- Time:
- 2:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Topology and Related Topics Seminar**Tuesday, 5 Sept 2023, 2:15 pm

**=========================****Venue:**Ramanujan Hall**Host:**Rekha Santhanam**Speaker:**Priyanka Magar**Affiliation:**IIT Bombay**Title:**Quillen equivalent stable homotopy categories

**Abstract:**We will proceed by building upon the previous lectures, and explore different Quillen equivalent stable homotopy categories.

- Time:
- 3:45pm
- Location:
- Room No 105, Department of Mathematics
- Description:
**Seminar on Analysis of PDE**

Tuesday, 05 September 2023, 03.45 pm

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

**Venue:**Room 105, Department of Mathematics

**Host:**Harsha Hutridurga

**Speaker:**Subrata Majumdar

**Affiliation:**IIT Bombay

**Title:**Stabilization of heat equation by the backstepping method - I.

**Abstract:**This presentation considers the one-dimensional heat equation

with Dirichlet boundary conditions. We will study how we can make an

unstable (heat) system stable by means of some external input (control

function) through the boundary using the backstepping method. Our main

goal of this talk is to understand the backstepping method for the

simple 1-d heat case.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Groups seminar**Tuesday, 5 September 2023, 4 pm

**====================****Venue:**Ramanujan Hall**Host:**Shripad Garge**Speaker:**Chayan Karmakar**Affiliation:**IIT Bombay**Title:**Differentials & Smooth Points - I

**Abstract:**We study differentials with the aim of introducing Lie algebras for algebraic groups.

- Time:
- 4:00pm
- Location:
- Room No 215, Department of Mathematics
- Description:
**Commutative Algebra Seminar**Tuesday. 5 September, 4 pm

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

**Venue:**Room 215**Host:**Tony Puthenpurakal**Speaker:**Tony Puthenpurakal**Affiliation:**IIT Bombay**Title:**Triangulated and Derived Categories 4**Abstract:**We continue our introduction to Triangulated categories

- Time:
- 11:30am - 1:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Lecture series on Hodge Theory**Wednesday and Thursday

6 and 7 September, 11:30 am – 1.00 pm

**------------------------------------------------****Venue:**Ramanujan Hall**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. The next two lectures will finish the proof of the de Rham theorem, via sheaf cohomology, and if time permits, a beginning will be made on some linear algebra needed for the Hodge theory, as in Chapter 1 of Huybrechts' book.

- Time:
- 5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**CACAAG Seminar**Wednesday, 6 September, 5:30 PM

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

**Venue:**Ramanujan Hall**Host:**Madhusudan Manjunath**Speaker:**Madhusudan Manjunath, IIT Bombay**Title:**The Chow Ring of a Simplicial Toric Variety III.**Abstract:**We will continue our study of the Chow ring of a simplicial toric variety.

- Time:
- 11:30am - 1:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Lecture series on Hodge Theory**Wednesday and Thursday

6 and 7 September, 11:30 am – 1.00 pm

**------------------------------------------------****Venue:**Ramanujan Hall**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. The next two lectures will finish the proof of the de Rham theorem, via sheaf cohomology, and if time permits, a beginning will be made on some linear algebra needed for the Hodge theory, as in Chapter 1 of Huybrechts' book.

- Time:
- 2:30pm
- Location:
- Room No 215, Department of Mathematics
- Description:
**Topology and Related Topics Seminar**Thursday, 7 Sept 2023, 2:30 pm

**========================****Venue:**Room 215**Host:**Rekha Santhanam**Speaker:**Soumyadeb Samanta**Affiliation:**IIT Bombay**Title:**Some topological aspects of Riemannian geometry**Abstract: In**this talk, I plan to prove the Cartan-Hadamard theorem which talks about the universal cover of a complete Riemannian manifold with non-positive sectional curvature. We shall also see a proof of Myer's theorem about the fundamental group of a complete Riemannian manifold with positive sectional curvature.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Lectures on algebraic stacks

Date and Time: Friday, 8th September at 11:30 am

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

Venue: Ramanujan Hall

Host: Sudarshan GurjarSpeaker: Nitin Nitsure

Affiliation: TIFR (retd)Title: Algebraic Stacks

Abstract: Prof. Nitsure will continue his lectures on Algebraic Spaces.

- Time:
- 3:45pm
- Location:
- Room No 105, Department of Mathematics
- Description:
**Seminar on Analysis of PDE**

Friday, 08 September 2023, 03.45 pm

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

**Venue:**Room 105, Department of Mathematics

**Host:**Harsha Hutridurga

**Speaker:**Subrata Majumdar

**Affiliation:**IIT Bombay

**Title:**Stabilization of heat equation by the backstepping method - II.

**Abstract:**This presentation considers the one-dimensional heat equation

with Dirichlet boundary conditions. We will study how we can make an

unstable (heat) system stable by means of some external input (control

function) through the boundary using the backstepping method. Our main

goal of this talk is to understand the method of backstepping for the

simple 1-d heat case.

- Time:
- 2:30pm - 3:45pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Topology and Related Topics Seminar**Tuesday, 12 September 2023, 2.30 -3:45 pm

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

**Venue:**Ramanujan Hall**Host:**Rekha Santhanam**Speaker:**Bittu Singh**Affiliation:**IIT Bombay**Title:**Quillen stratification theorem"**Abstract:**In the 1st talk I'll describe group cohomology,restrictions transfer, L-H-S and Quillen Venkov Lemma.

- Time:
- 4:00pm
- Location:
- Room No 113, Department of Mathematics
- Description:
**Seminar on Analysis of PDE**Tuesday, 12 September 2023, 04.00 pm

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

**Venue:**Room 113, Department of Mathematics**Host:**Harsha Hutridurga**Speaker:**Bikram Bir**Affiliation:**IIT Bombay**Title:**A Splitting Discontinuous Galerkin Finite Element Method for the Vlasov-Navier-Stokes equation.

Abstract: In this talk, we shall discuss a splitting algorithm that we have developed to simulatesolutions to a two-phase flow model arising in the study of aerosols.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Groups seminar**Tuesday, 12 September 2023, 4 pm

**====================****Venue:**Ramanujan Hall**Host:**Shripad Garge**Speaker:**Chayan Karmakar**Affiliation:**IIT Bombay**Title:**Differentials & smooth points - II

**Abstract:**We study differentials with the aim of introducing Lie algebras for algebraic groups.

- Time:
- 4:00pm
- Location:
- Room No 215, Department of Mathematics
- Description:
**Commutative Algebra Seminar**Tuesday. 5 September, 4 pm

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

**Venue:**Room 215**Host:**Tony Puthenpurakal**Speaker:**Tony Puthenpurakal**Affiliation:**IIT Bombay**Title:**Triangulated and Derived Categories-VI**Abstract:**We conclude our introduction to Triangulated categories.

- Time:
- 9:30am
- Location:
- Mini Conference Room
- Description:
**Representation Theory seminar**Wednesday, 13 September 2023, 9:30 am

**====================****Venue: Mini Conference Room****Host:**U. K. Anandavardhanan**Speaker:**Mohammed Saad Qadri**Affiliation:**IIT BombayTitle:

Abstract

**:**Let $F$ be a non-archimedean local field. Let $\Pi$ be a principal series representation of $\GL_n(F)$ induced from a cuspidal representation of a Levi subgroup. When $\pi$ is an essentially square integrable representation of $\GL_{n-1}(F)$ we prove that $\Hom_{\GL_{n-1}}(\Pi,\pi)$ $= \mathbb{C}$ and $\Ext^i_{\GL_{n-1}}(\Pi,\pi) = 0$ for all integers $i\geq 1$, with exactly one exception (up to twists), namely, when $\Pi= \nu^{-(\frac{n-1}{2})} \times \nu^{-(\frac{n-3}{2})} \times \ldots \times \nu^{(\frac{n-1}{2})}$ and $\pi$ is the Steinberg. When $\Pi= \nu^{-(\frac{n-1}{2})} \times \nu^{-(\frac{n-3}{2})} \times \ldots \times \nu^{(\frac{n-1}{2})}$ and $\pi$ is the Steinberg of $\GL_{n-1}(F)$, then $\dim \Hom_{\GL_{n-1}(F)}(\Pi,\pi)=n$. We also exhibit specific principal series for which each of the intermediate multiplicities $2, 3, \cdots, (n-1)$ are attained.

Along the way, we also give a complete list of those irreducible non-generic representations of $\GL_{n}(F)$ that have the Steinberg of $\GL_{n-1}(F)$ as a quotient upon restriction to $\GL_{n-1}(F)$. We also show that there do not exist non-generic irreducible representations of $\GL_{n}(F)$ that have the generalized Steinberg as a quotient upon restriction to $\GL_{n-1}(F)$.

- Time:
- 11:30am - 1:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Lecture series on Hodge Theory**Wednesday and Thursday

13 and 14 September, 11:30 am – 1.00 pm

**---------------------------------------------****Venue:**Ramanujan Hall**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:
- 5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**CACAAG seminar**Wednesday, 13 September, 5:30 PM

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

**Venue:**Ramanujan Hall.**Host:**Madhusudan Manjunath**Speaker:**Madhusudan Manjunath, IIT Bombay**Title:**The Chow Ring of a Simplicial Toric Variety IV.**Abstract:**We will continue our study of the Chow ring of a simplicial toric variety.

- Time:
- 11:30am - 1:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Lecture series on Hodge Theory**Wednesday and Thursday

13 and 14 September, 11:30 am – 1.00 pm

**---------------------------------------------****Venue:**Ramanujan Hall**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:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Lecture series on algebraic stacks**Friday, 15 September, 11:30 am

**----------------------------------------------****Venue**: Ramanujan Hall**Host:**Sudarshan Gurjar

**Speaker :**Nitin Nitsure**Affiliation:**TIFR, Mumbai (retd)**Title:**Fibered groupoids and stacks.**Abstract:**Schemes can be understood via their functors of points. Descent theory shows that these functors are big etale sheaves over Spec Z. Amongst such sheaves, schemes and algebraic spaces are characterized by further 'algebraicity' conditions. Similarly, algebraic stacks are fibered groupoids which are stacks, which are the analogue of the sheaf and descent conditions. A further 'algebraicity' condition defines algebraic stacks. In the next few lectures, we will look at fibered groupoids and stacks, and give many examples. This will prepare the ground for introducing the algebraicity conditions that characterize algebraic stacks.

- Time:
- 11:30am
- Location:
- Room No 113, Department of Mathematics
- Description:
Annual Progress Seminar

Wednesday ,

20 September 2023, 10:30 - 11:30 am

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

Venue: Room 113

Host: Rekha Santhanam

Speaker: Bittu Singh

Affiliation: IIT Bombay

Title: Schwarz Genus of Fibration and Higher TC of Milnor Manifold

Abstract:

In my presentation, I will be discussing the Schwarz genus of fibration, with a particular focus on the intriguing genus known as Topological Complexity, which arises from free path space fibration. My research explores the Topological Complexity (TC) of several spaces. We finally obtained bounds for higher TC of Milnor manifolds. Our result also gives the higher TC of Klein Bottle

- 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