Talk
Speaker: NAMAN KRISHNA PANDE, Indian Institute of Technology Ropar
Host: S Baskar
Title: Scientific Machine Learning for Complex Systems
Time, day and date: 11:30:00 AM – 12:30:00 PM, Monday, August 10
Venue: Online (https://meet.google.com/jxd-pimp-pox)
Abstract: Multi-agent systems (MAS) are ubiquitous to various natural phenomena such as flocks of birds, crowd motion, vehicular flow and insect swarms, etc. These systems involve a large number of interacting agents whose collective behaviour gives rise to complex emergent phenomena. Analysing and controlling such systems poses major problems in various scientific and engineering fields. Optimal control (OC) of MAS aims to learn strategies that enable the agents to achieve common or individual objectives while adhering to some dynamical constraints. We aim to develop and analyse these systems through the mean-field game theoretical approach that considers each agent as rational and utility-optimising and comprehends their dynamics at the macroscopic scale. Furthermore, we will utilise physics-informed neural networks (PINN) based models to learn the dynamics of such complex physical systems typically governed by a system of partial differential equations. However, despite enjoying great success, PINNs have some fundamental flaws when dealing with various complex physical problems. We aim to address various limitations of PINNs by developing robust and scalable physics-informed learning frameworks that incorporate improved neural network architectures, efficient sampling techniques and integration of discrete representations of the governing physics directly into the network architecture and training process.

PDE seminar
Speaker: Harsh Prasad, Universität Bielefeld
Host: Harsha Hutridurga
Title: Nonlocal Ground States Are Superharmonic
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, August 10
Venue: Ramanujan Hall
Abstract: he first eigenfunction of the fractional Laplacian is expected to share many of the geometric properties of the classical ground state, yet even its superharmonicity has remained open in general. Previous results were limited to special exponents, low dimensions, or particular classes of domains.

Based on joint work with Florian Grube, I will present a new proof showing that every first Dirichlet eigenfunction $\phi$ satisfies
[
-\Delta\phi \ge \lambda_1^{1/s}\phi
]
for every $s\in(0,1)$. In one dimension, this yields strict log-concavity and resolves a long-standing conjecture of Bañuelos, Kulczycki and Méndez-Hernández.

The proof is remarkably short and is based on a new combination of Bernstein function theory and maximum principle arguments. Besides establishing the superharmonicity estimate, the method suggests a broader framework for comparing local and nonlocal elliptic operators and may extend to more general subordinate processes.

Finally, I will discuss the Brascamp–Lieb type log-concavity questions that originally motivated this line of research. I will present evidence indicating that the nonlocal picture may be considerably more subtle than in the classical setting, including indications that natural Brascamp–Lieb analogues may fail for symmetric $\alpha$-stable processes, and I will conclude with several open problems and possible future directions.
Combinatorics seminar

Number theory seminar
Speaker: Sabyasachi Dhar, IIT Bombay
Host: U.K. Anandavardhanan
Title: Tate cohomology and local base change for p-adic groups
Time, day and date: 5:00:00 PM - 6:00:00 PM, Monday, August 10
Venue: Room No .215
Abstract: In 2016, Treumann and Venkatesh proposed a remarkable conjecture on local Langlands functoriality for l-modular representations of p-adic groups, which predicts that the mod-l functoriality is realized by Tate cohomology. In this talk, we discuss this conjecture in the context of local base change lifting.

Combinatorics seminar
Speaker: Nitesh Prajapati, IIT Bhilai
Host: Niranjan Balachandran
Title: Some Direct and Inverse Problems for Sumsets, Restricted Sumsets, and Product Sets
Time, day and date: 11:30:00 AM - 12:30:00 PM, Tuesday, August 11
Venue: Online (meet.google.com/jwm-qugk-hmu)
Abstract: Attached https://drive.google.com/open?id=1rQbYHeVo2HChZTTNjMldNDPOwk0AShj3

Statistics/Probability Seminar
Speaker: Sabyasachi Chatterjee, University of Illinois Urbana-Champaign
Host: Parthanil Roy
Title: A New Min–Max Representation for Univariate Total Variation Denoising
Time, day and date: 4:00:00 PM – 5:00:00 PM, Tuesday, August 11
Venue: Ramanujan Hall
Abstract: Total variation denoising (TVD) is a classical and widely used method for estimating signals with piecewise constant structure. Although the estimator is defined through a simple convex optimization problem and has been studied extensively, no explicit pointwise characterization of the fitted values was previously known.
In this talk, I will present a new min–max/max–min representation for TVD that gives an explicit pointwise description of the fitted values in terms of local averages over intervals. This representation reveals a hidden multiscale structure underlying the estimator, provides new insight into its bias and variance, and leads to sharp pointwise risk bounds that adapt to the local smoothness of the underlying signal.
I will then show that this pointwise perspective extends naturally to quantile regression. In this setting, the fitted values admit an exact characterization as an interval determined by local order statistics, reflecting the non-strict convexity of the quantile loss. This characterization yields new structural insights into quantile TVD, including automatically non-crossing quantile curves without the need for additional constraints.
The talk is based on the following two papers:
(1) https://arxiv.org/pdf/2410.03041
(2) https://arxiv.org/pdf/2605.01237

Deep Learning in Finance – Lecture 3
Speaker: Prof. Ovidiu Calin, Eastern Michigan University
Host: S Baskar
Title: Learning Stochastic Processes Part I: Calibration
Time, day and date: 5:00:00 PM – 6:00:00 PM, Tuesday, August 11
Venue: Ramanujan Hall
Abstract: This presentation introduced modern approaches for learning and calibrating stochastic processes from data using machine learning. Beginning with Gaussian processes, we showed how neural networks can be used to approximate the time-dependent mean and variance functions, transforming the observations into a standardized process that should follow a standard normal distribution. This viewpoint naturally leads to calibration methods based on quantile matching, which compare the entire empirical distribution rather than only its first moments, providing a more robust alternative to classical moment-matching techniques. We then extended the framework to learning covariance kernels, enabling the recovery of temporal dependence in Gaussian processes, with simplified formulations for stationary models. The second part focused on the calibration of stochastic differential equations, using the Langevin (Ornstein–Uhlenbeck) process as a representative example. After deriving its explicit solution and statistical properties, we discussed several calibration strategies, including moment matching, quantile matching, and autoregressive estimation. Throughout the presentation, neural-network-based calibration was presented as a flexible and powerful alternative to traditional estimation methods, capable of learning unknown statistical quantities directly from observed trajectories while providing a unified framework applicable to a broad class of stochastic models encountered in finance, physics, engineering, and data science.

Colloquium
Speaker: Prosenjit Roy, IIT Kanpur
Host: Parthanil Roy
Title: On Boundary Hardy Inequality
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, 12th August 2026
Venue: Ramanujan Hall
Abstract: https://drive.google.com/file/d/1h3XP_VjXa2RFxRiRCtpLGueUAAG_eMi3/view?usp=sharing

Talk
Speaker: Dr. Biplab Maity, NDMC
Host: Siuli Mukhopadhyay
Title: Mathematical Modeling of Infectious Disease Dynamics and Control Strategies
Time, day and date: 4:30:00 PM – 5:30:00 PM, Wednesday, August 12
Venue: Room 105 (https://meet.google.com/jpd-irwv-prm)
Abstract: Emerging infectious diseases continue to pose major global health and economic challenges. Mathematical models provide a useful framework for understanding disease transmission and evaluating control strategies, particularly when resources are limited. My research focuses on developing mathematical models that incorporate disease-specific epidemiological and ecological features to understand epidemic dynamics and identify effective intervention strategies.
I will first present a theoretical framework for resource-constrained epidemic control, where resources can be allocated between interventions that reduce transmission and those that enhance recovery. I will show how the optimal balance between these interventions depends on their cost-efficiency and on the functional relationship, such as production functions, between resource investment and health outcomes.
I will then discuss how environmental reservoirs and pathogen ecology can shape epidemic dynamics, with a particular focus on cholera. I will show how interactions between pathogen and plankton populations can influence the timing and persistence of outbreaks and why incorporating ecological processes can improve disease prediction and control planning. In particular, I will present our study of the seasonal synchrony between cholera outbreaks and plankton blooms in coastal ecosystems. Our results show that plankton-mediated transmission can prolong outbreaks by sustaining low-level infections after the epidemic peak, increasing post-peak infections and promoting pathogen persistence between outbreaks.
Building on these theoretical results, I will present an empirical analysis of the 2017–18 cholera outbreak in Lusaka, Zambia, and a stochastic framework for assessing endemic persistence and estimating the expected time to disease extinction.
Overall, my research combines mathematical modeling, environmental reservoir ecology, data-driven calibration, and optimal control to understand infectious disease dynamics and develop actionable, context-specific strategies for disease prevention and public health decision-making.

Advanced Applied Mathematics Seminar
Speaker: Arpita Mondal, IIT Bombay
Host: Manas Rachh
Title: Statistical Learning and Data Science for Climate Risk Assessment
Time, day and date: 3:00:00 PM – 4:00:00 PM, Thursday, August 13
Venue: Ramanujan Hall
Abstract: Risk of hydroclimatic extreme events informs engineering decision-making and sustainable environment management. This talk will highlight recent research efforts using advanced statistical frameworks, extreme value theory, unsupervised learning, predictive data-driven modeling and multi-criteria decision-making for attribution of hydroclimatic hazards in India to climate change, assessing their impact and quantifying their interactions with socio economic exposure and vulnerability. While the applied mathematical, statistical or data-driven methods are applicable to a class of extreme events, the talk will focus on the risk of hot extremes and heat waves in India and their interactions with other hazards such as droughts and air pollution.

Algebraic Groups Seminar
Speaker: Hariom Sharma, IIT Bombay, Mumbai
Host: Shripad M. Garge
Title: Iwahori Hecke algebras
Time, day and date: 5:00:00 PM - 7:00:00 PM, Thursday, August 13
Venue: Conference Room
Abstract: Hecke algebras

Deep Learning in Finance – Lecture 4
Speaker: Prof. Ovidiu Calin, Eastern Michigan University
Host: S Baskar
Title: Learning Stochastic Processes Part II: Ito Diffusion
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, August 13
Venue: Ramanujan Hall
Abstract: This presentation extends the learning of stochastic processes from parameter calibration to the more general problem of discovering stochastic differential equations directly from observed data. The objective is to learn the unknown drift and diffusion coefficients of Itô diffusions using neural networks trained on multiple sample trajectories. Separate learning strategies are developed for time-dependent, state-dependent, and fully general stochastic models, exploiting either explicit analytical solutions when available or Euler discretizations when closed-form solutions do not exist. The methodology estimates the local statistical moments of the process increment and uses them to train neural networks that provide smooth approximations of the drift and volatility functions, leading to the framework of Stochastically Informed Neural Networks (SINNs), a stochastic counterpart of Physics-Informed Neural Networks (PINNs). The approach is illustrated for generalized Brownian motion with drift, generalized geometric Brownian motion, and autonomous Itô diffusions, where suitable transformations, such as the logarithmic transformation for stock-price models, simplify the learning problem. The resulting framework enables the identification of stochastic models directly from data and provides flexible, data-driven representations of time-varying and state-dependent dynamics with applications in finance, physics, engineering, and other scientific disciplines.

Number Theory Seminar
Speaker: Arijit Chakraborty, Department of Mathematics, UCSD
Host: Keshav Aggarwal
Title: Counting Number Fields by Discriminant: Power-Saving Error Terms and New Directions
Time, day and date: 10:00:00 AM – 10:50:00 AM, Friday, August 14
Venue: Online (https://us06web.zoom.us/j/82517817235?pwd=afanPYlw2EJOEv7Xl0BipJKkm6jBKz.1)
Meeting ID: 825 1781 7235
Passcode: p8fAMa
Abstract: Malle's conjecture predicts the asymptotic growth of number fields with prescribed Galois groups when ordered by discriminant. In this talk, I will discuss my work on obtaining power-saving error terms for counting (C_2 \wr H)-extensions of an arbitrary number field, under mild assumptions on (H), and briefly highlight the main ideas behind the result. I will conclude with ongoing directions involving more general wreath products and Malle's conjecture for non-concentrated groups, including joint work on degree-(16 (D_8)-extensions.

Geometry and Topology seminar
Speaker: Devadatta Hegde
Host: Sudarshan Gurjar
Title: An introduction to equivariant cohomology through an example
Time, day and date: 11:30:00 AM – 12:30:00 PM, Friday, August 14
Venue: Room 215
Abstract: Equivariant cohomology was introduced by A. Borel in the late 1950s. It has since found applications in many parts of mathematics, including, more recently, automorphic forms. In this talk, we give an introduction to this topic by using it to prove the classical result in enumerative geometry that a generic cubic surface contains exactly 27 lines.

Talk
Speaker: Hariom Sharma, IIT Bombay
Host: Ravi Raghunathan
Title: Symplectic Model for Zelevinsky Modules of GL(n, D)
Time, day and date: 4:00:00 PM – 5:00:00 PM, Friday, August 14
Venue: Ramanujan Hall
Abstract: Let D be a quaternion division algebra over a non-Archimedean local field F of characteristic zero. Let m = (Δ₁,..., Δₖ) be a well-ordered multisegment, and let π(m) = Z(Δ₁) × ··· × Z(Δₖ) be the associated Zelevinsky module of GL(n, D). In this talk, we study the existence and uniqueness of symplectic models for Zelevinsky modules. Under the assumption that no representation occurring in the cuspidal support of m admits a symplectic model, we prove that π(m) admits a symplectic model if and only if every segment in m has even length. We further show that, whenever such a model exists, it is unique. As a consequence, if the unique irreducible quotient Z(m) of π(m) admits a symplectic model, then every segment in m has even length.

Analysis seminar 
Speaker: Sheetal Wankhede, SRM University
Host: Prachi Mahajan
Title: Univalent harmonic functions and their applications to special functions
Time, day and date: 4:00:00 PM – 5:00:00 PM, Friday, August 14
Venue: Online (https://meet.google.com/ezq-gmpb-esb)
Abstract: The theory of univalent functions has been a central area of research in geometric function theory due to its deep connections with complex analysis and its wide range of applications. This work investigates integral operators and coefficient conditions for analytic, harmonic, and logharmonic mappings, with particular emphasis on their geometric properties such as univalence, close-to-convexity, and starlikeness.

The first part of the study focuses on a Cesàro-type integral transform defined through Hornich operations. Sufficient conditions are established on the parameters of the operator to guarantee univalence in the analytic and harmonic settings. These results are further extended to logharmonic mappings, where new univalence criteria are obtained and a connection between harmonic and non-vanishing logharmonic functions is revealed.

The second part of the work develops new monotone coefficient conditions that ensure the univalence and close to-convexity of harmonic mappings. These criteria generalize several classical results from the analytic setting and provide effective tools for studying harmonic functions. As an application, the obtained conditions are employed to investigate the geometric behavior of harmonic mappings associated with Gaussian hypergeometric functions. Furthermore, new coefficient conditions characterizing starlikeness are derived and applied to shifted Gaussian hypergeometric functions.

Students' Seminar
Speaker: Aditya Khambete, IIT Bombay
Host: Suman Kumar Sahoo
Title: An elementary proof of the Strong Law of Large Numbers
Time, day and date: 5:15:00 PM – 6:00:00 PM, Friday, August 14
Venue: Room 114
Abstract: Most of you are already familiar with the Strong Law of Large Numbers. But have you ever wondered about how to prove it? The Strong Law of Large Numbers is a fundamental result in probability theory, asserting that normalized partial sums converge almost surely to the expected value. In this talk, I present Etemadi's elementary proof for identically distributed, pairwise independent random variables with finite first moment. The talk would be accessible to anyone who has completed a probability course.