Seminar
Speaker: Ravi Raghunathan, IIT Bombay
Title: The Weak Law, the Strong Law and the Central Limit Theorem or "What I tried to learn last semester".
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, March 02
Venue: Ramanujan Hall
Abstract: If one already knows the language of measure theory, the main theorems of a first course in probability are quite easy to state (and prove). This is what I will do in the lecture. The main difficulty for the uninitiated is the translation of terms used by probabilists into standard terms in measure theory. Thus, this will be a lecture on basic probability shorn of all probabilistic intuition. The lecture should be accessible to anyone with a basic knowledge of measure theory.

Online seminar
Speaker: Dr. Tuhin Majumder
Host: Koushik Saha
Title: Fitting Sparse Markov Models to Categorical Time Series Using Convex Clustering
Time, day and date: 10:00:00 AM – 11:00:00 AM, Thursday, March 05
Venue: Online (https://meet.google.com/wjs-deag-ysh)
Abstract: Higher-order Markov chains are widely used to model categorical time series. However, a major challenge in fitting such models is the exponentially growing number of parameters as the model order increases. Sparse Markov Models (SMMs) provide a parsimonious framework in which all possible histories of order m are partitioned into groups such that histories within the same group share identical transition probability vectors. In this paper, we develop a novel method for fitting SMMs based on convex clustering with regularization. The regularization parameter is selected using the Bayesian Information Criterion (BIC). We establish model selection consistency of the proposed estimator under increasing sample size. Extensive simulation studies under diverse settings demonstrate strong finite-sample performance and consistently improved cluster recovery compared to existing competing approaches. Applications to real data on modeling and classifying disease sub-types further highlight the practical advantages of our method, showing superior classification performance.

Commutative algebra seminar
Speaker : R.V.Gurjar, TFR  Bombay (Retd.)
Host : Tony Puthenpurakal
Title : Singularities of plane curves II
Time, day and date : 03:00:00 PM – 04:00:00 PM, Thursday, March 05
Venue : Ramanujan Hall
Abstract : We will consider reduced power series f(X,Y) over an algebraically closed field k of characteristic 0. Following topics about R=k[[X,Y]]/(f) will be discussed. Algebraicity results of Artin, Hironaka-Rossi, Samuel, Basic intersection theory of place curves, Conductor ideal, Value semi-group of R, Gorenstein's result, Dedekind's Conductor Formula, Jung's formula connecting the Milnor number and conductor, Applications of Dedekind's formula. We will give Abhyankar's proofs of Dedekind and Gorenstein results. If time permits, Abhyankar-Moh result about generators of the value semi-group will be discussed. 

Algebraic groups seminar
Speaker: Ankita Parashar, IIT Bombay
Host: Shripad Garge
Title: Bruhat decomposition and its applications
Time, day and date: 4:00:00 PM – 5:00:00 PM, Thursday, March 05
Venue: Room No 215
Abstract: We begin the third chapter of the book by Digne and Michel.

Finance Seminar
Speaker: Dr. Himalaya Senapati, AVP at HSBC
Host: Keshav Aggarwal
Title: Introduction to Mathematical Finance: Theory and Practice
Time, day and date: 05:15:00 PM – 06:15:00 PM, Friday, March 06
Venue: Ramanujan Hall
Abstract: We will begin by discussing expectation versus arbitrage-based pricing and introduce the notion of risk-neutral probabilities. We will then present the binomial tree model and use it to price a vanilla call option. We will conclude with a brief overview of the industry landscape and possible career opportunities in mathematical finance.