Title: Norm of Composition Operators with Affine Symbols
Speaker: Ms. Preeti Kumari
Abstract: It is well known that composition operators are bounded on the Hardy Hilbert space of the unit disc; however, their norms are not explicitly known in general. In this talk, we review the computation of the norm of composition operators induced by affine maps. The argument uses adjoint calculations together with the Denjoy-Wolff theorem for the unit disc.

Date: 27 March 2026
Time: 5:00 PM
Venue: FB567

Title: Introduction to Mapping Class Group
Speaker: Mr. Souvik Pal
Abstract: The mapping class group of a surface describes the symmetries of the surface up to isotopy and plays an important role in low-dimensional topology. This talk gives a short introduction to mapping class groups of surfaces. We begin by discussing some basic notions about surfaces, homotopy, and isotopy, which motivate the definition of the mapping class group. After introducing the definition, several simple examples are considered to illustrate the idea. Some important generators of mapping class groups, particularly Dehn twists, are also discussed. Finally, we briefly outline Thurston's classification of surface diffeomorphisms into periodic, reducible, and pseudo-Anosov types, and mention some extensions of these ideas to non-orientable surfaces.

Date: 20 March 2026
Time: 5:00 PM
Venue: FB567

Title: Large Solutions: Laplacian vs Fractional Laplacian
Speaker: Mr. N N Dattatreya
Abstract: We consider the notion of a large, or boundary blow-up, solution in two different settings: the classical Laplacian and the fractional Laplacian. We compare these two frameworks and show that, while the theory for the Laplacian is relatively well understood and structurally rigid, the situation for the fractional Laplacian is far richer and more delicate. We also explore how the nonlocal nature of the operator fundamentally influences the theory in the latter case.

Date: 20 February 2026
Time: 5:00 PM
Venue: FB567

Title: How the Grassmannian Lives in Projective Space
Speaker: Archita Gupta
Abstract: The Grassmannian is the set of all $d$-dimensional subspaces of a vector space. It generalizes projective space, which is the collection of lines in a vector space. In this talk, we introduce the exterior algebra framework underlying Plücker coordinates and use it to prove that this construction embeds the Grassmannian as a projective variety.

Date: 13 February 2026
Time: 5:00 PM
Venue: FB567

Title: A brief introduction to homological algebra
Speaker: Dr. Abhishek Das
Abstract: Homology and cohomology are fundamental tools that appear in many areas of mathematics, including algebraic topology, representation theory, algebraic geometry, number theory etc. This talk aims to introduce these objects from an abstract and categorical viewpoint that unifies the general theory. We begin by motivating homology as a way to measure the failure of exactness, leading naturally to chain complexes and derived functors in abelian categories. Finally, we indicate by illustrative examples how they appear in different branches of mathematics.

Date: 06 February 2026
Time: 5:00 PM
Venue: FB567

Title: Variational Multiscale Finite Element Method for Cardiovascular Flows in Complex Arterial Domains
Speaker: Dr. Dipak Kumar Sahoo
Abstract: Click Here

Date: 30 January 2026
Time: 5:00 PM
Venue: FB567

Title: A pedagogical overview of Hamiltonian Monte Carlo
Speaker: Mr. Arghya Mukherjee
Abstract: Click Here

Date: 16 January 2026
Time: 5:00 PM
Venue: FB567

Title: Group Measure Space Construction
Speaker: Mr. Silambarasan C
Abstract: The group measure space construction provides a natural link between group actions and operator algebras. Given a discrete countable group G acting in a measure-preserving way on a probability space, one can form the crossed product, called the group measure space von Neumann algebra. This construction encodes both the dynamics of the group action and the structure of the measure space. In this talk, we outline the main ideas of this construction and show how it can be used to obtain a type II1 factor.

Date: 14 November 2025
Time: 5:00 PM
Venue: FB567

Title: An introduction to the Kobayashi Distance and its Geometric properties
Speaker: Mr. Chandan Sur
Abstract: The Kobayashi distance was introduced by Shoshichi Kobayashi (1967) as a natural generalization of the Poincaré distance on the unit disc, D to an arbitrary complex manifolds. The motivation arose from the classical Schwarz–Pick lemma, which states that any holomorphic map f:D→D is distance-decreasing with respect to the Poincaré metric.Kobayashi sought to define an intrinsic pseudodistance on complex manifolds, that preserves this contractive property for all holomorphic maps, thereby extending the notion of hyperbolic geometry from the unit disc to general complex spaces.

In this talk, we will introduce the construction of the Kobayashi distance, discuss its key properties such as invariance and contractivity under holomorphic maps and compute it explicitly on few classical domains like the unit disc, unit ball.

We will also see few central applications and consequences, including a direct proof of the Schwarz lemma in the language of Kobayashi distance and a short proof of Liouville’s theorem using contractivity of the Kobayashi distance.
Date: 04 November 2025
Time:  5:00 PM
Venue: FB567

Title: Linear maps preserving products of involutions
Speaker: Dr. Tejbir Lohan
Abstract: Linear preserver problems concern the characterization of linear maps on matrix spaces that leave certain functions, subsets, or relations invariant, while matrix decomposition problems focus on expressing matrices as products of matrices with special structural properties. Both areas are historically rich and remain active fields of research in matrix theory.

A classical topic in matrix analysis is the decomposition of matrices into products of involutions--square matrices whose square is the identity. It is well known that a matrix is a product of two involutions if and only if it is similar to its inverse, and that any product of involutions can be written as a product of at most four. This connection naturally leads to a fundamental linear preserver problem: characterizing linear maps on matrices that preserve products of involutions.

In this talk, we will begin by introducing linear preserver problems through illustrative examples and reviewing classical results on matrix decompositions into products of involutions. We will then present a characterization of bijective linear maps that preserve matrices expressible as products of two, three, or four involutions. This is joint work with Chi-Kwong Li and Sushil Singla.
Date: 28 October 2025
Time:  5:00 PM
Venue: FB567

Title: XEventNet: Extreme Weather Event Prediction using Convolutional Neural Networks and In Situ Visualization
Speaker: Mr. Muzafar Ahmad Wani
Abstract: Extreme weather phenomena such as cyclones, torrential rainfall, snow storms, flash floods and landslides pose serious threat to living beings and property all over the world. An accurate and early prediction system for these extreme events may minimize the loss of life and property. However, this requires an online prediction system integrated with the weather simulation model for faster prediction such that low I/O bandwidth does not hinder performance. In this talk we present an _in situ_ framework, XEventNet, that integrates weather simulation, deep learning-based prediction, and visualization. XEventNet predicts extreme events in real-time while the simulation is running using a Convolutional Neural Network (CNN). XEventNet is trained and tested on 400 events (extreme and non-extreme). Data is streamed online from XEventNet simulation processes to prediction processes for parallel inference. XEventNet uses the prediction values with high confidence to selectively transfer sub-domains of the large parent simulation domain. We use ADIOS2 for parallel data transfers via memory between groups of processes. This helps in timely prediction and visualization of critical weather events despite large volume of simulation data. We performed weather simulations at 9 km resolutions, thereby producing gigabytes of data per time step. XEventNet is able to classify four extreme events at real-time and visualize the same. We achieved an average prediction accuracy of 90.25% for all extreme events using a single CNN model. We ran weather simulations on up to 512 processes and parallel predictions on up to 64 processes, thereby streaming gigabytes of data in parallel within seconds. This was possible due to efficient data transfer and process mapping. Furthermore, our selective data transfer for visualization resulted in more than 70% reduction in data size, thereby improving the end-to-end simulation-prediction-visualization times.
Date: 21 October 2025
Time:  5:00 PM
Venue: FB567

Title: On Bergman spaces
Speaker: Mr. Kanha Behera
Abstract: Click Here
Date: 14 October 2025
Time:  5:00 PM
Venue: FB567

Title: Conditionally Unbiased Estimation of a Random Estimand
Speaker: Mr. Yogesh Katariya
Abstract: In many multistage designs in agriculture, manufacturing, and clinical trials, the parameter of interest is not fixed in advance. Instead, it depends on data-driven selection rules, resulting in a random estimand whose value is determined by the observed sample rather than being fixed a priori. Standard estimators, such as the sample mean or MLE, suffer from selection bias in these settings. To address this issue, in this talk, we study a framework for conditionally unbiased estimation of a random estimand, where unbiasedness is defined with respect to the conditional distribution given the selection event. Specifically, we construct the uniformly minimum variance conditionally unbiased estimator (UMVCUE) for Normal means, assuming a known common variance. These results contribute to the statistical theory of post-selection inference. If time permits, we will also discuss extensions to the case of an unknown common variance.
Date: 09 October 2025
Time:  5:00 PM
Venue: FB567

Title: An Introduction to the Mean Field Game system (MFGs)
Speaker: Mr. Govind Kureel
Abstract: In this talk, we will explore the Mean Field Game system, which consists of two coupled partial differential equations(PDEs) with specified initial and terminal conditions. The first equation is known as the Hamilton-Jacobi-Bellman equation, while the second is the Fokker-Planck equation. We will begin by examining a real-world example where this system is applicable, followed by a rigorous mathematical discussion concerning the existence and uniqueness of it's solutions. The Mean Field Game framework has broad applications, including traffic flow, crowd dynamics, epidemic modeling, and financial markets.
Date: 25 September 2025
Time:  5:00 PM
Venue: FB567

Title: Interpolation in Banach Spaces : The K-Method
Speaker: Dr. Vivek Sahu (FARE-IPDF, IITK)
Abstract: In this seminar I will present the basic ideas of abstract interpolation theory using the K-method. I will explain how to construct interpolation spaces and the related interpolation operators in a simple manner. To make the ideas clear, I will give examples, such as the interpolation space between bounded continuous functions and their derivative. If time permits, I will also discuss interpolation between Lebesgue spaces and Sobolev spaces. The goal is to show how interpolation naturally connects different function spaces, which is useful in analysis and partial differential equations.
Date: 11 September 2025
Time:  5:00 PM
Venue: FB567

Title: An Introduction to Topological Complexity
Speaker: Dr. Manas Mandal (IPDF, IITK)
Abstract: How hard is it to plan motion in a continuous way? This question lies at the heart of topological complexity, a concept introduced by M. Farber. It assigns a numerical homotopy invariant to a space, capturing the unavoidable number of discontinuities in any motion planning algorithm. In this talk, we will begin with the basic concepts of algebraic topology, and then introduce the definition of topological complexity in an accessible way. Finally, we will work through a few concrete examples.
Date: 04 September 2025
Time:  5:00 PM
Venue: FB567

Title: Isoperimetric inequality for hyperbolic polygons and its applications
Speaker: Dr. Bhola Nath Saha (FARE - IPDF, IITK)
Abstract: The classical isoperimetric problem originated from practical considerations in antiquity, and it asks: among all closed curves in the Euclidean plane with a fixed perimeter, which one encloses the largest area? In this talk, we discuss an analogue of this question in hyperbolic geometry, focusing on isoperimetric inequalities for hyperbolic polygons. In particular, we establish that among all hyperbolic polygons with a given number of sides and fixed perimeter, the regular polygon encloses the maximum area. We will also discuss some applications of this inequality.
Date: 28 August 2025
Time:  5:00 PM
Venue: FB567

Title: RIEMANN–ROCH THEOREM
Speaker: Dr. Sabyasachi Dhar (FARE - IPDF, IITK)
Abstract: The Riemann–Roch theorem is a foundamental result in mathematics, specially in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeros and poles. It relates the geometry of a connected compact Riemann surface with the topological genus of the surface. Initially proved as Riemann’s inequality by Riemann, the theorem reached its definitive form for Riemann surfaces after the work of Riemann’s student Roch. It was later generalized to algebraic curves, to higher-dimensional varieties and beyond. In this talk, we discuss the algebro-geometric version of Riemann–Roch theorem.
Date: 21 August 2025
Time:  5:00 PM
Venue: FB567

Title: The Firefly Monte Carlo Algorithm: An Exact MCMC Method Based on Subsets of Data
Speaker: Anupama Das
Abstract: In Bayesian inference, we often come across posteriors that are not of closed form, and drawing inference for such posteriors typically involves generating samples from the posterior distribution. Markov Chain Monte Carlo methods are commonly used to generate representative samples from the desired distribution. However, regular MCMC algorithms scale poorly with the size of the data because of the need to evaluate the likelihood for each data point every time a sample is generated. The Firefly Monte Carlo algorithm cleverly bypasses this bottleneck by introducing auxiliary “brightness” variables that effectively turn the data points on and off, enabling us to use only a subset of the dataset for each iteration, while still generating samples from the exact full-data posterior distribution. This significantly speeds up the process without any loss and only requires a lower-bound per data-point likelihood factor. In this discussion, I will give a brief idea of how MCMC is different when dealing with tall datasets and how the Firefly Monte Carlo algorithm works and illustrate its performance with an example.
Date: 14 August 2025
Time:  5:00 PM
Venue: FB567

Title: Controllability of Linear Ordinary Differential Equations
Speaker: Dr. Mohmedmunavvar Mubarak Bapu
Abstract: In this talk, we will start with an introduction to control theory and some simple examples. We will focus on linear Ordinary Differential Equations (ODEs) and explain three main concepts: exact controllability, approximate controllability, and null controllability. We will see that for linear ODEs, these concepts are equivalent. We will also briefly mention how things can be different for nonlinear ODEs. Then we will see how to find a control with minimum $L^2$-norm for linear ODEs. At the end, we will see an example of a PDE where these concepts are not equivalent.
Date: 07 August 2025
Time:  5:00 PM
Venue: FB567

Title: Introduction to proximal operators
Speaker: Apratim Shukla
Abstract: Optimising a given objective function is a problem of interest across various domains. It specifically finds its use in areas like image deconvolution, image denoising, signal denoising, image super-resolution, tomographic reconstruction etc. Proximal operators are popularly used in solving these problems owing to their nice properties. The idea revolves around constructing smooth approximations to non-differentiable objective functions which are then used as a proxy for the optimisation of the latter. The use of highly efficient iterative algorithms to solve these problems, also known as proximal algorithms, have also been proposed and have gained traction recently. In this talk, I shall give an introduction about the the fundamental problem of interest and the use of proximal operators to solve it. I would also briefly talk about some of their properties and possible applications.
Date: 22 April 2025
Time:  5:00 PM
Venue: NCL303B

Title: Zermelo's Theorem in Game Theory
Speaker: Dr. Soumyarup Sadhukhan
Abstract: In this talk, we will discuss briefly the first formal work in Game Theory due to Ernst Zermelo. The logician Zermelo proved that in the game of chess either White has a winning strategy (i.e., can always win), or Black has a winning strategy, or each player can always enforce a draw. Up to the present, however, it is still not known which of these three cases is the true one.
Reference: Zermelo, E. (1913). Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels. In Proceedings Fifth International Congress of Mathematicians (Vol. 2, pp. 501–504).
Date: 15 April 2025
Time:  5:00 PM
Venue: NCL303B

Title: Conjugacy Theorem for Lie algebra
Speaker: Yogendra Sing
Abstract: Click Here
Date: 08 April 2025
Time:  5:00 PM
Venue: NCL303B

Title: An Introduction to Fractional Stochastic Processes
Speaker: Dr. Ritik Soni
Abstract: In this talk, we will briefly discuss the theory of fractional calculus and its connection to stochastic processes. Our primary focus will be on the Poisson process and its fractional counterpart, known as the Fractional Poisson Process (FPP). We will examine several key properties of the FPP that make it more suitable than the classical Poisson process for real-world applications. Additionally, we will explore an alternative characterization of the FPP using the stochastic subordination technique.
Date: 01 April 2025
Time:  5:15 PM
Venue: NCL303B

Title: Isotonic Regression-Theory, Computation & Applications
Speaker: Adarsh Dubey
Abstract: Click Here
Date: 18 March 2025
Time:  05:00 PM
Venue: FB567

Title: Polynomial Invariants of a Finite Group
Speaker: Subham Garai
Abstract: Click Here
Date: 04 March 2025
Time:  05:00 PM - 06:00 PM
Venue: FB567

Title: Topological Data Analysis
Speaker: Tuhin Subhra Mahato
Abstract: Topological Data Analysis (TDA) is an advanced statistical framework for characterizing the topological structure of a population. It provides robust and interpretable summaries of data by identifying topological features such as connected components, loops, and voids, which remain stable under noise and continuous transformations.
In this seminar, we present persistent homology, a fundamental technique in TDA that quantifies the persistence of topological features across multiple scales, yielding persistence diagrams as statistical representations of the topological structure of a population. The statistical analysis of persistence diagrams, including distance metrics such as the bottleneck distance and Wasserstein distance, will be discussed in the context of classification.
Date: 18 February 2025
Time:  05:00 PM - 06:00 PM
Venue: FB567

Title: Viscosity Solutions
Speaker:  Govind Kureel
Abstract: In this talk, we will discuss the viscosity solution to fully nonlinear elliptic partial differential equations (PDEs). PDEs can be classified into two forms: Divergence and Non-Divergence. If the given PDEs are in divergence form, one can use the weak formalism to discuss the weak solution. On the other hand, if the PDEs are in non-divergence form, we cannot directly talk about the weak solution. Viscosity solution concept help to resolve this issue. We can define the viscosity solution for fully nonlinear PDEs, which are used in various fields, such as optimal control problems, mathematical finance, and differential games. The notion was introduced by Michael G. Crandall, Lawrence C. Evans, and Pierre-Louis Lions in the 1980s.
Date: 11 February 2025
Time:  05:00 PM - 06:00 PM
Venue: FB567

Title: Classification of simple superalgebras
Speaker:  Tinu Dhali
Abstract: We will recall some notions of super Algebras and lie algebras for example- center, queer super Algebras,matrix superalgebras,graded modules and graded ideals of super Algebras.Then will prove the classification theorem of simple super Algebras using Artin-wedderburn theorem of semi simple Algebras.
Date: 4 February 2025
Time:  05:00 PM - 06:00 PM
Venue: FB567

Title: 1st Quantum Weyl Algebra and Its Representation
Speaker:  Dr. Snehashis Mukherjee
Abstract: The quantum Weyl algebra is a deformation of the classical Weyl algebra. The first quantum Weyl algebra is defined as a K-algebra with generators x and y and the relation xy-qyx=1, where q is a nonzero element of K. In this talk, we will explore the finite-dimensional representations of this algebra.
Date: 28 January 2025
Time:  05:00 PM - 06:00 PM
Venue: FB567

Title: Reversibility in Groups
Speaker:  Dr. Tejbir Lohan
Abstract: An element of a group is called reversible if it is conjugate to its inverse. Reversible elements in a group are closely related to strongly reversible elements, which can be expressed as a product of two involutions. Classifying reversible and strongly reversible elements in a group has been a problem of broad interest. In this talk, we will introduce the concept of reversibility in groups and explore related questions through various examples.
Date: 23 January 2025
Time:  05:00 PM - 06:00 PM
Venue: FB567

Title: Informal Session On Presentation Skills
Speaker:  Prof. Sasmita Patnaik
Date: 16 January 2025
Time:  05:00 PM - 06:00 PM
Venue: FB567

Title: Importance of the General Equivalence Theorem on Optimal Designs
Speaker:  Soumadeb Pain
Abstract: The General Equivalence Theorem (GET) plays a pivotal role in the theory and practice of optimal experimental design, providing a rigorous framework for identifying designs that maximize statistical efficiency. By establishing conditions under which different optimality criteria, such as D-optimality and G-optimality, are equivalent, GET enables a unified approach to evaluating and constructing designs that minimize imprecision in parameter estimation. This equivalence is crucial because it allows researchers to select designs that not only satisfy one criterion but are also optimal under alternative criteria, leading to more robust and versatile experimental designs. In this seminar, I will try to explain how the GET provides a foundational framework for constructing and verifying optimal experimental designs that are efficient, robust, and adaptable across various statistical criteria.
Date: 13 November 2024
Time:  03:00 PM - 04:00 PM
Venue: FB567

Title: Exact MCMC for Intractable Proposals
Speaker:  Dwija Kakkad (4th year, BS - Math. & Sc. Comp.)
Abstract: Accept-reject based Markov chain Monte Carlo (MCMC) methods are the workhorse algorithm for Bayesian inference. These algorithms, like Metropolis-Hastings, require the choice of a proposal distribution which is typically informed by the desired target distribution. Surprisingly, proposal distributions with unknown normalizing constants are not uncommon, even though for such a choice of a proposal, the Metropolis-Hastings acceptance ratio cannot be evaluated exactly. Across the literature, authors resort to approximation methods that yield inexact MCMC or develop specialized algorithms to combat this problem. We show how Bernoulli factory MCMC algorithms, originally proposed for doubly intractable target distributions, can quite naturally be adapted to this situation. We present three diverse and relevant examples demonstrating the usefulness of the Bernoulli factory approach to this problem.
Date: 06 November 2024
Time:  03:00 PM - 04:00 PM
Venue: FB567

Title: Approximation method of Matern Gaussian field through SPDE approach
Speaker:  Sayan Bhowmik
Abstract: Handling large spatial data is quite challenging if there are large number of spatial locations due to inversion of dense covariance matrix. Assuming Gaussian field across spatial locations may not be a suitable choice as the computational time is of order O(n^3) for n spatial locations. Discretizing the continuous domain by defining fine mesh across the space quite helpful by using an explicit link between Gaussian field (GF) and Gaussian Markov random field (GMRF). Gaussian field with having Matern covariance function, can be represented as a solution of a specific stochastic partial differential equation (SPDE). A possible analytical method is integrated nested Laplace approximation (INLA). I will try to explain different kind of SPDE equations which are used in different situations.
Date: 30 October 2024
Time:  03:00 PM - 04:00 PM
Venue: FB567

Title: Classification of symplectic toric manifolds
Speaker:  Yogendra Singh
Abstract: Symplectic toric manifolds are smooth compact connected 2n-manifolds equipped with a symplectic structure and an action of a torus T^n with associated moment maps. The moment polytope, a convex shape in R^n, encodes the geometry of these manifolds.

In this talk, we will discuss the classification of symplectic toric manifolds in terms of specific polytopes, known as Delzant polytopes. More precisely, there exists a bijective correspondence between symplectic toric manifolds and Delzant polytopes. This correspondence, called Delzant's correspondence theorem, plays a fundamental role in understanding the geometry and topology of these manifolds.
Date: 23 October 2024
Time:  03:00 PM - 04:00 PM
Venue: FB567

Title: Von Neumann-Wold decomposition
Speaker:  Amritha K S
Abstract: We shall discuss a decomposition theorem for isometric operators on a Hilbert space by von Neumann and Wold. The theorem states that any isometric operator can be written as a direct sum of a unitary operator and copies of shift operator. We will see a proof of this theorem.
Date: 16 October 2024
Time:  03:00 PM - 04:00 PM
Venue: FB557

Title: Abelian and Tauberian Theory
Speaker:  Stuti Das
Abstract: Since early days of mathematics, summability methods have been used to assign a reasonable sum to an infinite series, whether it is convergent or not. In its simplest form, Tauberian theory deals with the problem of finding conditions under which a summable series is actually convergent. One of the first results in this direction, which applies to Abel summability was given by Alfred Tauber in 1897. However, Tauberian theory began in earnest only around 1910 with the work of Hardy and Littlewood.
In the this talk, I will briefly go through the notions of Abelian and Tauberian results, in particular focusing on the celebrated Hardy-Littlewood Tauberian theorem and elaborate the proof(Karamata’s version). In the remaining time, I will introduce integral versions of Tauberian theorems and if time permits, we will see one application of Karamta Tauberian theorem to prove the prime number theorem.
Date: 01 October 2024
Time:  06:00 PM - 07:00 PM
Venue: FB567

Title: The Müntz-Szász theorem
Speaker:  Prakhar Chaubey
Abstract: Click Here
Date: 24 September 2024
Time:  06:00 PM - 07:00 PM
Venue: FB567

Title: Denjoy- Wolff Theorem
Speaker:  Kanha Behera
Abstract: The Denjoy- Wolff theorem is a beautiful result in complex analysis which you may not find in most analysis books. The beauty of this theorem lies in its simplicity and usefulness. Apart from its use in complex function theory, the Denjoy- Wolff theorem also has applications in operator theory and the study of dynamic systems.
To explore this theorem, we need to understand the concept of function iteration. In this context, iteration refers to the repeated composition of a function. Specifically, for an analytic self-mapping of the open unit disc, the theorem addresses the behavior of its iterates. We shall discuss the statement and the proof of the theorem highlighting its applications.
Date: 10 September 2024
Time:  06:00 PM - 07:00 PM
Venue: FB567

Title: Random Walks on Homogeneous Spaces
Speaker: Tarun Goyal
Abstract: Click Here
Date: 02 September 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Navier Stokes Equation
Speaker: Dr. Prabir Barman
Abstract: Click Here
Date: 27 August 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Feynman-Kac formula
Speaker: Mangala Prasad
Abstract: Itô's formula is a fundamental result in stochastic calculus, which provides a way to compute the differential of function of a stochastic process. It works as a bridge between stochastic processes and partial differential equations.
Starting with basics of stochastic calculus, I shall explain Brownian motion, stochastic integral and Itô's formula. In this talk, we shall see an application of Itô's formula to get stochastic representation for the solution of the Cauchy problem for the backward heat equation with potential and Langrangian functions. This reprentaion is known as Feynman-Kac formula.
Date: 20 August 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Nevanlinna-Pick interpolation
Speaker: Santu Bera
Abstract: Click Here
Date: 13 August 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Nevanlinna-Pick interpolation
Speaker: Santu Bera
Abstract: Click Here
Date: 05 August 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: A Glimpse of Borel–Harish Chandra Theorem
Speaker: Sabyasachi Dhar
Abstract: Click Here
Date: 03 June 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Probability of Correct Selection: Insights into Ranking and Selection Procedures
Speaker: Yogesh Katariya
Abstract: In many practical situations, it is of interest to choose the best (or worst) of k (≥ 2) populations among several populations, where the quality of populations is assessed in terms of an unknown parameter associated with it. In the literature, such procedures are classified as “Ranking and Selection Procedures.” The goal is to develop effective and optimal selection/decision rules, ensuring a high probability of correctly identifying the best population or a nonempty subset of populations that include the best population.
In this talk, we will discuss some practical real-life examples of Ranking and Selection problems and emphasize the calculation of the probability of correctly selecting the best population by using standard selection rules. Key insights and general results for calculating the probability of correct selection for a given selection rule will be discussed to facilitate understanding and application in diverse contexts. Additionally, we will discuss critical general findings and insights essential for tackling such challenges across various domains.
Date: 20 May 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Homogeneous Dynamics and Its Application to Number Theory
Speaker: Sourav Das
Abstract: Recently, it has been observed that the ergodic theory of group actions on homogeneous spaces plays a crucial role in solving remarkable number-theoretic problems. Some notable instances include Margulis's proof of the Oppenheim conjecture, Furstenberg's proof of the Szemerédi theorem, Einsiedler, Katok, and Lindenstrauss's work on Littlewood's conjecture, and Kleinbock and Margulis's work on the Baker-Sprindžuk conjecture.
Starting with the basics of Diophantine approximation and Homogeneous dynamics, I will explain how the Diophantine properties of vectors in Euclidean space can be studied by examining the orbit behavior of diagonal flows on the space of all unimodular Euclidean lattices. In particular, I will delve into the details of the Baker-Sprindžuk conjecture, and time permitting, demonstrate how this problem of Diophantine approximation can be solved through Homogeneous dynamics. The content of this talk will be kept elementary to ensure accessibility to a broader audience.
Date: 15 April 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Frequentist validation of the Bayesian problems: A brief note on posterior contraction rate
Speaker: Arghya Mukherjee
Abstract: Click Here
Date: 08 April 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Solutions that explode
Speaker: N N Dattatreya
Abstract: The word 'explode' isn't a gimmick, we do have solutions that explode, so to say, to infinity, these solutions are called explosive solutions or large solutions. We will look at such solutions for ∆u=f(u) in one dimension; more precisely these are solutions to equations with singular boundary data. We will state the existence theorem in any bounded set in a Euclidean space and non-existence results in a whole Euclidean space. Finally, we will construct maximal and minimal large solutions in any bounded domain. Perhaps we will also discuss one of the most important tools to study such solutions, the comparison principle. We rely mostly on intuition and geometry rather than technicalities.
Date: 01 April 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Fully Homomorphic Encryption: Cryptography's Holy Grail
Speaker: Indranil Thakur(Ph.D. student, CSE IITK).
Abstract: Fully Homomorphic Encryption (FHE) has long been hailed as the "holy grail" of cryptography, promising to revolutionize data security and privacy. With FHE, arbitrary computations can be performed directly on encrypted data without decrypting it. It is very beneficial in the context of privacy-preserving outsourced storage and computation. This talk will explore the fascinating journey of FHE, from its theoretical inception to recent breakthroughs in practical implementations. We delve into the mathematical foundations of FHE, discussing the challenges and advancements that have propelled its development.
Date: 20 March 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Topological Complexity
Speaker: Dr. Gopal Chandra Dutta
Abstract: Click Here
Date: 11 March 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Exploring the Johnson-Lindenstrauss Lemma with Random Projection
Speaker: Annesha Deb
Abstract: Click Here
Date: 26 February 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Shannon Sampling Theorem
Speaker: Dr. Ankus Kumar Garg
Abstract: Click Here
Date: 20 February 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: On Pimsner-Popa probability constant.
Speaker: Mr. Guruprasad
Abstract: Click Here
Date: 12 February 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Proof of Riemann mapping theorem using potential theory
Speaker: Mr. Nishith Mandal
Abstract: Click Here
Date: 06 February 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Frostman's Theorem
Speaker: Mr. Chandan Sur
Abstract: Click Here
Date: 29 January 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Next word prediction using Markov Chains.
Speaker: Mr. Ojasvi Rajput
Abstract: In our increasingly digitized world, the ability to predict the next word in a sequence has become a fundamental aspect of natural language processing and human-computer interaction. This talk delves into the realm of next word prediction using Markov Chains, a probabilistic model that captures the essence of sequential dependencies within language.
The talk commences with an exploration of the underlying principles of Markov Chains, elucidating how these mathematical models encapsulate the idea that the probability of a future event depends on the current state. We delve into the application of Markov Chains to language, showcasing their versatility in capturing patterns and dependencies in text data.
Through engaging examples and demonstrations, we will be exploring the methodology behind implementing a Markov Chain-based next word prediction system.

Date: 22 January 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: Von Neumann's inequality for contractions
Speaker: Paramita Pramanick
Abstract: Click Here
Date: 15 January 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567

Title: When two commuting isometries are doubly commuting
Speaker: Shubham Jain
Abstract: Click Here
Date: 08 January 2024
Time: 06:00 PM - 07:00 PM
Venue: FB567