Algebra Seminar
Speaker: Neena Gupta, ISI Kolkata
Host: Manoj Kumar Keshari
Title: On Affine Forms
Time, day and date: 11:30:00 AM – 12:30:00 PM, Wednesday, July 01
Venue: Ramanujan Hall
Abstract: Let k be a field and A be a k-algebra.  A is said to be an A^n-form over k if there exists a field extension L of k such that A\otimes_k L is isomorphic to a polynomial ring in n indeterminates over L. A is said to be a separable A^n-form if L can be taken to be a separable extension over k. It is an important question when an A^n form over k is necesarily a polynomial ring. It is well known that separable A^1 and A^2 forms are necessarily polynomial rings, and that there exist examples of A^n-forms over non-perfect fields, which are not polynomial rings.

In this talk we shall discuss a few recent developments on this problem. It will be mainly based on joint works with A.K. Dutta, Animesh Lahiri and Parnashree Ghosh and an independent work of Debojyoti Saha.

Combinatorics seminar
Speaker: Dhruv Mubayi, University of Illinois, Chicago
Host: Niranjan Balachandran
Title: Pentagons in triple systems
Time, day and date: 11:30:00 AM - 12:45:00 PM, Tuesday, July 07
Venue: Ramanujan Hall
Abstract: We consider the question of determining the minimum number of pentagons in a linear triple system with many edges and show some connections to number theory, graph theory, theoretical computer science, and geometry. This is joint work with Jozsef Solymosi

Algebra Seminar
Speaker: Chayan Karmakar, IIT Bombay
Host: Shripad M. Garge
Title: lectures on Digne-Michel
Time, day and date: 4:00:00 PM – 5:30:00 PM, Wednesday, July 08
Venue: Room 105
Abstract: -

Topology Seminar
Speaker: Sumanta Das, IIT Bombay
Host: Rekha Santhanam
Title: Mapping Class Groups: Teichmüller Space and Representation Varieties
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, July 09
Venue: Room 215
Abstract: In previous talks, we discussed Teichmüller space from the viewpoint of complex structures. In this talk, we will adopt a representation-theoretic approach. We will first establish the natural bijection between the Teichmüller space of a surface and the space of Fuchsian representations of its fundamental group, up to conjugation.
Motivated by this, we will consider the variety of representations into a Lie group and discuss its geometric interpretation in terms of conjugacy classes and flat principal bundles.

Real Algebra Seminar
Speaker: Amrutha Ruddarranu
Host: Manoj Kumar Keshari
Title: A basic theory of power series
Time, day and date: 10:00:00 AM – 11:15:00 AM, Friday, July 17
Venue: Room 105
Abstract: -

Real Algebra Seminar
Speaker: Niladri Sekhar Patra, IIT Bombay
Host: Niladri Sekhar Patara
Title: Geometry of linear matrix inequality
Time, day and date: 11:30:00 AM – 12:45:00 PM, Friday, July 17
Venue: Room 105
Abstract: -

Real Algebra Seminar
Speaker: Amrutha Ruddarraju, BITS Hyderabad
Host: Manoj Keshari
Title: Power Series: Noether's projection lemma
Time, day and date: 10:30:00 AM - 11:30:00 AM, Monday, July 20
Venue: Room No .105
Abstract: Noether's projection lemma for convergent power series will be proved.

Real Algebra Seminar
Speaker: Niladri Sekhar Patra, IIT Bombay
Host: Manoj Keshari
Title: Geometry of LMI: Interlacing
Time, day and date: 11:40:00 AM - 12:40:00 AM, Monday, July 20
Venue: Room No .105
Abstract: Interlacing polynomials will be discussed.

Algebraic Geometry seminar
Speaker: Mohit Upmanyu
Host: Sudarshan R. Gurjar
Title: Cancellation property for Briskon-Pham varieties.
Time, day and date: 11:30:00 AM – 12:30:00 PM, Tuesday, July 21
Venue: Ramanujan Hall
Abstract: Let a_1,..., a_n be integers greater than 2. Then the variety defined by x_1^{a_1} + ... + x_n^{a_n} = 0, is called a Briskon-Pham variety. In this talk we will prove that the following statement :

Let X and Y be Briskon Pham varieties. Let X×Z and Y×Z be isomorphic for some variety Z. Then X is isomorphic to Y.

Real Algebra Seminar
Speaker: Amrutha Ruddarraju, BITS Hyderabad
Host: Manoj Keshari
Title: Power Series: Noether's projection lemma
Time, day and date: 10:30:00 AM - 11:30:00 AM, Wednesday, July 22
Venue: Room No .105
Abstract: Abhyankar and Ruckert's parametrization for convergent power series will be proved.

Real Algebra Seminar
Speaker: Niladri Sekhar Patra, IIT Bombay
Host: Manoj Keshari
Title: Geometry of LMI: Interlacing
Time, day and date: 11:40:00 AM - 12:40:00 AM, Wednesday, July 22
Venue: Room No .105
Abstract: Hyperbolic curves will be discussed.

Algebraic groups seminar
Speaker: Shripad M. Garge, IIT Bombay
Title: Composition algebras and Cayley-Dickson doubling
Time, day and date: 4:00:00 PM - 5:30:00 PM, Wednesday, July 22
Venue: Room No .105
Abstract: Composition algebras are finite dimensional real algebras endowed with a positive-definite multiplicative quadratic form. We see the classification of such algebras using the Cayley-Dickson doubling process.

Special Colloquium
Speaker: Tathagata Basak, Iowa State University
Host: Niranjan Balachandran
Title: Building hyperbolic lattices
Time, day and date: 12:00:00 PM - 1:00:00 PM, Tuesday, July 28
Venue: Ramanujan Hall
Abstract: Given a graph D such that the second largest eigenvalue of its adjacency matrix is a positive integer, one can define an integer lattice L of signature (g, 1) such that the symmetries of D act on L. This kind of construction goes back to at least [Neumaier and Seidel, 1983] and is analogous to building a root lattice from a Dynkin diagram.

The aim of this talk is to illustrate that this kind of construction produces interesting Lorentzian lattices and interesting complex reflection groups in U(g, 1). In particular, an example in U(4, 1) is related to the moduli space of cubic surfaces, and an example in U(13, 1) is conjecturally related to the monster simple group.

We’ll try to describe the new information we obtain about the moduli space of cubic surfaces from this point of view.

Some of this is joint work with Daniel Allcock and Eduard Looijenga and some of this is joint work with Jon McCammond.

Probability Seminar
Speaker: Sunita Rani, School of Basic Sciences (Mathematics), IIT Bhubaneswar
Host: Koushik Saha
Title: Spectrum of Inter-Correlated Random Matrices
Time, day and date: 5:00:00 PM - 6:00:00 PM, Tuesday, July 28
Venue: Online (meet.google.com/gdd-yimr-gds)
Abstract: In this talk, we study the central limit theorem (CLT) for linear eigenvalue statistics (LES) of several classes of random matrices for different types of test functions. We establish CLTs for various structured random matrix ensembles, including complex- and real-valued centrosymmetric matrices. For centrosymmetric matrices, we also develop combinatorial techniques to compute the asymptotic moments and the variance of the limiting Gaussian distribution. Furthermore, we establish the CLT for LES of correlated non-Hermitian block matrices, where the limiting fluctuations depend on the correlation structure of the matrix entries. All these results are obtained under suitable bounded moment assumptions.

We then extend the analysis to random matrices with exploding moments, where the moments of the matrix entries grow with the matrix dimension. In this setting, we study the asymptotic behavior and the CLT for normalized traces of several matrix models, including elliptic matrices, non-Hermitian matrices, correlated non-Hermitian block matrices, centrosymmetric matrices, and circulant matrices.

Real Algebra Seminar
Speaker: Ruddarraju Amrutha, BITS Hyderabad
Host: Manoj Keshari
Title: Convergent power Series : Nagata's Jacobian Criteria
Time, day and date: 11:00:00 AM - 12:30:00 PM, Wednesday, July 29
Venue: Room No .215
Abstract: Nagata's Jacobian Criteria will be discussed.

Presynopsis seminar
Speaker: Unnati Nigam, IIT Bombay
Host: Radhendushka Srivastava
Title: Quasi-Periodic Gaussian Processes: Statistical Foundations, Predictive Control, and Deep Generative Models
Time, day and date: 11:30:00 AM – 12:30:00 PM, Wednesday, July 29
Venue: Ramanujan Hall
Abstract: Quasi-periodic signals arise naturally in a wide range of applications, including engineering systems, robotics, and biomedical data, yet existing modeling approaches often lack either computational scalability or the flexibility to capture complex temporal structures. This talk presents a unified framework based on Quasi-Periodic Gaussian Processes (QPGPs) that addresses these challenges through a dynamic equation formulation. The framework enables efficient modeling and prediction of quasi-periodic processes and is subsequently applied to predictive Iterative Learning Control, where it is shown to improve trajectory tracking in both simulation and real robotic experiments. The talk further introduces an extension to heterogeneous quasi-periodic processes for modeling non-stationary disturbances with theoretical performance guarantees and concludes by demonstrating how the same mathematical framework can be incorporated into deep generative models through a QPGP-constrained Variational Autoencoder for structured latent representation learning. The presentation will highlight the key mathematical developments, theoretical results, and experimental validations that form the main contributions of my thesis.

Statistics and Probability Seminar
Speaker: Dr. Koushik Bera, IIT Guwahati
Host: Radhendushka Srivastava
Title: Statistical and Deep Learning Approaches to Volatility Forecasting in Financial Time Series
Time, day and date: 3:00:00 PM – 4:00:00 PM, Wednesday, July 29
Venue: Online (https://meet.google.com/zac-sksd-szo)
Abstract: Volatility measures the time-varying uncertainty in financial markets and plays a central role in risk assessment, portfolio allocation, and investment decisions. Its forecasting is challenging because financial time series are noisy, non-stationary, heteroscedastic, and driven by dynamics operating at different time scales. In this talk, I will discuss statistical and deep learning approaches developed to address these features. I will first describe how decomposition methods can be combined with Realized GARCH models to capture multi-scale volatility dynamics using high-frequency information. I will then present a leakage-aware forecasting framework based on optimized Variational Mode Decomposition and state-space learning, designed to avoid the use of future information. Finally, I will discuss heteroscedastic deep learning models that integrate GARCH-type volatility signals with extended LSTM architectures. The usefulness of these forecasts will also be examined through Value-at-Risk, stress testing, and volatility-based portfolio optimization. In particular, I will discuss how improved volatility forecasts can be translated into dynamic covariance estimates and used in minimum-variance and maximum-Sharpe-ratio portfolio strategies. This provides a way to evaluate not only statistical forecasting accuracy but also the economic relevance of the proposed models.

Geometry and Topology seminar
Speaker: Rivu Bardhan, Shiv Nadar University
Host: Anusha Mangala Krishnan
Title: Higher Genus Lorentzian Chen–Gackstatter Surfaces and Angel Surfaces
Time, day and date: 3:00:00 PM - 4:00:00 PM, Wednesday, July 29
Venue: Online. (https://meet.google.com/xmd-uxyq-rxp)
Abstract: Please see attachment. (https://drive.google.com/open?id=1XP3cx7lSC5QoFq6oBZGScVCNjdxe4U_l)

Algebraic groups seminar
Speaker: Hariom Sharma, IIT Bombay, Mumbai
Host: Shripad Garge
Title: Iwahori Hecke algebras
Time, day and date: 4:00:00 PM - 5:30:00 PM, Wednesday, July 29
Venue: Room No .105
Abstract: We continue studying Digne Michel with the study of Iwahori-Hecke algebras.

Mathematics Colloquium
Speaker: Sagnik Nandy, Ohio State University
Host: Parthanil Roy
Title: Data Integration in Single-Cell Genomics: Message Passing for Multimodal Fusion
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, July 29
Venue: Ramanujan Hall
Abstract: Modern single-cell technologies increasingly measure multiple modalities — transcriptome, epigenome, proteome — on the same cell, but each view remains noisy and heterogenous. In this talk, we shall explore different ways to combine information in such multimodal datasets. In particular, we shall develop a message passing based framework for principled multimodal fusion, built on empirical Bayes denoising: shrinking noisy estimates toward a prior learned directly from the data.

I will first present OrchAMP, an Approximate Message Passing-based method that jointly denoises multiple modalities by estimating a shared prior on cell signatures, achieving Bayes-optimal signal recovery without collapsing weak-signal modalities the way naive joint SVD does. I will then discuss DAIF, which extends this framework to supervised prediction by adaptively choosing the fusion granularity — bridging early and late fusion in a data-driven way — and show on TEA-seq and TCGA-BRCA data that this adaptivity translates into real predictive gains over existing pipelines (MOFA+, Multigrate, JAFAR, Cooperative Regression).
This talk is based on joint works with Zongming Ma, Samriddha Lahiry, Subhabrata Sen and Pragya Sur.

Topology seminar
Speaker: Lekha Das, IIT Bombay
Host: Rekha Santhanam
Title: Admissible sets and N_infinity operads
Time, day and date: 2:30:00 PM – 3:30:00 PM, Thursday, July 30
Venue: Room 215
Abstract: We discuss the admissible sets for linear isometries operad and little disk operad, and we explain the relationship between them.

Statistics and Probability seminar
Speaker: Sagnik Nandy, Ohio State University
Host: Parthanil Roy
Title: How does limma-trend work? An empirical partially Bayes perspective
Time, day and date: 4:00:00 PM - 5:00:00 PM, Thursday, July 30
Venue: Ramanujan Hall
Abstract: In high-throughput biology, we often want to test thousands of genes or proteins at once, but each one is measured with very few samples — so noise estimates are unreliable, and standard tests find almost nothing. A widely used fix, called limma-trend, works by "borrowing strength" across all the measured units: instead of trusting each unit's own noisy variance estimate, it shrinks that estimate toward a shared trend learned from the whole dataset. This talk explains what limma-trend is actually doing statistically, why it works, and when it can fail. We then introduce two more flexible versions of the method that adapt automatically to the data rather than assuming a fixed mathematical form and prove that they reliably control the false discovery rate — even when the underlying trend is estimated imperfectly. On real cancer genomics and proteomics datasets, these new methods substantially increase the number of genuine findings recovered, while avoiding a bias problem that affects several existing tools. (This talk will be based on a joint work with Wanyi Ling and Nikos Ignatiadis.)

Real Algebra seminar
Speaker: Niladri Sekhar Patra, IIT Bombay
Host: Manoj Keshari
Title: Geometry of LMI - hyperbolic curves
Time, day and date: 11:00:00 AM - 12:30:00 PM, Friday, July 31
Venue: Room No .215
Abstract: Hyperbolic curves will be discussed.

Talk
Speaker: Dr. Manish Chaurasia, NISER
Host: Chandan Biswas
Title: Certain Schrödinger Equations and Patterns in Sparse Sets via Harmonic Analysis
Time, day and date: 4:00:00 PM – 5:00:00 PM, Friday, July 31
Venue: Online (https://us06web.zoom.us/j/83654639378?pwd=YRbY1LmsxJ4587M2KH0oJNjLixSzeT.1
Meeting ID: 836 5463 9378
Passcode: 748925)
Abstract: The talk consists of two parts. In the first part, we shall discuss an uncertainty principle in connection with the harmonic oscillator Schrödinger equation and the well-posedness of inhomogeneous nonlinear Schrödinger equations in Lorentz–modulation spaces. In the second part, we shall discuss patterns in sparse sets from the perspective of harmonic analysis.