Pre-Synopsis Seminar

Date: 27 September, 2023 (Wednesday),

Time: 11:00 AM to 12:00 noon

==========================

Venue: Room 105
Host: Niranjan Balachandran

Speaker: Brahadeesh Sankarnarayanan

Title: Some problems in combinatorics: Excursions in graph colorings and
extremal set theory

All are cordially invited.

Lecture series on Hodge Theory

Wednesday  27 September, 11:30 am and 3.30 pm

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Venue: Ramanujan Hall at 11.30 and 215 at 3.30

Host: Sudarshan Gurjar

Speaker: V. Srinivas
Affiliation: IIT Bombay

Title: Introduction to Hodge Theory

Abstract : These are part of an ongoing series of lectures on the basics 
of Hodge theory. We will finish the proof of the de Rham theorem, via 
sheaf cohomology, and discuss some linear algebra needed for the Hodge 
theory, as in Chapter 1 of Huybrechts' book.

Annual Progress Seminar
Wednesday, 27th September 2023, 12 noon
=======================================
Venue: Room 105
Host: Debraj Das

Speaker: Ms. Janhvi Patel
Affiliation: IIT Bombay

Title: High-Dimensional Berry Essen Bounds for M-estimators

Abstract: M-estimation refers to a general method of estimation methods, 
where the estimators are obtained by maximizing certain criterion 
functions. M-estimators include the maximum likelihood estimator, lease 
square estimator, and many other estimators that appear in robust 
regression. Here we are interested in high dimensional asymptotics of 
M-estimators. More precisely, our goal is to find the Berry-Essen bound 
on the difference between the law of properly centered and scaled M 
estimator and an appropriate Gaussian distribution.

Annual Progress Seminar
Wednesday, 27th September 2023, 3.00 pm
=====================================
Venue: Ramanujan Hall

Host: Debraj Das

Speaker: Mr. Mayukh Choudhury
Affiliation: IIT Bombay

Title: Bootstrapping LASSO in Generalized Linear Models
Abstract: Generalized linear models or GLM is an important set of models 
that generalizes the ordinary linear regression by connecting the 
response variable with the covariates through arbitrary link functions 
and thus allowing the responses to have arbitrary distributions. On the 
other hand, the Least Absolute Shrinkage and Selection Operator or the 
Lasso is a popular and easy-to-implement penalization method in 
regression especially when all the covariates are not relevant. However, 
Lasso has complicated asymptotic distribution which is not useful in 
practice and hence development of an alternative method of 
distributional approximation is required for the purpose of statistical 
inference. Bootstrap generally works as an alternative in most of the 
inference problems. In that spirit, here we develop a Bootstrap method 
that works as an approximation of the distribution of the Lasso 
estimator for all the sub-models of GLM. However, it is the usual 
practice that cross-validation is used to choose a data-dependent choice 
of the penalty parameter in Lasso. To bridge the gap between the 
developed Bootstrap theory and the use of cross-validation, we also 
establish the asymptotic property of the K-fold cross-validated choice 
of the penalty parameter.

Lecture series on Hodge Theory

Wednesday  27 September, 11:30 am and 3.30 pm

----------------------------------------------------

Venue: Ramanujan Hall at 11.30 and 215 at 3.30

Host: Sudarshan Gurjar

Speaker: V. Srinivas
Affiliation: IIT Bombay

Title: Introduction to Hodge Theory

Abstract : These are part of an ongoing series of lectures on the basics 
of Hodge theory. We will finish the proof of the de Rham theorem, via 
sheaf cohomology, and discuss some linear algebra needed for the Hodge 
theory, as in Chapter 1 of Huybrechts' book.