Special Colloquium
Speaker: Apala Majumdar, University of Manchester
Host: Neela Nataraj
Title: Continuum Theories for Liquid Crystals and their Applications
Time, day and date: 12:00:00 PM – 1:00:00 PM, Thursday, November 06
Venue: Ramanujan Hall
Abstract: Liquid crystals are classical examples of partially ordered materials that combine fluidity with the directionality and ordering of solids. Liquid crystals are anisotropic materials, with direction-dependent physical, optical and rheological properties, making them the working material of choice for a range of opto-electronic devices, e.g., liquid crystal displays, photonics, sensors, photovoltaics etc. In this talk, we review the mathematical theories for two canonical liquid crystal phases: nematic and smectic liquid crystals. Nematic liquid crystals are complex liquids with orientational ordering or special material directions whereas smectic liquid crystals can be regarded as layered liquid crystals, i.e., orientationally ordered layers of liquid crystal molecules with the layers stacked on top of each other. We focus on Landau-de Gennes type theories for these phases and describe the essential mathematical frameworks - the liquid crystal order parameters, the free energies, the governing systems of partial differential equations and their solution landscapes. We then discuss the applications of these theories to a prototype liquid crystal device - the planar bistable nematic device. We conclude with some recent work on inverse problems in the Landau-de Gennes theory for nematic liquid crystals, i.e., how to reconstruct material properties from relevant experimental measurements using Bayesian methods? All collaborations will be acknowledged throughout the talk.

Student Seminar
Speaker: Suraj Mishra, IIT Bombay
Host: Suman Kumar Sahoo
Title: Rooted Tree Modules
Time, day and date: 5:30:00 PM – 6:30:00 PM, Thursday, November 06
Venue: Class 215
Abstract: In this talk we will discuss a particular type of module over path algebra of a locally bound Quiver, called a rooted tree module and a combinatorial criterion for checking the indecomposability of the rooted tree module. If time permits, we can also talk about the direct sum decomposition of a decomposable rooted tree module into indecomposable summands.

Analysis seminar
Speaker: Prof. S. Thangavelu
Host: Sanjoy Pusti
Title: On Hardy's inequality for fractional powers of the sublaplacian
Time, day and date: 4:00:00 PM – 5:15:00 PM, Friday, November 07
Venue: Ramanujan Hall
Abstract: In these lectures we plan to give an introduction to Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group. We will recall the case of the standard Laplacian on $ \R^n $ and give a proof of Hardy's inequality for $ (-Delta)^s $ using extension problem and trace Hardy inequality. We will then develop necessary background for studying the modified extension problem for the sublaplacian, establish an analogue of trace Hardy inequality and deduce Hardy's inequality.

Student Seminar
Speaker: Om Milind Joglekar, IIT Bombay
Host: Suman Kumar Sahoo
Title: Classification of Moore graphs
Time, day and date: 5:30:00 PM – 6:30:00 PM, Friday, November 07
Venue: Room 215
Abstract: Moore graphs are the “perfect” examples in the degree–diameter problem — regular graphs that exactly meet the Moore bound for given degree k and diameter d. They’re extremely rare, and understanding when they can exist turns out to be a surprisingly rigid question. In this talk I’ll look at Moore graphs in general diameter and show how strong algebraic constraints narrow down the possibilities. Specializing to diameter 2, this leads to the famous condition that k can only be 3, 5, 7 or 57. *The asterisk in the title is because the k=57 case is still an unsolved problem. All in all, we know every Moore graph that exists except possibly the one corresponding to k=57.

Analysis Seminar
Speaker: Nilabha Saha, IIT Bombay
Host: Sutanu Roy
Title: Unfolding the Spectrum of Bounded Normal Operators
Time, day and date: 5:00:00 PM - 6:00:00 PM, Monday, November 10
Venue: Ramanujan Hall
Abstract: The spectral theorem provides the bridge between abstract $C^*$-algebra theory and the concrete analysis of operators on Hilbert spaces. Rather than beginning with special cases such as compact or self-adjoint operators, this talk explores the general formulation for normal bounded operators through the structure of commutative $C^*$-algebras.

This talk will develop the spectral theorem in three interrelated formulations. First, we will examine the correspondence between elements of a commutative $C^*$-subalgebra of bounded operators and integrals of their Gelfand transforms against a unique projection valued measure. Second, we will present the representation of such algebras as multiplication operators on suitable $L^2$-spaces, highlighting the role of the measure space constructed from the spectrum. Finally, we will specialise to normal bounded operators and describe a result that assigns to each bounded function a corresponding operator.

Topology and Related Topics seminar
Speaker: Omkar Ramdas, IIT Bombay
Host: Rekha Santhanam
Title: An introduction to Lawvere theory and their applications
Time, day and date: 11:00:00 AM – 12:00:00 PM, Tuesday, November 18
Venue: Room 215
Abstract: Lawvere theory is a unique categorical framework which unifies the ideas of algebraic structures like groups, rings, etc into one category using their "logical signatures”.

Seminar
Speaker: Dr Chaman Kumar Sahu, IIT Bombay
Host: Bata Krishna Das
Title: Multiplier varieties and multiplier algebras of CNP Dirichlet series kernels
Time, day and date: 2:30:00 PM – 3:30:00 PM, Wednesday, November 19
Venue: Ramanujan Hall
Abstract: In this talk, we provide a complete characterization of the set of all normalized complete Nevanlinna-Pick (CNP) Dirichlet series kernels by their weight and frequency data. Using this description of normalized CNP Dirichlet series kernels, we explicitly determine the corresponding multiplier varieties, which turn out to be zeros of polynomials, highlighting the arithmetic structure. We examine the isomorphism problem for a significant class of CNP Dirichlet series kernels, and show that any algebraic isomorphism in this class is automatically an isometric isomorphism - a strong rigidity phenomenon. In particular, we shall address an open question posed by McCarthy and Shalit, resolving it negatively. This talk is based on joint work with B. K. Das and H. Ahmed.

All are invited to attend the talk.

Mathematics Colloquium
Speaker: Sourav Sarkar, University of Cambridge
Host: Parthanil Roy
Title: Brownian regularity of the KPZ fixed point
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, November 19
Venue: Ramanujan Hall
Abstract: Since Kardar, Parisi and Zhang introduced the KPZ equation in their seminal paper in 1986 as a model of interface growth, the equation has made appearances everywhere from the edge of a bacterial colony in a petri dish, a fire front, the spread of water in a napkin, the top edge of a randomized game of Tetris to the advancing edge of a coffee stain on a surface; and this field has become a subject of intense research interest in both physics and mathematics for the last 20 to 25 years. The random growth processes that are expected to have the same scaling and asymptotic fluctuations as the KPZ equation and converge to the universal limiting object called the KPZ fixed point are said to lie in the KPZ universality class. Universality in disordered systems has always played a central role in the direction of research in probability and mathematical physics, a classical example being the Gaussian universality class (the central limit theorem and Donsker’s Theorem), where the Brownian motion plays the analogous role of the KPZ fixed point.

A central question in the study of the KPZ universality class has been the local Brownian nature of the KPZ fixed point. Whether the KPZ fixed point looks “locally like a Brownian motion” has been a topic of intense research, even before the fixed point was formally constructed. 

In this talk, I will show that the KPZ fixed point with general initial data is in fact absolutely continuous with respect to a Brownian motion in any compact interval. I will also discuss what bounds we can get on the Radon Nikodym derivative of the KPZ fixed point with respect to Brownian motion. This solves a conjecture by Hammond.

The talk will be based on joint works with Balint Virag and Pantelis Tassopoulos.

Statistics and Probability seminar
Speaker: Dipali Vasudev Mestry, Institute of Chemical Technology, Mumbai
Host: Radhendushka Srivastava
Title: Identifying Ecological Drivers of Decline in the Abundance of Chitala Populations Through Bayesian Analysis of an Intraguild Predation System
Time, day and date: 4:00:00 PM - 5:00:00 PM, Thursday, November 20
Venue: Ramanujan Hall
Abstract: Understanding how populations grow, interact, and respond to environmental pressures is central to ecological science. Mathematical models provide a principled framework for representing these processes, while Bayesian statistical methods offer powerful tools for analysing noisy ecological data, quantifying uncertainty, and formally evaluating competing ecological hypotheses. This study integrates Bayesian modelling, Monte Carlo computation, and sensitivity analysis to investigate ecological dynamics through a data-driven lens. In this study, we analysed the rapid decline of Notopterus chitala, an endangered freshwater fish species widely distributed across South and Southeast Asia. Motivated by field evidence and ecological theory, the study investigates the trophic mechanisms contributing to this decline within a three-species intraguild predation (IGP) system involving Chitala (IG predator), Mugil (IG prey), and shrimp (resource). Two variants of coupled ordinary differential equation (ODE) models were studied: one assuming that Chitala feeds solely on Mugil and shrimp, and another incorporating an alternative food source. Parameter estimation was conducted within a fully Bayesian framework. Posterior distributions of the model parameters wereobtained using the Gibbs sampler, enabling rigorous quantification of parameter uncertainty. To address structural uncertainty arising from competing model formulations, Reversible-Jump Markov Chain Monte Carlo (RJMCMC) was employed for Bayesian model selection and comparison. The results identify two dominant ecological drivers behind the decline of Chitala: (i) a substantial reduction in nutritional gain from Mugil, which forms a major component of its diet, and (ii) diminished predation efficiency on shrimp during periods when Mugil is scarce. These mechanisms limit the species’ ability to compensate for fluctuations in prey availability, thereby accelerating its decline. The findings underscore the ecological importance of restoring Mugil populations as a central component of conservation strategies. More broadly, the study demonstrates the value of Bayesian inference for extracting mechanistic insights from multi-species ecological systems and for informing evidence-based management decisions.

Supervised Learning Project seminar
Speaker: Nirav Bhattad, IIT Bombay
Host: Prachi Mahajan
Title: Rado’s Theorem in Complex Analysis
Time, day and date: 4:00:00 PM – 5:00:00 PM, Thursday, November 20
Venue: Room 114

Statistics and Probability seminar
Speaker: Prof. Remco van der Hofstad, Department of Mathematics and Computer Science, Eindhoven University of Technology
Host: Ayan Bhattacharya
Title: Network Science: Structure and Function
Time, day and date: 2:30:00 PM - 5:00:00 PM, Monday, November 24
Venue: Ramanujan Hall
Abstract: Many phenomena in the real world can be phrased in terms of networks. Examples include the World-Wide Web, social interactions and Internet, but also the interaction patterns between proteins, food webs and citation networks. Many large-scale networks have, despite their diversity in backgrounds, surprisingly much in common. Many of these networks are small worlds, in the sense that one requires few links to hop between pairs of vertices. Also, the variability of the number of connections between elements tends to be enormous, which is related to the scale-free phenomenon.

In this lecture series, we describe a few real-world networks and some of their empirical properties. We also describe the effectiveness of abstract network modelling in terms of graphs, and how these models help us to make sense to the empirical findings. We continue by discussing some random graph models for real-world networks and their properties, as well as their merits and flaws as network models. We further discuss the implications of some of the empirical findings on information diffusion, such as the spread of fake news, and competition on such scale-free networks, as well as the local and `almost local' structure of random graphs.

Statistics and Probability seminar
Speaker: Remco van der Hofstad, Department of Mathematics and Computer Science, Eindhoven University of Technology
Host: Ayan Bhattacharya
Title: Network Science: Structure and Function
Time, day and date: 2:30:00 PM - 5:00:00 PM, Tuesday, November 25
Venue: Ramanujan Hall
Abstract: Many phenomena in the real world can be phrased in terms of networks. Examples include the World-Wide Web, social interactions and Internet, but also the interaction patterns between proteins, food webs and citation networks. Many large-scale networks have, despite their diversity in backgrounds, surprisingly much in common. Many of these networks are small worlds, in the sense that one requires few links to hop between pairs of vertices. Also, the variability of the number of connections between elements tends to be enormous, which is related to the scale-free phenomenon.

In this lecture series, we describe a few real-world networks and some of their empirical properties. We also describe the effectiveness of abstract network modelling in terms of graphs, and how these models help us to make sense to the empirical findings. We continue by discussing some random graph models for real-world networks and their properties, as well as their merits and flaws as network models. We further discuss the implications of some of the empirical findings on information diffusion, such as the spread of fake news, and competition on such scale-free networks, as well as the local and `almost local' structure of random graphs.

Special Colloquium
Speaker: Prof. Remco van der Hofstad, Department of Mathematics and Computer Science, Eindhoven University of Technology
Host: Ayan Bhattacharya
Title: Surprises in percolation on random graphs
Time, day and date: 2:30:00 PM - 3:30:00 PM, Wednesday, November 26
Venue: Ramanujan Hall (
Abstract: Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light, connectivity is hardly affected. We study the location and nature of the phase transition on random graphs. In particular, we focus on the connectivity structure close to, or below, criticality, where components display intricate scaling behaviour such that a typical connected component has a bounded size, while the maximal connected component sizes grow like powers of the network size.

We review the recent progress that has been made on percolation on random graphs whose expected adjacency matrix is close to being rank-1, the most prominent examples being the configuration model and rank-1 inhomogeneous random graphs. Time permitting, I will also discuss the surprising phase transition on dynamic random graphs, i.e., random graphs that grow with time, such as uniform attachment models. Remarkably, these two settings behave rather differently. In all cases, the inhomogeneity of the underlying random graph on which we perform percolation is of crucial importance.

In my presentation, I focus on the surprising behaviour of percolation on random graphs with infinite-variance degrees, and on growing random graphs.

[This is joint work with Sayan Banerjee, Shankar Bhamidi, Souvik Dhara, Rajat Hazra, Johan van Leeuwaarden, and Rounak Ray.]

Mathematics Colloquium
Speaker: Sudesh Kaur Khanduja, Panjab University and IISER Mohali
Host: Dipendra Prasad
Title: Newton Polygons and Irreducibility of Polynomials with Integer Coefficients
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, November 26
Venue: Ramanujan Hall
Abstract: URL attached

Student Seminar
Speaker: Advaith Nair, IIT Bombay
Host: Rekha Santhanam
Title: Proof of when a fibre bundle is a fibration
Time, day and date: 10:30:00 AM – 11:30:00 AM, Thursday, November 27
Venue: Room 113
Abstract: -

Partial Differential Equations seminar
Speaker: Neeraj Rawat, IIT Bombay
Host: Harsha Hutridurga
Title: Stefan problems in dimension one with rapidly oscillating coefficients
Time, day and date: 10:30:00 AM – 11:30:00 AM, Thursday, November 27
Venue: Ramanujan Hall
Abstract: We examine a simple setting involving the one phase and the two-phase Stefan problems in dimension one. We prove existence and uniqueness of classical solutions to these free boundary problems. The novelty of the present work is that we are able to handle rapidly oscillating periodic coefficients (in space).

All interested re cordially welcome.

Student Seminar
Speaker: Ujjwal Kumar, IIT Bombay
Host: Rekha Santhanam
Title: Proof of Quillen's Theorem A.
Time, day and date: 10:00:00 AM – 11:00:00 AM, Friday, November 28
Venue: Room 113
Abstract: In this I talk will introduce concept of geometric realisation of simplicial sets, classifying space of category and then use lemma's related to geometric realisation to prove Quillen's Theorem A

Topology Seminar
Speaker: Aparajita Karmakar, IIT Bombay
Host: Rekha Santhanam
Title: Presheaves and Diagrams on the Burnside 2-categroy
Time, day and date: 11:00:00 AM – 12:00:00 PM, Friday, November 28
Venue: Room 113
Abstract: Mackey functors play a central role in equivariant algebraic topology: classically, they are additive (abelian-group-valued) functors on the Burnside category of a group. In this talk we introduce and explore higher analogues of Mackey functors. Concretely, we replace the Burnside category by the Burnside 2-category, and replace the target category of abelian groups by the 2-categorical world of strict symmetric monoidal (permutative) categories. Our objects of study are then enriched presheaves and diagrams on the Burnside 2-category.
Our principal goal is to establish an equivalence of homotopy theories between these enriched presheaf and diagram categories, paralleling the classical self-duality of the Burnside category. In the 1-categorical setting this self-duality yields both covariant and contravariant structure for Mackey functors. However, in the 2-categorical context the duality fails to hold strictly. To overcome this obstacle, we employ a strictification technique on coloured-operad pseudo-algebras restoring the duality up to equivalence. This approach builds on recent advances in the homotopy theory of enriched Mackey functors.
Thus, the talk will outline the construction of higher Mackey functors, explain why 2-categorical self-duality fails, and present the strictification via operadic methods that recovers an equivalence of homotopy theories — shedding light on how classical Mackey‐theoretic phenomena generalize in a higher-categorical setting.

PDE and Numerical Analysis seminar
Speaker: Chinmay Patwardhan, Karlsruhe Institute of Technology
Host: Harsha Hutridurga
Title: Computational aspects of radiative transfer: from asymptotics to uncertainty quantification
Time, day and date: 11:00:00 AM - 12:00:00 PM, Friday, November 28
Venue: Ramanujan Hall
Abstract: Thermal radiative transfer (TRT) governs phenomena ranging from supernovas in astrophysics to laser-driven fusion experiments in plasma physics. The interaction of radiation and matter involves prohibitively small-time scales, nonlinear coupling, and high-dimensional particle dynamics, making conventional numerical methods prohibitively expensive. Dynamical low-rank approximation (DLRA), combined with asymptotic-preserving discretizations, offers a promising direction, but until now its use for nonlinear TRT has been fundamentally limited: stability regions of existing DLRA integrators are unknown in realistic nonlinear regimes, and coefficient updates remain computationally costly. In this talk I present an asymptotic-preserving, locally conservative, rank-adaptive, and parallel integrator for a macro–micro decomposition-based DLRA of the nonlinear TRT equations. 

Moreover, since reality is rarely deterministic, including uncertainties, stemming from modelling errors, measurement errors, and device errors, in these models provides a more realistic description of the phenomena. Quantifying these is thus essential for robustness and reliability in applications. In this talk, I present a low-rank multilevel Monte Carlo method for quntifying uncertainties in the TRT equations.