Seminar
Speaker: Chandan Bhaumik, IIT Bombay
Host: Manoj Keshari
Title: Computations in the Steinberg group
Time, day and date: 11:30:00 AM – 12:30:00 PM, Wednesday, April 01
Venue: Ramanujan Hall
Abstract: The Steinberg symbol {-,-} is a fundamental tool for studying the K_2 group. In this talk, I will discuss some computational approaches to computing the Steinberg symbol. If A is a finite field or if A is the ring of integers modulo a power of an odd prime, I will show that all Steinberg symbols are trivial in K_2(A).

Talk
Speaker: Sooraj A P, IIT Bombay
Host: Harsha Hutridurga
Title: Topics in Optimal Transportation
Time, day and date: 2:30:00 PM – 3:30:00 PM, Wednesday, April 01
Venue: Room 105
Abstract: This talk will be an introduction to the Optimal transportation problem and some of its formulations. We shall see some basic motivating examples and, if time permits, sufficient conditions for existence of solutions to these problems.

Commutative Algebra seminar
Speaker: Kaushik Khamari, IIT Bombay
Host: Tony Puthenpurakal
Title: On Cohen-Macaulay Property of Affine Semigroup Rings
Time, day and date: 3:00:00 PM - 4:00:00 PM, Thursday, April 02
Venue: Ramanujan Hall
Abstract: In this talk, we discuss the Cohen-Macaulay property of affine semigroup rings. In the process, we describe the relationship between local cohomology modules of these rings and the homology of certain simplicial complexes. As an application, we present a proof of Hochster's Theorem, which asserts that normal semigroup rings are Cohen-Macaulay. We follow the paper of N.V. Trung and L.T. Hoa, "Affine Semigroups and Cohen-Macaulay Rings generated by monomials.

Algebraic groups seminar
Speaker: Patrick Polo, IIT Bombay
Host: Shripad Garge
Title: Properties of Harish Chandra induction and restriction
Time, day and date: 4:00:00 PM - 5:30:00 PM, Thursday, April 02
Venue: Room No .215
Abstract: We will explain how properties like transitivity of induction and Mackey formula rely on structural properties of parabolic subgroups and their unipotent radicals.

Statistics Seminar
Speaker: Savita Pareek, Post doctoral fellow MIT Sloan
Host: Siuli Mukhopadhyay
Title: Semiparametric Dynamic Copula Models using Rolling-window Portfolio Optimization
Time, day and date: 4:30:00 PM – 5:30:00 PM, Thursday, April 02
Venue: Ramanujan Hall
Abstract: The mean-variance portfolio model, based on the risk-return trade-off for optimal asset allocation, remains fundamental in portfolio optimization. However, its reliance on restrictive assumptions about asset return distributions limits its applicability to real-world data. Parametric copula structures provide a novel way to overcome these limitations by accounting for asymmetry, heavy tails, and time-varying dependencies. Existing methods have been shown to rely on fixed or static dependence structures, thus overlooking the dynamic nature of the financial market. 
In this study, a semiparametric model is proposed that combines nonparametrically estimated copulas with parametrically estimated marginals to allow all parameters to dynamically evolve over time. A novel framework was developed that integrates time-varying dependence modelling with flexible empirical beta-copula structures. Marginal distributions were modeled using the skewed generalized t-family. This effectively captures asymmetry and heavy tails and makes the model suitable for predictive inferences in real-world scenarios. Furthermore, the model was applied to rolling windows of financial returns from the USA, India, and Hong Kong economies to understand the influence of dynamic market conditions. The approach addresses the limitations of models that rely on parametric assumptions. By accounting for asymmetry, heavy tails, and cross-correlated asset prices, the proposed method offers a robust solution to optimize diverse portfolios in an interconnected financial market. Through adaptive modeling, it allows for better management of risk and return across varying economic conditions, leading to more efficient asset allocation and improved portfolio performance.

Student Seminar
Speaker: Rajendra Meena, IIT Bombay
Host: Suman Kumar Sahoo
Title: The Brahmagupta-Pell Equation: Solutions and Structure
Time, day and date: 5:35:00 PM – 6:35:00 PM, Thursday, April 02
Venue: Ramanujan Hall
Abstract: The Brahmagupta–Pell equation x 2 − dy2 = 1, where d is a non-square integer, is a classical Diophantine equation that has fascinated mathematicians for centuries due to its simple form yet surprisingly rich structure. A natural question is whether such an equation admits non-trivial integer solutions, and if so, how one can describe all of them. In this talk, we address these questions by proving the existence of non-trivial solutions and introducing the notion of a fundamental solution, from which all other solutions can be generated. We also describe all solutions explicitly and briefly discuss method for solving the generalized equation x 2 − dy2 = n, where n ∈ Z. The ideas will be illustrated with examples. If time permits, we will also mention the classical Indian” Chakravala method” for computing the fundamental solution.

IPDF extension seminar
Speaker: Dr. Suman Mukherjee, IIT Bombay
Host: Sanjoy Pusti
Title: Fractional Leibniz Rules for the Dunkl Laplacian
Time, day and date: 4:00:00 PM - 5:00:00 PM, Monday, April 06
Venue: Room 215
Abstract: Attached (https://drive.google.com/file/d/178K8ZVTL7Ca_2v56tEYM5RRfAI869X0I/view)

Mathematical analysis of reaction-diffusion equations
Speaker: Saumyajit Das, HRI
Host: Harsha Hutridurga
Title: Reaction-Diffusion equations and related topics in kinetic theory
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, April 06
Venue: Ramanujan Hall
Abstract: We consider various Reaction-Diffusion equations with finitely many unknowns and prove related existence results. We show how to extend these techniques to address kinetic models such as the fragmentation coagulation models where we have infinitely many unknowns.

Mathematical analysis of reaction-diffusion equations
Speaker: Saumyajit Das, HRI
Host: Harsha Hutridurga
Title: Reaction-Diffusion equations and related topics in kinetic theory
Time, day and date: 11:00:00 AM – 12:30:00 PM, Tuesday, April 09
Venue: Ramanujan Hall
Abstract: We consider various Reaction-Diffusion equations with finitely many unknowns and prove related existence results. We show how to extend these techniques to address kinetic models such as the fragmentation coagulation models where we have infinitely many unknowns.

Topology Seminar
Speaker: Lekha Das, IIT Bombay
Host: Rekha Santhanam
Title: Equivariant operads and transfer systems
Time, day and date: 3:30:00 PM – 4:30:00 PM, Tuesday, April 07
Venue: Room 215
Abstract: We will discuss N_infinity operads and its connection to transfer systems. Using their correspondence, we will try to relate the notion of pairings of operads and compatible pairs of transfer systems.

Optimal transportation problem
Speaker: Sooraj A P, IIT Bombay
Host: Harsha Hutridurga
Title: Topics in Optimal Transportation
Time, day and date: 2:30:00 PM – 3:45:00 PM, Wednesday, April 08
Venue: Room 105
Abstract: -

Mathematics Colloquium
Speaker: Anusha Mangala Krishnan, IIT Bombay
Title: On the long-time behaviour of ancient homogeneous Ricci flows
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, April 08
Venue: Ramanujan Hall
Abstract: The Ricci flow is a means of evolving a Riemannian metric with time, with the goal of improving it, for example, to smoothen it out or to make it more round. The regularizing properties of the Ricci flow have made it a powerful tool in studying problems in geometry and topology.

In many situations, it is important to study the behaviour of the flow near singularities, that is, points where curvature becomes concentrated. Zooming into such a region gives rise to another Ricci flow solution, which then serves as a model for that singularity. Singularity models for the Ricci flow arising in this manner turn out to be ancient, that is, defined for all negative times. The simplest example of an ancient solution is the Ricci flow evolution of an Einstein metric of positive Einstein constant, which evolves by rescaling the metric linearly in time.

On a compact homogeneous space, the Ricci flow restricts to a finite-dimensional dynamical system on the space of left-invariant metrics. Within this setting, I will discuss a symmetry theorem for ancient Ricci flows, and also discuss how ancient solutions essentially emanate from Einstein metrics, possibly on a lower dimensional space.

Topology Seminar
Speaker: Udit Mavinkurve, IIT Bombay
Host: Rekha Santhanam
Title: Quasicategories vs Segal spaces, Part 1
Time, day and date: 11:45:00 AM – 12:45:00 PM, Thursday, April 09
Venue: Room 215
Abstract: This is Part 1 in a series of 4 expository talks that will culminate in Joyal and Tierney's proof of two Quillen equivalences between the Joyal model structure for quasicategories and the Rezk model structure for complete Segal spaces, both of which present the homotopy theory of (oo,1)-categories.

In this first talk, we will introduce (oo,1)-categories, where they come from, why they are useful, and look at various models of (oo,1)-categories.

Commutative Algebra seminar
Speaker: Kaushik Khamari, IIT Bombay
Host: Tony Puthenpurakal
Title: On Cohen-Macaulay Property of Affine Semigroup Rings II
Time, day and date: 3:00:00 PM - 4:00:00 PM, Thursday, April 09
Venue: Ramanujan Hall
Abstract: In this talk, we discuss the Cohen-Macaulay property of affine semigroup rings. In the process, we describe the relationship between local cohomology modules of these rings and the homology of certain simplicial complexes. As an application, we present a proof of Hochster's Theorem, which asserts that normal semigroup rings are Cohen-Macaulay. We follow the paper of N.V. Trung and L.T. Hoa, "Affine Semigroups and Cohen-Macaulay Rings generated by monomials.

Algebraic groups seminar
Speaker: Patrick Polo, IIT Bombay
Host: Shripad Garge
Title: Harish-Chandra Series
Time, day and date: 4:00:00 PM - 5:30:00 PM, Thursday, April 09
Venue: Room No .215
Abstract: We will finish the proof of Mackey formula. We will then prove that Harish-Chandra series forms a partition of the set of irreducible representations.

Reaction-Diffusion equations
Speaker: Saumyajit Das, HRI
Host: Harsha Hutridurga
Title: Reaction-Diffusion equations and related topics in kinetic theory
Time, day and date: 4:00:00 PM – 5:30:00 PM, Thursday, April 09
Venue: Ramanujan Hall
Abstract: We consider various Reaction-Diffusion equations with finitely many unknowns and prove related existence results. We show how to extend these techniques to address kinetic models such as the fragmentation coagulation models where we have infinitely many unknowns.

Graphicality of prime gap graphs
Speaker: Mr. Martand Puri, IIT Bombay
Host: Keshav Aggarwal
Title: On the Vijay-Tripathi theorem
Time, day and date: 5:30:00 PM – 6:00:00 PM, Thursday, April 09
Venue: Room 113
Abstract: We present proof of the Vijay-Tripathi theorem, which is a simplification of the Erdos-Gallai criterion for graphicality of a sequence.

Graphicality of prime gap graphs
Speaker: Mr. Nirav Bhattad, IIT Bombay
Host: Keshav Aggarwal
Title: An explicit upper bound for logarithmic derivative of zeta at positive real part
Time, day and date: 6:00:00 PM – 6:30:00 PM, Thursday, April 09
Venue: Room 113
Abstract: We present an explicit bound of logarithmic strength for the logarithmic derivative of the Riemann zeta function at positive real part.

Fractional Borg–Levinson Problems
Speaker: Saumyajit Das, HRI
Host: Suman Kumar Sahoo
Title: Fractional Borg–Levinson Problem
Time, day and date: 3:30:00 PM – 4:30:00 PM, Friday, April 10
Venue: Ramanujan Hall
Abstract: In this talk, we will explore how Gel'fand spectral data can be used to determine the perturbation potential associated with the fractional Laplacian on a smooth bounded domain.

Student Seminar
Speaker: Samiun Ali Molla, IIT Bombay
Host: Suman Kumar Sahoo
Title: Free Boundary methods and scattering phenomena
Time, day and date: 2:00:00 PM – 3:00:00 PM, Wednesday, April 15
Venue: Ramanujan Hall
Abstract: We study Schrödinger-type equations with potentials supported in a bounded domain and investigate the existence of nontrivial solutions. The problem is reformulated as a free boundary problem, allowing the use of tools such as unique continuation and approximation techniques. We present the main existence results and highlight the connection with free boundary theory. This talk is based on one of fundamental result of Mikko Salo and Henrik Shahgholian.

Mathematics Colloquium
Speaker: Kévin Le Balc'h, Jacques-Louis Lions Laboratory, Sorbonne Université à Paris
Host: Debanjana Mitra
Title: Control of the Heat Equation
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, April 15
Venue: Ramanujan Hall
Abstract: The study of controllability and observability for the heat equation is a central topic in the control theory of parabolic partial differential equations, at the crossroads of spectral analysis, functional analysis, and geometry. This talk presents an overview of null-controllability for the heat equation, beginning with the seminal work of Fattorini and Russell (1971), who established the one-dimensional case via moment methods, and continuing with the multidimensional breakthroughs of Lebeau–Robbiano and Fursikov–Imanuvilov (1995–1996), which rely on Carleman estimates to obtain observability from arbitrary nonempty open subsets. Building on these foundational results, I will discuss more recent developments concerning the characterization of the reachable space for the controlled heat equation, as well as the minimal size or “dimension” of observable sets.

Topology seminar
Speaker: Bittu Singh, IIT Bombay
Host: Rekha Santhanam
Title: Rational Homotopy theory
Time, day and date: 11:45:00 AM – 1:00:00 PM, Thursday, April 16
Venue: Room 215
Abstract: Dennis Sullivan introduced a framework in which the rational homotopy type of a topological space is encoded by commutative differential graded algebras (CDGAs). Earlier, Daniel Quillen established an equivalence between the rational homotopy category and an algebraic category, although this equivalence arises through a sequence of intermediate categorical constructions. In their paper "On PL De Rham Theory and Rational Homotopy Type", A. K. Bousfield and Victor K. A. M. Guggenheim gave a precise formulation of Sullivan's equivalence using the language of model category theory.

In this talk, we outline this approach and discuss the relationship between topological spaces and CDGAs in rational homotopy theory.

Commutative algebra seminar
Speaker: Aditya Diwedi, IIT Bombay
Host: Tony Puthenpurakal
Title: Deformation of F-injectivity and other F-singularities
Time, day and date: 3:00:00 PM – 4:00:00 PM, Thursday, April 16
Venue: Ramanujan Hall
Abstract: In positive characteristic, the question of whether F-singularities deform remains a central problem. While the deformation of F-injectivity is known in special cases, it remains open in general. This problem is particularly interesting due to its implications for local cohomology.

It is well-known that F-injectivity deforms if the ring is Cohen-Macaulay, a result later generalized by Horiuchi, Miller, and Shimomoto to generalized Cohen-Macaulay rings. In this talk, we present the work of Ma and Quy on F-full and F-anti-nilpotent singularities. We prove that F-injectivity deforms for these classes of rings, providing a generalisation to Horiuchi,Miller and Shimomoto's work.

Algebraic groups seminar
Speaker: Patrick Polo, IIT Bombay, Mumbai
Host: Shripad Garge
Title: Harish-Chandra series (cont.) and Deligne-Lusztig induction
Time, day and date: 4:00:00 PM - 5:30:00 PM, Wednesday, April 16
Venue: Room No .215
Abstract: We complete the chapter on HC induction by proving that the HC series form a partition of the irreducible representations. This shows the importance of cuspidal representations. We then define Deligne-Lusztig induction, which allows to get a large number of cuspidal representations as we will see in the next lectures.

Seminar
Speaker: Dr Hariom Sharma, IIT Bombay
Host: Dipendra Prasad
Title: Global Jacquet-Langlands Correspondence
Time, day and date: 5:30:00 PM – 6:45:00 PM, Thursday, April 16
Venue: Room 105
Abstract: In this talk, we discuss the work of Alexandru Ioan Bădulescu on the extension of the Jacquet–Langlands correspondence to a broader setting. We begin with a brief overview of the classical local correspondence between representations of general linear groups and their inner forms. We then present its generalization to all irreducible unitary representations. The main focus of the talk is the global Jacquet–Langlands correspondence in characteristic zero, which establishes a precise relationship between automorphic representations of GL(n) and those of its inner forms. As important consequences of this correspondence, we obtain the multiplicity one and strong multiplicity one theorems for inner forms of GL(n).

Graphicality of prime gap graphs
Speaker: Ms. Annesha Das, IIT Bombay
Host: Keshav Aggarwal
Title: An explicit upper bound for logarithmic derivative of zeta at negative real part
Time, day and date: 5:30:00 PM – 6:00:00 PM, Thursday, April 16
Venue: Room 113
Abstract: We present an explicit bound of logarithmic strength for the logarithmic derivative of the Riemann zeta function at negative real part.

Graphicality of prime gap graphs
Speaker: Mr. Divye Goyal, IIT Bombay
Host: Keshav Aggarwal
Title: Bounds towards the first moment of Large prime gaps
Time, day and date: 6:00:00 PM – 6:30:00 PM, Thursday, April 16
Venue: Room 113
Abstract: We do not expect the gaps between primes to be too big. Therefore, the first moment of large prime gaps is expected to be small. Using asymptotic expansion of the Chebyshev function, the problem is transformed into bounding an integral. We present the bounds on this integral.

Algebraic groups seminar
Speaker: Patrick Polo, IIT Bombay, Mumbai
Host: Shripad Garge
Title: Galois cohomology and/of algebraic groups
Time, day and date: 11:00:00 AM - 12:30:00 PM, Friday, April 17
Venue: Room No .215
Abstract: This will be an informal discussion around Galois cohomology and algebraic groups. This is meant especially for students. They will be allowed to ask questions on the topic and get their doubts cleared which will help them follow the seminar on "Finite Groups of Lie Type".

Algebraic groups seminar
Speaker: Patrick Polo, IIT Bombay
Host: Shripad Garge
Title: Galois cohomology of a finite field (cont.)
Time, day and date: 4:00:00 PM - 5:15:00 PM, Monday, April 20
Venue: Room No .215
Abstract: Following with the lectures on April 16 and 17, we take steps describing the G(k) conjugacy classes of maximal tori in G.

Small gaps between prime numbers
Speaker: Rajendra Meena, IIT Bombay
Host: Kummari Mallesham
Title: Small Gaps Between Primes- The Work of James Maynard
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, April 20
Venue: Ramanujan Hall
Abstract: Attached

Algebraic groups seminar
Speaker: Shripad M. Garge, IIT Bombay
Title: Schur-Weyl duality
Time, day and date: 5:30:00 PM - 6:30:00 PM, Monday, April 20
Venue: Room No .215
Abstract: This is the first lecture in a series of talks on Schur-Weyl duality. This lecture will give an overview of the subject.

Algebraic groups seminar
Speaker: Sulakhana Chowdhury, IIT Bombay
Host: Shripad Garge
Title: Schur-Weyl duality - II
Time, day and date: 4:00:00 PM - 5:30:00 PM, Wednesday, April 22
Venue: Room No .105
Abstract: This lecture will start studying the representations of the symmetric groups, S_n, over complex numbers.

Student Seminar
Speaker: Aryan Gupta, IIT Bombay
Host: Manas Rachh
Title: Finding Structure with Randomness: The Randomized Rangefinder
Time, day and date: 10:00:00 AM – 11:00:00 AM, Thursday, April 23
Venue: Ramanujan Hall
Abstract: Computing the singular value decomposition of a large dense matrix costs O(n³) operations which is prohibitive when only the leading rank-k structure is needed. The randomized rangefinder (Halko–Martinsson Tropp, 2011) replaces this with an O(n²k) algorithm: multiply the matrix by a short, random Gaussian test matrix, orthogonalize, and project. The resulting approximation is provably close to the Eckart–Young optimum, and a single step of power iteration makes it near-optimal even on slowly decaying spectra.
This talk presents the algorithm, its error guarantee, and three experiments run on the IIT Bombay math cluster: (1) wall-clock scaling showing a 759× speedup at n = 15,000; (2) spectral-norm near-optimality across power iteration depths; and (3) a free adaptive stopping criterion via an exact Frobenius-norm identity. The talk closes with a brief look at how the same ideas extend to kernel matrices through randomly pivoted Cholesky.
No background beyond linear algebra is assumed.

Topology and Geometry seminar
Speaker: Dr. Sumanta Das, IIT Bombay
Host: Rekha Santhanam
Title: Mapping Class Groups: Teichmüller Theory and Geometry
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, April 23
Venue: Ramanujan Hall
Abstract: he problem of parametrizing all possible complex structures on a given surface dates back to Riemann and can be studied via Teichmüller spaces. This subject lies at the intersection of complex manifolds, Fuchsian groups, differential geometry, algebraic geometry, and several other areas.
In this and subsequent talks, we will define and explore Teichmüller space through several equivalent points of view: complex structures, hyperbolic metrics, representation varieties, and quasiconformal deformations.
Moreover, we will discuss the moduli space of Riemann surfaces of genus g, defined as the set of all biholomorphism classes of closed Riemann surfaces of genus g. We will explain how this moduli space is obtained as the quotient of Teichmüller space by the action of the Mapping Class Group.

Optimal Transport 
Speaker: Sooraj AP, IIT Bombay
Host: Harsha Hutridurga
Title: Topics in Optimal Transportation
Time, day and date: 11:00:00 AM – 12:00:00 PM, Monday, April 27
Venue: Ramanujan Hall
Abstract: -

IPDF Extension Talk
Speaker: Chandan Bhaumik, IIT Bombay
Host: Manoj K Keshari
Title: Symplectic modules over certain subrings of a polynomial ring
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, April 27
Venue: Ramanujan Hall
Abstract: In this talk, I will discuss the cancellation and splitting problems of symplectic modules over two families of subrings of a polynomial ring: the geometric subring and the graded subring.

Schur-Weyl duality
Speaker: Sulakhana Chowdhury, IIT Bombay
Host: Shripad Garge
Title: -
Time, day and date: 5:00:00 PM – 6:00:00 PM, Monday, April 27
Venue: Room 105
Abstract: -

Pre-Synopsis
Speaker: Ankita Dargad, IIT Bombay
Host: Niranjan Balachandran
Title: Games and Puzzles in Combinatorics: A Study of Wealth Nim, Partizan Subtraction, and Connected Ferry Covers
Time, day and date: 11:00:00 AM – 12:00:00 PM, Wednesday, April 29
Venue: Ramanujan Hall
Abstract: Combinatorial games and puzzles provide a rich framework for mathematical analysis, intertwining strategy, discrete mathematics, and computational complexity. This thesis investigates three distinct problems within this domain. First, we introduce and analyze the ``Robin Hood'' game, which models a territorial dispute in the Era of Pingala. Using Combinatorial Game Theory, we analyze its thermographs, temperatures, and mean values under varying rulesets. Second, we explore Partizan Subtraction games with Full and Truncated Support. We evaluate their canonical forms and atomic weights, establishing key structural properties of these subtraction games. Finally, we shift to Alcuin’s classical River Crossing Problem, generalized as the Ferry Cover problem. We show that the existing results on the Ferry cover problem extends to any hereditary property bank constraint. We then introduce a novel variant with connectivity constraints, departing from hereditary bank properties. We completely characterize ``boat-1'' graphs—where a single-capacity boat suffices to cross without violating connectivity—proving that a connected graph is boat-1 if and only if its block-cut tree is a path. We also provide a linear time algorithm to find minimum boat capacity required to transfer a tree under connectivity constraint.

Topology Seminar
Speaker: Lekha Das, IIT Bombay
Host: Rekha Santhanam
Title: N_infinty operads and indexing systems
Time, day and date: 12:00:00 PM – 1:00:00 PM, Wednesday, April 29
Venue: Room 113
Abstract: In this talk er will investigate the close connection between the category of N_infinity operads and the poset of indexing systems.