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.