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