Analysis seminar
Speaker: Sushil Singla, University of Regina, Canada
Host: Santanu Dey
Title: Representations of noncommutative cubes and prisms
Time, day and date: 3:45:00 PM - 4:45:00 PM, Tuesday, August 04
Venue: Ramanujan Hall
Abstract: In this talk, I will describe certain noncommutative realizations of three classical geometric objects: cubes, polydiscs, and prisms. I will establish the connection of representations of discrete groups with the noncommutative extreme points of the noncommutative state space of the operator systems generated by the canonical unitaries that correspond to the generators of the group. Using this connection, I will be shedding light on the noncommutative geometry of noncommutative dcubes and k-prisms via the representations of the operator system determined by the canonical generators of the free product of two cyclic groups of order 2 and k, or d cyclic groups of order 2. By way of the duality of the categories NCConv and OpSys of noncommutative convex sets and operator systems, respectively, I will also establish an analysis of tensor products of the operator system under consideration.
Finally, I will apply classical dilation theorems of Halmos and Mirman to give a complete description of the maximal noncommutative triangular prism in terms of joint unitary dilations. This is joint work with D. Farenick, R. Maleki, and S. Medina Varela, and has been accepted for publication in J. Noncommut. Geom. The preprint of the article is available on Arxiv:2601.16902.

Deep Learning in Finance – Lecture 1
Speaker: Prof. Ovidiu Calin, Eastern Michigan University
Host: S Baskar
Title: Deep Learning for Stock Price Prediction: Convolutional Networks, Recurrent Neural Networks and Transformers
Time, day and date: 5:00:00 PM – 6:00:00 PM, Tuesday, August 04
Venue: Ramanujan Hall
Abstract: This presentation introduced modern deep learning methods for stock price prediction, emphasizing three major neural network architectures: Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and Transformers. We began by discussing the challenges posed by financial time series, including temporal dependence, nonlinearity, nonstationarity, and market noise, which make stock prediction substantially more difficult than standard regression problems. CNNs were presented as effective tools for extracting local temporal patterns through one-dimensional convolutions and pooling operations, while RNNs, particularly those based on LSTM and GRU cells, were shown to model long-term temporal dependencies using recurrent hidden states. Finally, Transformers were introduced as the current state-of-the-art architecture, employing self-attention mechanisms to capture global interactions among all observations in the input sequence while allowing highly parallel training. Throughout the presentation, practical implementations were discussed, including interactive programs for training these models on financial data, selecting hyperparameters, visualizing training losses, and forecasting future stock prices. Together, these architectures illustrate the evolution of deep learning methods from local feature extraction to sequential memory and, ultimately, to global attention mechanisms for financial time-series prediction.

Thesis Defence
Speaker: Chayan Karmakar, IIT Bombay
Host: Ravi Raghunathan
Title: Character Values at Special Elements in Complex Classical Groups
Time, day and date: 12:00:00 PM – 1:00:00 PM, Wednesday, August 05
Venue: Ramanujan Hall
Abstract: -

Colloquium
Speaker: Sutanu Roy, IIT Bombay
Title: On the path correspondences of quantum graphs
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, August 05
Venue: Ramanujan Hall
Abstract: In this talk we will describe a theory of paths for quantum graphs. In the spirit of the edge correspondence of Brannan–Hamidi–Ismert–Nelson–Wasilewski, we associate to each quantum graph a sequence of path correspondences modelling its quantum paths of every length. These assemble into a subproduct system over the centre of the underlying vertex algebra, and I will illustrate the construction on classical, complete, and trivial quantum graphs. This is based on a joint work in progress with Sourav Khatua.

Student Seminar
Speaker: Ankita Parashar, IIT Bombay
Host: Suman Kumar Sahoo
Title: From Symmetry to Representation theory
Time, day and date: 5:30:00 PM – 6:30:00 PM, Wednesday, August 05
Venue: Ramanujan Hall
Abstract: Symmetry appears everywhere in mathematics, from the rotations of a square and a sphere to the hidden structures behind Fourier analysis and number theory. Representation theory provides a powerful language to study these symmetries by translating groups into matrices and linear transformations. In this talk, we will explore how simple geometric symmetries lead to the idea of representations, and their surprising connections to Fourier series and modular forms, which are key objects in the two subjects: Fourier Analysis and Number theory.

Statistics and Probability Seminar
Speaker: Raghavendra Tripathi, NYU Abu Dhabi
Host: Parthanil Roy
Title: Efficient sampling from almost all monotone sets
Time, day and date: 11:00:00 AM – 12:00:00 PM, Thursday, August 06
Venue: Conference Room
Abstract: Sampling from the uniform measure on a monotone subset of Boolean hypercube arises in several contexts. For example, sampling a configuration in bond percolation with left to right crossing, or sampling a Knapsack. One popular and oft used method to sample from such sets is to restrict the random walk on the full hypercube to the monotone set. The random walk on the full hypercube mixes in $O(nlogn)$ time.Ding and Mossel (2014) conjectured that restricted chain on any monotone set with fixed positive measure also mixes in $O(nlogn)$ time and proved an upper bound $O(n^3)$. This was recently improved to $O(n^2)$ by proving a sharp Poincare inequality. We prove that for almost all monotone subsets, the log-Sobolev constant is order $n$ which in turn implies the Ding and Mossel’s conjecture for almost all monotone sets. This talk is based on joint work with Patrick O. Santos and Pierre Youssef.

Deep Learning in Finance – Lecture 2
Speaker: Prof. Ovidiu Calin, Eastern Michigan University
Host: S Baskar
Title: Machine Learning Methods for Financial Model Calibration
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, August 06
Venue: Ramanujan Hall
Abstract: This presentation introduced machine learning methods for the calibration of financial models, focusing on the recovery of unknown model parameters from observed market data. We began by formulating model calibration as an inverse problem in which parameters are estimated so that theoretical option prices closely match market prices. After reviewing the mathematical optimization framework, we showed how machine learning can replace repeated numerical optimization by directly learning the inverse mapping from market prices to model parameters, enabling fast real-time calibration. Samuelson's geometric Brownian motion model
was then presented as a fundamental example, together with its stochastic differential equation, probabilistic properties, and explicit maximum likelihood estimators for drift and volatility. To account for changing market conditions, we introduced sliding-window estimation, which produces time-dependent parameter estimates capable of identifying volatility clustering, market regimes, and trend changes. Finally, the limitations of constant-volatility models motivated the introduction of the Heston stochastic volatility model, whose additional parameters provide a more realistic description of financial markets. Throughout the presentation, interactive implementations demonstrated how modern machine learning techniques can efficiently estimate model parameters, visualize their evolution over time, and support practical applications in option pricing, hedging, and quantitative risk management.

Combinatorics Seminar
Speaker: Raghavendra Tripathi, NYU Abu Dhabi
Host: Parthanil Roy
Title: Counting the Erdos matrices
Time, day and date: 3:00:00 PM – 4:00:00 PM, Friday, August 07
Venue: Conference Room
Abstract: Marcus and Ree (1959) showed that any n x n doubly stochastic matrix satisfies
\[
\max_{P \in S_n} Trace(AP^T) \leq \|A\|_F^2,
\]
where $S_n$ is the set of permutation matrices of size $n$ and $\|A\|_F$ is the Frobenius norm of $A$. Erdos asked to characterize those matrices which saturate the above inequality. The set of all such matrices in dimension $3$ was obtained in 2023 by Bouthat, Mashregi and Morneau-Gurin. Surprisingly, there are only 6 such matrices in dimension 3. I subsequently proved that in each dimension there are only finitely many such matrices and it naturally leads to the question—can we find the asymptotic for the number of such matrices? The exact numbers are known only in dimensions upto 6. We show that the number of Erdos matrices in dimension n is asymptotically $2^{n^2}$. We further show that one can construct an Erdos matrix corresponding to every d-regular bipartite graphs.

Analysis Seminar
Speaker: Dr. Subhankar Mahapatra, IIT Ropar
Host: Sourav Pal
Title: De Branges Spaces of Entire Functions: Functional Model and Sampling Theory
Time, day and date: 4:15:00 PM – 5:15:00 PM, Friday, August 07
Venue: Online (https://meet.google.com/cqv-doha-gfc)
Abstract: https://drive.google.com/drive/folders/1XKWgYpYHmsRa6d-pyyHchxHEky-uQ9Ey

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.

Commutative Algebra seminar
Host: Tony J Puthenpurakal
Title: Intersection theorem in char p > 0.  III
Time, day and date: 11:30:00 AM – 12:30:00 PM, Monday, August 17
Venue: Room 215
Abstract: -

APS
Speaker: Sagnik Roy, IIT Bombay
Host: Saurav Bhaumik
Title: Orientation of Manifolds and Poincaré Duality
Time, day and date: 3:30:00 PM – 4:30:00 PM, Monday, August 17
Venue: Room 215
Abstract: This presentation explores the geometric and topological foundations of manifold orientation and its theoretical culmination in Poincaré Duality. It establishes orientability criteria using differential and topological frameworks, contrasting orientable manifolds like spheres with non-orientable spaces such as the Möbius strip and Klein bottle. By formalizing local orientations, the talk introduces the fundamental class and the cap product. These mathematical tools establish the canonical Poincaré Duality isomorphism for closed manifolds. Finally, the presentation extends this duality to non-compact manifolds by introducing singular cohomology with compact support alongside inductive proof techniques.

Seminar on the Plancherel measure
Speaker: Ravi Raghunathan, IIT Bombay
Title: On the support of the Plancherel measure (d'après Bernstein)
Time, day and date: 5:00:00 PM – 6:15:00 PM, Monday, August 17
Venue: Room 215
Abstract: -

APS
Speaker: Lavanya, IIT Bombay
Host: Shripad M. Garge
Title: Affine algebraic groups are linear
Time, day and date: 11:00:00 AM – 12:00:00 PM, Tuesday, August 18
Venue: Room 215
Abstract: -

Statistics and Probability seminar
Speaker: Soham Bonnerjee, University of Pennsylvania
Host: Debraj Das
Title: Fast Watermark Segmentation in LLM generated texts (and other application of epidemic change-points)
Time, day and date: 5:00:00 PM - 6:00:00 PM, Tuesday, August 18
Venue: Ramanujan Hall
Abstract: Epidemic change-points has seldom received attention in statistics community; however, it has  important, and somewhat surprising applications in critically important and modern problems. In this talk, we primarily focus on the "watermark segmentation" problem. With the growing use of large language models, concerns over content authenticity have spurred a variety of watermarking schemes. These schemes use secret keys to detect machine-generated text while remaining imperceptible to readers. Detection typically reduces statistical hypothesis testing for the presence of watermarks, a topic that is now well studied. In contrast, the finer grained task of localizing which segments of a text are watermarked is much less explored; existing approaches often lack scalability or guarantees robust to paraphrasing and post-editing. We bring a new perspective to this segmentation problem through the lens of epidemic change-points and, by exploiting this connection, propose WISER, a novel and computationally efficient watermark segmentation algorithm. We establish finite-sample error bounds and consistency for detecting multiple watermarked segments in a single text. Complementing these theoretical results, our extensive numerical experiments show that WISER outperforms state-of-the-art baseline methods, both in terms of computational speed as well as accuracy, on various benchmark datasets embedded with diverse watermarking schemes. Together, these theoretical and empirical results position WISER as an effective tool for watermark localization. Towards the end of the talk, we will briefly discuss spatial anomaly detection as another important application of the epidemic change-points in "space", and show how similar ideas lead to computationally fast algorithms with optimal detection-accuracy results for single and multiple patches. Based on joint works with Subhrajyoty Roy (Washington University at St. Louis), Sayar Karmakar (University of Florida), and George Michailidis (UCLA).

Partial Differential Equations seminar
Speaker: Aritro Pathak, visiting fellow, TIFR Mumbai
Host: Harsha Hutridurga
Title: Uniform domains with Ahlfors-David regular boundaries, and uniform rectifiability.
Time, day and date: 11:30:00 AM – 12:30:00 PM, Wednesday, August 19
Venue: Ramanujan Hall
Abstract: Uniform rectifiability is a quantitative notion of rectifiability that is closely related to the (L^2) boundedness of Riesz transforms. Uniform domains satisfy quantitative openness and quantitative path connectivity conditions. When the Ahlfors-David regular boundary of a uniform domain is uniformly rectifiable, one obtains solvability of the Dirichlet problem for the Laplacian with rough boundary data, as well as quantitative absolute continuity of harmonic measure. We will discuss some recent results in this active area at the interface of geometric measure theory and harmonic analysis. In particular, we will present a new result concerning the Weak Geometric Lemma and uniform rectifiability for Ahlfors-David regular sets whose complements are uniform domains.

Mathematics Colloquium
Speaker: Prof(Retd.). Sadanand D. Agashe, Electrical Engineering, IIT Bombay
Host: Sivaji Ganesh Sista
Title: New Formulas and Results for 3-Dimensional Vector Fields
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, August 19
Venue: Ramanujan Hall
Abstract: New formulas are derived for once-differentiable 3-dimensional fields, using the operator (x d/dx + y d/dy + z d/dz). This new operator has a property similar to that of the Laplacian operator; however, unlike the Laplacian operator, the new operator requires only once-differentiability. A simpler formula is derived for the classical Helmholtz decomposition. Orthogonality of the solenoidal and irrotational parts of a vector field, the uniqueness of the familiar inverse-square laws, and the existence of solution of a system of first-order PDEs in 3 dimensions are proved. New proofs are given for the Helmholtz Decomposition Theorem and the Divergence theorem. The proofs use the relations between the rectangular-Cartesian and spherical-polar coordinate systems. Finally, an application is made to the study of Maxwell’s equations.
Keywords: Spherical-Polar Coordinates, Helmholtz Decomposition, Divergence Theorem, Orthogonality, Maxwell’s Equations

Talk
Speaker: Arkadev Ghosh, Chennai Mathematical Institute (CMI)
Host: Saurav Bhaumik
Title: GIT quotients of Schubert varieties and Hessenberg varietiesmodulo a one-dimensional torus
Time, day and date: 5:00:00 PM – 6:00:00 PM, Wednesday, August 19
Venue: Online (https://meet.google.com/imq-fzbd-vez)
Abstract: In this talk, we present some results on Geometric Invariant Theory (GIT) quotients of Schubert varieties and Hessenberg varieties in flag varieties, for the action of a one-dimensional torus.

We begin with GIT quotients of Schubert varieties in partial flag varieties, for ample line bundles linearized with respect to a one-parameter subgroup dual to a simple root. We establish a criterion for the existence of semistable points. In the case of the Grassmannian Gr(r,n), we identify the unique minimal-dimensional Schubert variety admitting semistable points. Further, we describe the corresponding GIT quotient as a projective space of matrices, with the natural action of a product of two special linear groups arising as the semisimple part of a Levi subgroup.

We then extend these techniques to study the action of a higher-dimensional subtorus on certain Schubert varieties in Gr(r,n), determined by the peak set of the associated permutation. Under a natural divisibility condition on r and n, we describe the semistable locus explicitly and show that the GIT quotient is an iterated projective space bundle over a projective space.

In another direction, we study the action of a one-parameter subgroup on the irreducible components of semisimple Hessenberg varieties associated with a diagonal matrix having two distinct eigenvalues. We show that, for suitable line bundles, the resulting GIT quotients are isomorphic to homogeneous fiber bundles over a flag variety whose fibers are products of projective lines. Furthermore, we describe the space of global sections of the descended line bundle as a module over a suitable Levi subgroup.

Topology seminar
Speaker: Udit Mavinkure, IIT Bombay
Host: Rekha Santhanam
Title: Quasicategories vs. Segal Spaces, Part 3
Time, day and date: 2:30:00 PM – 3:30:00 PM, Thursday, August 20
Venue: Room 215
Abstract: This talk is the third installment in a four-part expository series on higher category theory. The goal of the series is to establish the following result of Joyal and Tierney: the Joyal model structure for quasicategories and the Rezk model structure for complete Segal spaces are Quillen equivalent. (NB: Newcomers are welcome; background from the April and May talks will not be assumed!)

We will begin with a brief recap of quasicategories: their definition, and how they generalize ordinary categories. We will then discuss the Joyal model structure, and its specific properties that enable a straightforward description of its simplicial completion, à la Cisinski.

PDE and Numerical Analysis seminar
Speaker: Ketan Savla, University of Southern California
Host: Harsha Hutridurga
Title: LQR for finite extent linear evolution PDEs.
Time, day and date: 4:00:00 PM – 5:00:00 PM, Thursday, August 20
Venue: Ramanujan Hall
Abstract: We consider the linear quadratic regulator (LQR) problem for linear evolution PDEs on a bounded spatial interval, with control entering as an additive forcing term and arbitrary boundary data. Classical frequency-domain approaches to LQR for PDEs rely on the real-frequency Fourier transform, and work cleanly only on unbounded domains or under homogeneous boundary conditions; applied naively on a finite interval, they produce a control law that depends on future, unspecified boundary values. We resolve this using the unified transform of Fokas, which extends the Fourier transform on a bounded domain to complex frequencies. Decoupling the PDE in this complex frequency variable and solving the resulting family of finite-dimensional LQR problems yields a closed form control law; deforming the associated frequency integrals onto suitable contours in the complex plane then eliminates all dependence on the unknown boundary data. For the reaction-diffusion equation, we show that the resulting integral representation is equivalent to a state-feedback law whose kernel splits into a Toeplitz part, as on the whole line, and a new Hankel part generated purely by the boundary.

Algebraic groups seminar
Speaker: Sabyasachi Dhar, IIT Bombay, Mumbai
Host: Shripad Garge
Title: Iwahori-Hecke Algebras. III
Time, day and date: 5:00:00 PM - 6:30:00 PM, Thursday, August 20
Venue: Room No .215
Abstract: We continue with the study of the Iwahori-Hecke algebras. We will be doing some examples in this lecture.

Student Seminar
Speaker: Aditya Dwivedi, IIT Bombay
Host: Suman Kumar Sahoo
Title: The Algebra of Magic Squares
Time, day and date: 3:30:00 PM – 4:30:00 PM, Friday, August 21
Venue: Ramanujan Hall
Abstract: Magic squares have been studied by thinkers for centuries, often appearing in classical texts across cultures, such as the Lo Shu square, Buduh square, or the bhadra chaturashra. The problem of counting magic squares was also pursued by many thinkers over centuries, often leading to calculations in specific cases (see Al-Ashabb et al., Mandadi et al., Mattingly et al., Dvivedi et al.).
But what happens when we move beyond these specific historical constructions and ask a generalised question: exactly how many n x n magic squares exist for a given line sum r?
This talk explores the surprising bridge between this ancient combinatorial problem and modern commutative algebra. After reviewing the elementary 1 x 1 and 2 x 2 matrices, we will introduce the celebrated Anand-Dumir-Gupta conjectures. Using the Birkhoff-von Neumann theorem, we will construct a specific subring generated by permutation matrices. By analysing the Hilbert series of this ring, we arrive at the elegant final result: the number of n x n magic squares is simply a polynomial in the line sum r.

Number Theory seminar
Speaker: Dr. Sourabh Das, IIT Bombay
Host: Keshav Aggarwal
Title: An effective version of Chebotarev’s density theorem
Time, day and date: 11:30:00 AM – 12:30:00 PM, Monday, August 24
Venue: Ramanujan Hall
Abstract: Chebotarev’s density theorem asserts that the prime ideals are equidistributed among the conjugacy classes of the Galois group of any normal extension of number fields. An effective version of this theorem was first established by Lagarias and Odlyzko in 1977. In this talk, we present an explicit refinement of their statement that applies to all non-rational fields, with every implicit constant expressed explicitly in terms of the field invariants. Additionally, we provide a sharper bound for extensions of sufficiently small degree.

We describe the main analytic tools that lead to our results, including an explicit formula for a smoothed prime ideal counting function, zero-free regions for Dedekind zeta functions, and precise bounds for sums over the non trivial zeros of Dedekind zeta-functions. We further explain how these ingredients improve upon and differ from previous approaches in the literature.

This is joint work with Habiba Kadiri and Nathan Ng (University of Lethbridge, Canada). The preprint is available on arXiv at https://arxiv.org/abs/2508.09480.

Statistics/Probability Lecture Series
Speaker: Prof. Arindam Chatterjee, ISI Delhi
Host: Debraj Das
Title: Stein's method and its application to networks – Lecture 1
Time, day and date: 12:00:00 PM – 1:00:00 PM, Tuesday, August 25
Venue: Ramanujan Hall
Abstract: https://drive.google.com/file/d/1toQxgC_BAP_N0cVQ3FZkzD7Ta-f4D5U9/view?usp=sharing

Statistics/Probability Lecture Series
Speaker: Prof. Arindam Chatterjee, ISI Delhi
Host: Debraj Das
Title: Stein's method and its application to networks – Lecture 2
Time, day and date: 5:00:00 PM – 6:00:00 PM, Tuesday, August 25
Venue: Ramanujan Hall
Abstract: https://drive.google.com/file/d/1toQxgC_BAP_N0cVQ3FZkzD7Ta-f4D5U9/view?usp=sharing

Statistics/Probability Lecture Series
Speaker: Prof. Arindam Chatterjee, ISI Delhi
Host: Debraj Das
Title: Stein's method and its application to networks – Lecture 3
Time, day and date: 12:00:00 PM – 1:00:00 PM, Thursday, August 27
Venue: Ramanujan Hall
Abstract: https://drive.google.com/file/d/1toQxgC_BAP_N0cVQ3FZkzD7Ta-f4D5U9/view?usp=sharing

Talk
Speaker: Dr. Malavika
Host: Kummari Mallesham
Title: Distribution properties of some prime-indexed sequences, and exponential sums
Time, day and date: 3:00:00 PM – 4:00:00 PM, Thursday, August 27
Venue: Online (https://meet.google.com/csu-bknh-kkc)
Abstract: https://drive.google.com/file/d/1TlEUxi-1UOpnKF1Q_FfX645OJcIbjvnW/view?usp=sharing

Special Colloquium
Speaker: Jean-Marc Schlenker, University of Luxembourg
Host: Sanjoy Pusti
Title: Polyhedra inscribed in a quadric in Euclidean space
Time, day and date: 3:45:00 PM - 4:45:00 PM, Thursday, August 27
Venue: Ramanujan Hall
Abstract: Steiner asked in 1832: what are the possible combinatorial types of polyhedra with vertices on a quadric in R^3? We will review recent results on this question, as well as questions that are still open. The main results are based on the geometry of ideal polyhedra in the 3-dimensional hyperbolic or anti-de Sitter space, or in more exotic geometric spaces that we will also describe. Based on joint work with Hao Chen, Jeff Danciger and Sara Maloni.

Statistics/Probability Lecture Series
Speaker: Prof. Arindam Chatterjee, ISI Delhi
Host: Debraj Das
Title: Stein's method and its application to networks – Lecture 4
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, August 27
Venue: Ramanujan Hall
Abstract: https://drive.google.com/file/d/1toQxgC_BAP_N0cVQ3FZkzD7Ta-f4D5U9/view?usp=sharing

IPDF progress seminar
Speaker: Dr. Manabendra Giri, IIT Bombay
Host: Sutanu Roy
Title: Quantum Unitary Groups with Complex Deformation Parameters
Time, day and date: 4:30:00 PM – 5:30:00 PM, Friday, August 28
Venue: Ramanujan Hall
Abstract: In this talk, I want to discuss a family of quantum unitary groups associated with complex deformation parameters. I begin with the construction of the quantum unitary group $U_{q,\Phi}(n)$, extending the construction of Zhang and Zhao for $n=2$ to higher dimensions. I show that $U_{q,\Phi}(n)$ admits the structure of a compact quantum group in the sense of Woronowicz.

I then focus on the case $n=3$ and study the irreducible $*$-representations of the corresponding $C^*$ algebra $C(U_{q,\Phi}(3))$.It is possible to describe these representations in terms of irreducible representations of the rotational $C^*$-algebra generated by three unitaries.

Finally, I consider the crystalized algebra $C(U_{0,\Phi}(3))$ and investigate its $*$-irreducible representations.

Seminar on the Plancherel measure
Speaker: Ravi Raghunathan, IIT Bombay
Title: On the support of the Plancherel measure (d'après Bernstein)
Time, day and date: 5:00:00 PM – 6:15:00 PM, Monday, August 31
Venue: Ramanujan Hall
Abstract: -