramanujan Hall
Abstract: In this talk, I will discuss two approaches of Quantum Graphs. First, I will present the definition via an operator on (L^2(B,ψ)), where B is a finite dimensional C*-algebra and ψ is a faithful state. I will then introduce the operator bimodule formulation. The main objective is to show that these two definitions are equivalent in the tracial case, and that with mild additional assumptions the equivalence is also holds for general faithful state.

Student APS
Speaker: Omkar Ramdas, IIT Bombay
Host: Niranjan Balachandran
Time, day and date: 11:00:00 AM - 12:00:00 PM, Wednesday, February 18
Venue: Room 105
Title: Extremal properties of permutations
Abstract: This talk will broadly be divided into two parts. In the first part, I'll define some special families of permutations and we'll see some optimal bounds on the sizes of such families. In the second part, I'll define what caged sequences are, for any given permutation and we'll see their asymptotic properties.

Student APS
Speaker: Swapan Jana, IIT Bombay
Host: Sourav Pal
Title: ANDOˆ ’S DILATION AND BOHR-THEORETIC ASPECTS OF THE MULTIVARIATE VON NEUMANN INEQUALITY FOR BANACH SPACE OPERATORS
Time, day and date: 12:00:00 PM – 1:00:00 PM, Wednesday, February 18
Venue: Room 105
Abstract: The celebrated Bela Sz.-Nagy dilation theorem states that every contraction ´ T on a Hilbert space H dilates to an isometry and the minimal isometric dilation space is uniquely determined (up to unitary equivalence) by H ⊕2 `2(DT ), which equals H ⊕2 `2(H ) if T is a strict contraction. In 1963, Ando proved that a commuting pair of contractions on a Hilbert space ˆ H dilates to a commuting pair of isometries on H ⊕2 `2(H ⊕2 H ⊕2 H ⊕2 H ). We show that a commuting pair of strict contractions on a Hilbert space H admits an isometric dilation on H ⊕2 `2(H ⊕2 H ). Moreover, we prove that H ⊕2 `2(H ⊕2 H ) is a minimal isometric dilation space, which shows that minimal isometric dilation space is independent of the choice of the commuting pair of strict contractions on the underlying Hilbert space. An immediate application of our construction is that we extend this mechanism to construct an isometric dilation of a commuting pair of strict contractions on a Banach space. This part is based on a joint work with Prof. Sourav Pal. For c ∈ C n (n ≥ 1), let Gc be the collection of tuples (T1,...,Tn) of Banach space operators satisfying kTik ≤ |ci | for 1 ≤ i ≤ n. Using a multidimensional analogue of Bohr’s theorem, we show that the closed polydisk D n (R) is a spectral set for Gc if and only if c ∈ B(D n (R)), the Bohr zone of D n (R). In contract to the one-variable case, we prove that D n (R) is not a minimal spectral set of Gc for any c ∈ B(D n (R)) when n ≥ 2. This part is based on an ongoing joint work with Prof. Sourav Pal and Dr. Himadri Halder.

Student APS
Speaker: Shivani, IIT Bombay
Host: Neela Nataraj
Title: Discontinuous Galerkin finite element methods for linear and semilinear fourth-order problems in smectic liquid crystals
Time, day and date: 2:00:00 PM – 3:00:00 PM, Wednesday, February 18
Venue: Ramanujan Hall
Abstract: In this talk, we will discuss the analysis and numerical approximation of a regular solution to a semilinear fourth-order partial differential equation defined on a polygonal domain, modelling the density variation of Smectic-A liquid crystals. First, we will discuss the discontinuous Galerkin finite element method for the corresponding linear problem. Building upon this, we will discuss the analysis of the semilinear fourth-order problem. For the nonlinear model, we establish existence, local uniqueness, and optimal order error estimates in the energy norm under the assumption that the exact solution $u\in H^{2+\alpha}(\Omega)$ with $\alpha>0$. Numerical experiments validating the theoretical results will also be presented.

Special Session
Speaker: Madhusudan Manjunath, IIT Bombay
Title: Mathematics for Well-Being
Time, day and date: 4:00:00 PM - 5:15:00 PM, Wednesday, February 18
Venue: Ramanujan Hall
Abstract: We ask fundamental questions concerning Mathematics and its potential for Well-being. Taking guidance from an ancient school of Indian philosophy, we sketch candidate answers to these questions. The talk assumes no special background in either Mathematics or Philosophy.

Student Seminar
Speaker: Om Milind Joglekar, IIT Bombay
Host: Suman Kumar Sahoo
Title: Perron-Frobenius Theory: Matrices & Graphs
Time, day and date: 5:30:00 PM – 6:30:00 PM, Wednesday, February 18
Venue: Ramanujan Hall
Abstract: This talk examines the Perron-Frobenius theorem, focusing on the existence of a strictly positive eigenvector and the spectral consequences of irreducibility. We will specifically connect these analytic properties to graph-theoretic concepts like connectivity and cycle periodicity.

Student APS
Speaker: Pradip Roy, IIT Bombay
Host: Keshav Aggarwal
Title: Weyl bound for GL(2) in t-aspect via a trivial delta method.
Time, day and date: 11:00:00 AM – 11:45:00 AM, Thursday, February 19
Venue: Ramanujan Hall
Abstract: We use a trivial delta method to prove the weyl bound in t - aspect for the L-function of a hecke holomorphic (or Maass) cusp form of arbitrary level and nebentypus  and also we use voronoi summation formula, Poisson summation formula and stationary phase analysis.

Monge-Ampere equation
Speaker: Sooraj AP, IIT Bombay
Host: Harsha Hutridurga
Title: On the Monge-Ampere equation
Time, day and date: 11:00:00 AM – 12:00:00 PM, Thursday, February 19
Venue: Room 215
Abstract: We shall show C^1 regularity in 2D for solutions to the weak formulation of the Dirichlet problem for the Monge-Ampère equation when the initial data is locally essentially bounded. Along the way, we shall derive a dichotomy between the existence of regular solutions and the propagation of singularities along an entire line segment. The contents of this lecture are not reliant on that of the previous one.

Student APS
Speaker: Garima Khetawat, IIT Bombay
Host: Niranjan Balachandran
Title: A purely entropic approach to the rainbow triangle problem.
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, February 19
Venue: Room 113
Abstract: In this talk, we will discuss a proof that in a 3-edge colored simple graph with R red edges, B blue edges and G green edges, the number of rainbow triangles is at most \sqrt{2RGB}. This proof, given by Ting-Wei Chao and Hung-Hsun Hans Yu (2024), is different from other entropic proofs in the sense that in other proofs, entropy does not play a central role after all the terms are expressed in terms of probability of certain events. But this proof remains in the realm of the entropy method throughout.

Deep Learning Methods in Mathematical Physics
Speaker: Prof. Ovidiu Calin, Department of Mathematics & Statistics, Eastern Michigan University
Host: S Baskar
Title: Lagrangian Systems
Time, day and date: 12:00:00 PM – 1:00:00 PM, Thursday, February 19
Venue: Ramanujan Hall
Abstract: This lecture introduces Lagrangian systems from the perspective of neural-network-based modeling. We study classical variational systems such as the harmonic oscillator, catenary, brachistochrone, simple pendulum, and Euler’s elastica, and show how their dynamics can be learned and reproduced using neural networks. The lecture highlights the connection between variational principles, trajectory optimization, and modern data-driven approaches to classical mechanics.

Commutative Algebra seminar
Speaker: Prof. R. V. Gurjar, TIFR Bombay *Retd.)
Host: Tony Puthenpurakal
Title: Singularities of plane curves
Time, day and date: 3:00:00 PM - 4:00:00 PM, Thursday, February 19
Venue: Ramanujan Hall
Abstract: We will consider reduced power series f(X,Y) over an algebraically closed field k of characteristic 0. Following topics about R=k[[X,Y]]/(f) will be discussed.
Algebraicity results of Artin, Hironaka-Rossi, Samuel, Basic intersection theory of place curves, Conductor ideal, Value semi-group of R, Gorenstein's result, Dedekind's Conductor Formula, Jung's formula connecting the Milnor number and conductor, Applications of Dedekind's formula. We will give Abhyankar's proofs of Dedekind and Gorenstein results. If time permits, Abhyankar-Moh result about generators of the value semi-group will be discussed. 

Algebraic groups seminar
Speaker: Shripad M. Garge, IIT Bombay
Title: Basic results on Algebraic Groups. II
Time, day and date: 4:00:00 PM - 5:30:00 PM, Thursday, February 19
Venue: Room No .215
Abstract: We discussed the basics of linear algebraic groups in the first lecture and reached the notion of reductive groups. In this lecture, we will see the structure theory of reductive groups.

Deep Learning Methods in Mathematical Physics
Speaker: Prof. Ovidiu Calin, Department of Mathematics & Statistics, Eastern Michigan University
Host: S. Baskar
Title: Hamiltonian Systems
Time, day and date: 11:30:00 AM - 12:30:00 PM, Friday, February 20
Venue: Ramanujan Hall
Abstract: This lecture focuses on Hamiltonian systems and their formulation within the Hamiltonian framework. We study classical examples such as the harmonic oscillator, the simple pendulum, and charged particle motion in a magnetic field, and show how neural networks can be used to learn and reproduce Hamiltonian dynamics. Special attention is given to canonical transformations and generating functions, highlighting their role in structure-preserving, data-driven modeling of physical systems.

APS
Speaker: Sourav Khatua, IIT Bombay
Host: Sutanu Roy
Title: On path spaces of quantum graphs
Time, day and date: 4:15:00 PM – 5:15:00 PM, Friday, February 20
Venue: Ramanujan Hall
Abstract: Let (B,\psi_B, A) be a quantum graph, where B is a finite-dimensional C*-algebra equipped with a faithful state \psi_B and A is a quantum adjacency matrix. Using the notion of quantum edge correspondences, we construct path spaces of arbitrary length as C*-correspondences over B. We show that these path spaces form a sub-product system over the center Z(B). Furthermore, we prove that when two quantum graphs are classically isomorphic, then there is a correspondence isomorphism between the respective sub-product systems.

APS
Speaker: Lekha Das, IIT Bombay
Host: Rekha Santhanam
Title: Model Category Structures on an n-Cube.
Time, day and date: 4:30:00 PM – 5:30:00 PM, Friday, February 20
Venue: Room 215
Abstract: In this talk we are going to discuss the model category structures on an n-cube using the notion of 'proto-centers' of weak equivalence classes introduced by Droz and Zakharevich(2021). We also try to give an enumeration of model structures on 4-cube having only one 'non-trivial' weak equivalence class.

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.