- Time:
- 10:30am-11:30am
- Location:
- Room No 113, Department of Mathematics
- Description:
Annual Progress Seminar Tuesday, 26 September 2023, 10.30 - 11.30 am ============================== Venue: Room 113 Host: Ananthnarayan H. Speaker: Omkar Javadekar Affiliation: IIT Bombay Title: Associated Graded Modules and Pure Resolutions Abstract: Given a finitely generated module M over a Noetherian local ring R, one would like to know when the corresponding associated graded module G(M) has a pure resolution over the associated graded ring G(R). In this talk, we will construct a complex F* of free G(R)-modules using a minimal free resolution F of M over R, and show that F* is a minimal free resolution of G(M) if and only if G(M) is pure. We will apply this result to give sufficient conditions for R to be Cohen-Macaulay, and also prove a local version of Herzog-Kuhl equations.

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Topology and Related Topics Seminar Tuesday, 26 Sept 2023, 2:30 pm ======================== Venue: Ramanujan Hall Host: Rekha Santhanam Speaker: Bittu Singh Affiliation: IIT Bombay Title: Quillen stratification theorem Abstract: This is the second talk. Here I will describe the topological aspect of group cohomology, the Equivalence of the algebraic and topological definitions. Then I will move to L-H-S and Quillen Venkov Lemma.

- Time:
- 3:00pm-4:00pm
- Location:
- Room No 215, Department of Mathematics
- Description:
**Annual Progress Seminar**Tuesday

**,**September 26, 3 pm-4 pm=======================

**Venue:**Room-215**Host:**Tony J. Puthenpurakal

**Speaker:**Sayed Sadiqul Islam**Title:**Reductions of ideals in local rings**Abstract:**The reduction theory goes back to the influential 1954 paper by Northcott and Rees, the paper that introduced the basic notions. We will prove the existence of minimal reductions and will discuss some properties of minimal reductions. A closely related notion is that of analytic spread l(I) of I is defined to be the Krull dimension of the fiber cone of I. We will see how analytic spread behaves in some special cases. If time permits then will introduce some new notions.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Algebraic Groups seminar Tuesday, 26 September 2023, 4 pm ============================= Venue: Ramanujan Hall Host: Shripad Garge Speaker: Chayan Karmakar Affiliation: IIT Bombay Title: Differentials & Smooth Points - III Abstract: We study smooth points on a variety and will try to introduce the notion of Lie algebra of a linear algebraic group.

- Time:
- 11:00am-12:00pm
- Location:
- Room No 105, Department of Mathematics
- Description:
**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.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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.

- Time:
- 12:00pm
- Location:
- Room No 105, Department of Mathematics
- Description:
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.

- Time:
- 3:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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.

- Time:
- 3:30pm
- Location:
- Room No 215, Department of Mathematics
- Description:
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.

- Time:
- 11:05am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Annual Progress Seminar Friday, 29 September 2023, 11.05 am ======================= Venue: Ramanujan Hall Host: Prof. Sudhir Ghorpade Speaker: Rati Ludhani Affiliation: IIT Bombay Title: Projective Reed-Muller Codes and Minimal Free Resolutions

- Time:
- 12:05pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Annual Progress Seminar Friday, 29 September 2023, 12.05 pm =========================== Venue: Ramanujan Hall Host: Prof. Sudhir Ghorpade Speaker: Sakshi Affiliation: IIT Bombay Title: Minimum Weight Codewords and Permutation Automorphism Groups of Affine Cartesian Codes

- Time:
- 2:00pm-3:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Annual Progress Seminar**Wednesday, 27 September, 2.00-3.00 pm

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

**Venue:**Ramanujan Hall**Host:**Prof. Niranjan Balachandran**Speaker:**Ankita Dargad, IIT Bombay**Title:**Robin Hood Game

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Topology and Related Topics Seminar Friday, 29 Sept 2023, 2:30 pm ======================== Venue: Ramanujan Hall Host: Rekha Santhanam Speaker: Aparajita Karmakar Affiliation: ISI Kolkata Title: Homotopy invariant commutative algebra Abstract: The goal of this lecture will be to introduce the concept of Morita equivalences. In Morita theory, we study an object X of a category by considering Hom(k,X) as a module over the endomorphism ring End(k), where k is a test object. Towards that, we will develop some finiteness conditions on an R - complex, where R is a commutative local ring, and their applications in Morita Theorems.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Annual Progress Seminar

Friday, 29 September 2023, 4.00 pm

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

Venue: Ramanujan Hall

Host: Prof. Siuli Mukhopadhyay

Speaker: Pallab Kumar Sinha

Affiliation: IIT Bombay

- Time:
- 4:45pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Annual Progress Seminar

Friday, 29 September 2023, 4.45 pm

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

Venue: Ramanujan Hall

Host: Prof. Siuli Mukhopadhyay

Speaker: Niphadkar Shubham Sanjay

Affiliation: IIT Bombay

Title: Efficient Bivariate Crossover Designs in Correlated Setup