Kerala School of Mathematics - Official Website

Title: Research Talk: Riesz transforms associated with the twisted Laplacian with drift and the Grushin operator with drift

Date: Tuesday, 27 October 2026 · 04:00 PM to 05:00 PM IST

Speaker(s): Nishta Garg, IISER Bhopal

Venue: Online via Google Meet: https://meet.google.com/rex-kijc-crh

Abstract:

In the classical setup, Riesz transforms are fundamental examples of singular integral operators and are known to be bounded on $L^{p}$ spaces for $1 < p < \infty$ and weak type $(1,1)$. The measure considered here is the Lebesgue measure, which is known to satisfy the doubling condition. What happens if a measure is considered such that it no longer satisfies the doubling property? We start by answering this question in the Euclidean setup for one such measure which has an exponential volume growth. The Laplacian in this setup is referred to as the Laplacian with drift. Briefly, we shall discuss the Riesz transforms associated with the Laplacian with drift. Our main goal is to define the twisted Laplacian with drift and the Grushin operator with drift, which are essentially self-adjoint with respect to appropriate measures of exponential growth. We shall discuss the $L^{p}$ boundedness and weak type $(1,1)$ properties of the Riesz transforms associated with these operators.

You can join the meeting online using this Google Meet link.

Title: Research Talk: The Pure Infiniteness Transfer Problem

Date: Tuesday, 27 October 2026 · 05:00 PM to 06:00 PM IST

Speaker(s): Arindam Sutradhar, ISI Bangalore

Venue: Online via Google Meet: https://meet.google.com/rex-kijc-crh

Abstract:

I will talk about my recent work, the pure infiniteness transfer problem which answers whether a dense subalgebra A_0 of a C∗-algebra A that is purely infinite as a ring forces A to be purely infinite as a C∗-algebra under two hypothesis: A has real rank zero, and A_0 is closed under holomorphic functional calculus. I will provide a short summary of my previous work on essential codimension and spectral flow in multiplier algebras.

You can join the meeting online using this Google Meet link.

Title: Research Talk: Uprooted Spanning Tree Enumeration and Spherical Parking Functions

Date: Monday, 26 October 2026 · 04:00 PM to 05:00 PM IST

Speaker(s): Nayana Shibu Deepthi

Venue: Online via Google Meet: https://meet.google.com/rex-kijc-crh

Abstract:

Spherical G-parking functions form a distinguished subset of the standard monomials arising from the skeleton ideals of the G-parking function ideal, and explicit enumeration formulas are known for only a few graph classes. In this talk, I will present recent work on enumerating certain subsets of uprooted spanning trees and spherical G-parking functions associated with a specific family of graphs. I will discuss the main counting arguments and the role of the matrix tree theorem in establishing these results. I will also briefly summarise my PhD research on edge rings and outline future research directions, including extending these enumeration problems to other graph families and exploring connections between spanning trees, parking functions, and their associated algebraic structures.

You can join the meeting online using this Google Meet link.

Title: Research Talk: Minimizers of Eigenvalues under a Lower Curvature Bound

Date: Monday, 26 October 2026 · 05:00 PM to 06:00 PM IST

Speaker(s): Aditya Tiwari, Indian Institute of Science Education and Research Mohali

Venue: Online via Google Meet: https://meet.google.com/rex-kijc-crh

Abstract:

The unit sphere minimizes the first positive Laplacian eigenvalue among closed Riemannian n-manifolds with Ricci curvature at least n-1, due to a classical theorem of Lichnerowicz. In this talk, we discuss the minimization of higher Laplacian eigenvalues among closed surfaces under the same curvature constraint. We present rigidity results for smooth minimizers and show that minimizers in the measured Gromov-Hausdorff completion cannot collapse to lower-dimensional spaces.

You can join the meeting online using this Google Meet link.

Title: Research Talk: Isometric actions of compact quantum groups on graph C*-algebras

Date: Saturday, 24 October 2026 · 04:00 PM to 05:00 PM IST

Speaker(s): Jitender Sharma, Visiting Student, IISER Kolkata

Venue: Online via Google Meet: https://meet.google.com/rex-kijc-crh

Abstract:

In this talk we will talk about the quantum isometric actions in the context of graph C*-algebra using the language developed by D. Goswami. In particular we will show that quantum automorphism group of a finite graph acts quantum isometrically on the spectral triple (A, H, D) associated with strongly connected finite higher rank graph constructed by Farsi et al. The underlying Hilbert space H of the spectral triple arises from the infinite path space, which is a compact topological space equipped with Perron-Frobenius measure M. Using the semi-branching system one can represent higher rank graph algebras on the Hilbert space H. The unbounded Dirac operator is formal sum of finite rank projections defined using the infinite path space. Our main is result is to show that quantum automorphism group of the 1-graph acts on the spectral data (A, H, D).

You can join the meeting online using this Google Meet link.

Title: Research Talk: Differential central simple algebras and Picard-Vessiot splitting fields

Date: Friday, 23 October 2026 · 04:00 PM to 05:00 PM IST

Speaker(s): Manujith K Michel, IISER Mohali

Venue: Online via Google Meet: https://meet.google.com/rex-kijc-crh

Abstract:

Classical Galois theory studies polynomial equations through symmetries of their roots. Differential Galois theory develops a parallel viewpoint for linear differential equations: the symmetries of their solutions form algebraic groups and encode important information about the equations. In this talk, I will discuss how these ideas can be used to study central simple algebras equipped with a derivation. Central simple algebras include matrix algebras and division algebras, and they play a central role in noncommutative algebra and the theory of the Brauer group. Over a suitable Galois extension, every central simple algebra becomes a matrix algebra; such an extension is called a splitting field. When the algebra also carries a derivation, it is natural to ask whether one can find a splitting field that respects the differential structure and whether the symmetries of that field reveal the structure of the original algebra. Magid and Juan first studied this question over a base differential field of characteristic zero whose field of constants is algebraically closed. They proved that differential central simple algebras admit Picard–Vessiot splitting fields. Under the same hypothesis on the base differential field, I will explain how one can associate a natural Picard–Vessiot splitting field to each differential central simple algebra. This splitting field is minimal in a precise sense. Its differential Galois group acts through a projective representation, leading to a correspondence between differential central simple algebras split by a given Picard–Vessiot extension and projective representations of its differential Galois group. This correspondence translates questions about noncommutative algebras into questions about algebraic groups and their representations. For example, properties such as solvability or reductivity of the Galois group can be detected through suitable differential right ideals of the algebra. I will begin with a brief review of the basic material from differential Galois theory needed for the discussion, and conclude by describing extensions of these ideas to fields of positive characteristic, where ordinary derivations are replaced by iterative derivations. This talk is based on my PhD thesis prepared under the supervision of Dr. Varadharaj Ravi Srinivasan.

You can join the meeting online using this Google Meet link.

Title: Research Talk: Palindromic Automorphisms of Free Groups and Symmetries of Riemann Surfaces

Date: Friday, 23 October 2026 · 05:00 PM to 06:00 PM IST

Speaker(s): Dr. Lokenath Kundu, IISER Mohali

Venue: Online via Google Meet: https://meet.google.com/rex-kijc-crh

Abstract:

This talk gives an overview of my research, which studies groups through the finite symmetries they centralise or realise. The first part concerns the palindromic automorphism group $\Pi A(F_n)$ of a free group $F_n$. This group is the centraliser in $\mathrm{Aut}(F_n)$ of the involution inverting every basis element. It was introduced by D. J. Collins, who proved that it is finitely presented. I will discuss joint work with K. Gongopadhyay on the Dehn function of $\Pi A(F_n)$, and joint work with K. Gongopadhyay and S. V. Singh on the classification of $z$-classes in $\Pi A(F_n)$, where two elements lie in the same $z$-class when their centralisers are conjugate. I will also describe results on irreducible palindromic automorphisms and on the automorphism group of $\Pi A(F_n)$. The second part concerns finite groups acting on compact Riemann surfaces. Using Fuchsian groups and surface-kernel epimorphisms, I study the signatures of actions of the linear fractional groups $\mathrm{PSL}_2(\mathbb{F}_p)$, their stable upper genus (joint with K. Mukherjee), and an application to the growth of families of finite simple groups in the sense of S. Black. I will conclude with directions for future research and teaching.

You can join the meeting online using this Google Meet link.

Title: KSoM Seminar Talk: Monodromy of curves on an algebraic surface

Date: Friday, 16 October 2026 · 03:00 PM to 04:00 PM IST

Speaker(s): Ishan Banerjee, Research Visitor, Lodha Mathematical Sciences Institute, Mumbai

Venue: Seminar Hall, KSoM

Abstract:

Given an algebraic surface $X$ and an embedding of $X$ in $\mathbb{P}^n$, we can construct the family of smooth hyperplane sections of $X$ arising from the embedding. Let $\Sigma$ denote a fixed hyperplane section, this is a curve of some genus $g$. The above family of curves induces a monodromy representation, with target the mapping class group of $\Sigma$. In the case when $X$ is simply connected and the embedding is sufficiently ample, we determine that the image of this representation is a finite index subgroup of the mapping class group. This is based on joint work with Nick Salter.

Title: KSoM Lecture Series: Analysis Meets Geometry: Spectral Theory of Automorphic Forms

Date: 12–14 October 2026 · 04:00 PM to 05:00 PM IST (12th & 13th Oct), 03:00 PM to 04:00 PM (14th Oct)

Speaker(s): Devadatta Hegde, Postdoctoral Fellow, Tata Institute of Fundamental Research (TIFR), Mumbai

Venue: Seminar Hall, KSoM

Abstract:

A basic problem in the spectral theory of automorphic forms has recently been solved using methods from enumerative geometry. In three lectures, assuming little background, I will explain how. The series will cover the following topics:

1. Spectral theory of a differential operator: the analyst’s approach versus the geometer’s.
2. Why are there exactly 27 lines on a smooth cubic surface? equivariant localization and enumerative geometry.
3. Why does geometry enter a spectral problem? Eisenstein series and the residual spectrum.

Title: Frontiers in Mathematics

Date: October 2–4, 2026

Description:

The Kerala School of Mathematics (KSoM) invites applications for Frontiers in Mathematics, an intensive three-day workshop to be held from October 2nd to 4th, 2026, at KSoM, in association with the National Board for Higher Mathematics (NBHM), for advanced graduate students, research scholars, and postdoctoral fellows.

The program is built around a simple idea: devote one full day to one topic. A leading specialist takes participants from the foundations to the state of the art through lectures complemented by tutorial and problem-solving sessions, creating space for focused, deep learning and collaboration. This edition will focus on three areas: harmonic analysis, representation theory and probability.

Speakers:
• Prof. Parasar Mohanty, IIT Kanpur
• Prof. K. N. Raghavan, Krea University
• Prof. Manjunath Krishnapur, IISc Bangalore

Organizers:
• Dr. Debkumar Giri, Kerala School of Mathematics
• Dr. Arindam Jana, Kerala School of Mathematics
• Dr. Badri Vishal Pandey, Kerala School of Mathematics
• Dr. Kalachand Shuin, Kerala School of Mathematics

Local hospitality will be provided. Limited travel support may be available for selected participants.

Last date for receiving online applications: 20 September, 2026.

Title: Bernhard Riemann Memorial Colloquium: Modular forms, Motives and L-functions

Date: September 18, 2026 · 03:00 PM to 04:00 PM IST

Speaker(s): Dipendra Prasad, Emeritus Fellow, Department of Mathematics, IIT Bombay

Venue: Seminar Hall, KSoM

Abstract:

We discuss the inter-relationship between algebraic-geometric objects such as varieties and analytic objects such as modular forms, via the intermediary of L-functions which are generalizations of the Riemann Zeta function. This will serve as an introduction to the Langlands program, which is of central importance to mathematics. The talk will be addressed to a general scientific audience.

Title: KSoM Seminar Talk: Dimension Dependent Weak-Type (1,1) Estimates in Harmonic Analysis (and AI)

Date: September 16, 2026 · 11:30 AM to 12:30 PM IST

Speaker(s): Daniel Spector, Distinguished Professor, Department of Mathematics, National Taiwan Normal University

Venue: Online via Google Meet: https://meet.google.com/nuw-qbqg-cct

Abstract:

At the 1986 International Congress of Mathematicians, E. M. Stein presented on a program he had been developing for several years on infinite-dimensional harmonic analysis. The theme of this program is to establish estimates for various operators, e.g. the Hardy- Littlewood maximal function, Riesz transforms, Littlewood-Paley g-function, where the constants do not depend on the dimension. In the proceedings of the conference, he mentions several open problems, including the question of whether the Riesz transforms and Hardy-Littlewood maximal function admit dimension-free weak-type (1, 1) estimates. In this talk we discuss recent work obtained in collaboration with Lance Ouyuan and Cody Stockdale that resolve one of these questions and on work with Stockdale that give an improvement on the other. One key new idea in these proofs is partial balayage, which was discovered through interactions with an LLM. Besides the motivation and some ideas of the proof, we also discuss our use of AI on the problem in the talk.

Google Meeting Link: https://meet.google.com/nuw-qbqg-cct

Title: KSoM Seminar Talk: Shifted Convolution Problem

Date: September 9, 2026 · 03:00 PM to 04:00 PM IST

Speaker(s): Sampurna Pal, National Post Doctoral Fellow (NPDF), Department of Mathematics, IIT Kanpur

Venue: Seminar Hall, KSoM

Abstract:

In this talk we will discuss the concept of the Shifted Convolution Problem and its importance in Analytic Number Theory. In particular, we will also discuss the shifted convolution problem for the triple divisor function and Fourier coefficients of GL(3) forms and their importance in the study of Moments of L-functions. This is based on a recent joint work with Dr. Ritwik Pal.

Title: KSoM Seminar Talk: Parabolic Lie algebroid connections on parabolic principal bundles over curves

Date: September 2, 2026 · 03:00 PM to 04:00 PM IST

Speaker(s): Pritthijit Biswas, Postdoctoral Fellow, Kerala School of Mathematics (KSoM), Kozhikode

Venue: Seminar Hall, KSoM

Abstract:

Let X be a compact connected Riemann surface and S ⊂ X be a finite set. We consider a parabolic complex analytic principal G-bundle E on X with parabolic points being precisely the set S, the parabolic weights associated to each of these parabolic points being rational and G being a complex linear reductive algebraic group.

Let P be a parabolic subgroup of G and EP be a parabolic reduction of structure group of E to P. In this talk I will introduce a criterion for the existence of a parabolic Lie algebroid connection on EP for any given parabolic Lie algebroid on (X, S) with non-surjective anchor map. In particular from this criterion, it will follow that for the parabolic Harder–Narasimhan reduction EP of E, a parabolic Lie algebroid connection always exists on EP for any parabolic Lie algebroid on (X, S) with non-surjective anchor map.

All the relevant notions will be developed before a sketch of the proof is given, which could be elaborated further if time permits. This is joint work with Indranil Biswas.

Title: KSoM Seminar Talk: Convergences in L p (Ω), Multi-scale Convergence and an Application in Homogenization

Date: August 31, 2026 · 04:00 PM to 05:00 PM IST

Speaker(s): A. K. Nandakumaran, Honorary Professor, Department of Mathematics, Indian Institute of Science (IISc), Bangalore

Venue: Seminar Hall, KSoM

Abstract:

We introduce a notion of two-scale (or multi-scale) convergence in the space L 2 (Ω) of square integrable functions (more generally, we can consider L p (Ω)). When we need to treat different scales in problems of applications, the strong and weak convergences are inadequate. There are different applications including problems from homogenization where we see appearance of multi-scales. We also state a compactness theorem in two-scale (or multiscale) convergence (similar to weak compactness) which was introduced in the eighties. A more general approach is the method of unfolding. Again unfolding operators have been introduced and used to study homogenization problems which was more general than mulit-scale convergence. It was introduced for problems with rapidly oscillating coefficients and porous domains. Later, this has been developed for domains with various types of oscillating boundaries. Our research group have developed many new unfolding operators and it has been applied to several homogenization problems of interest. At the end of the talk, we briefly discuss a high contrast problem in oscillating domain.