- Time:
- 4:00pm
- Location:
- Room No 114, Department of Mathematics
- Description:
**Algebraic groups Seminar**Monday, 3 April at 4 pm

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

**Venue**: 114, Mathematics Department**Host:**Shripad Garge**Speaker:**Dibyendu Biswas**Affiliation:**IIT Bombay**Title:**Commutative linear algebraic groups I**Abstract:**We begin the study of commutative linear algebraic groups

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Geometry seminar**Wednesday, 5 April, 2023, 11.30 am

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

**Venue:**Ramanujan Hall**Host:**Sudarshan Gurjar**Speaker:**Nitin Nitsure**Former Affiliation:**TIFR, Mumbai**Title:**An introduction to derived categories

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Geometry and topology Seminar**Thursday, 6 April, 2023 at 11.30 am

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

**Venue**: Ramanujan Hall**Host**: Rekha Santhanam**Speaker:**Kashyap Rajeevsarathy**Affiliation:**IISER, Bhopal**Title:**Generating the liftable mapping class groups of regular cyclic covers**Abstract:**Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g \geq 1$. We show that the liftable mapping class group $\mathrm{LMod}_k(S_g)$ of the $k$-sheeted regular cyclic cover of $S_g$ is self-normalizing in $\mathrm{Mod}(S_g)$ and that $\mathrm{LMod}_k(S_g)$ is maximal in $\mathrm{Mod}(S_g)$ when $k$ is prime. Moreover, we establish the existence of a normal series of $\mathrm{LMod}_k(S_g)$ that generalizes a well-known normal series of congruence subgroups in $\mathrm{SL}(2,\mathbb{Z})$. Furthermore, we give an explicit finite generating set for $\mathrm{LMod}_k{S_g)$ for $g \geq 3$ and $k \geq 2$, and when $(g,k) = (2,2)$. As an application, we provide a finite generating set for the liftable mapping class group of the infinite-sheeted regular cyclic covering of $S_g$ for $g \geq 3$ by the infinite ladder surface.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Commutative algebra seminar**Thursday, 6 April 2023 at 4 pm

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

**Venue:**Ramanujan Hall**Host:**Tony Puthenpurakal**Speaker:**H. Ananthnarayan**Affiliation:**IIT Bombay**Title:**Boij-Soderberg Theory over Standard-Graded Rings**Abstract:**The Boij-Soderberg conjectures, which appeared in 2008, signified a paradigm shift in the study of Betti numbers of graded modules over polynomial rings. In this talk, we identify questions arising from these conjectures, that are relevant over standard graded k-algebras, and some attempts to resolve them.

- Time:
- 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**IPDF extension seminar****Date:**6 April, 5 pm**Venue:**Ramanujan Hall**Host:**J. K. Verma**Speaker:**Suprajo Das, IIT Bombay**Title:**Toward Computing the Epsilon Multiplicity

- Time:
- 4:00pm
- Location:
- Room No 114, Department of Mathematics
- Description:
**Algebraic Groups Seminar:**Tuesday, 11/04/2023, 4 pm=====================================

**Host:**Shripad M. Garge :**Venue:**114**Speaker:**Dibyendu Biswas,**Affiliation:**IIT Bombay**Title:**Commutative linear algebraic groups II**Abstract:**We initiate the study of tori in this lecture.

- Time:
- 2:30pm
- Location:
- Room 216, Mathematics Department
- Description:
**Number Theory Seminar :**Wednesday: 12/04/2023, 2.30 pm========================================

**Host:**Preeti Raman :**Venue:**Room 216**Speaker:**Parul Gupta :**Affiliation:**IISER, Pune**Title**: A ruled residue theorem for function fields of elliptic curves**Abstract:**Let E be a field and v be a valuation on E. The ruled residue theorem, proved by J. Ohm in 1983, characterizes residue field extensions for valuations on a rational function field E(X) in one variable. It states that for any extension of v from E to E(X), the corresponding field extension at the level of residue fields is either algebraic or ruled, i.e., it is a rational function field in one variable over a finite extension of the residue field of E. In this talk, we will discuss residue field extensions for valuation extensions of v to the function field F of an elliptic curve over E. In this case, we show that there exists at most one extension of v to F such that the corresponding residue field extension is neither algebraic nor ruled. We also describe the cases where such an extension occurs. This is joint work with K. J. Becher and S. Mishra.

- Time:
- 4:00pm
- Location:
- Room No 215, Department of Mathematics
- Description:
**Algebraic Geometry seminar**Wednesday, 12th April 2023 at 4 pm

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

**Host:**Madhusudan Manjunath**Venue:**Room 215**Speaker:**Saurav Bhaumik, IIT Bombay**Title:**The Hard Lefschetz Theorem**Abstract:**We will state and prove the hard Lefschetz theorem.

- Time:
- 11:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Ph.D. Defence Seminar**Thursday, 13th April 2023, 11 am

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

**Venue:**Ramanujan Hall**Host:**Debanjana Mitra**Speaker:**Sakil Ahamed**Title:**Control Problems for Certain Linear Coupled Systems.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Geometry seminar:**Thursday, 13 April at 11.30 am.==========================================

**Host:**Sudarshan Gurjar :**Venue:**Ramanujan Hall**Speaker:**Nitin Nitsure :**Affiliation:**TIFR (retd)**Title:****Derived Categories and derived functors: a first look-2**

**Abstract:**

greater ease.

- Time:
- 4:00pm
- Description:
**Commutative Algebra Seminar:**Thursday,========================================

**Venue:**Ramanujan Hall :**Host:**Tony J. Puthenpurakal**Speaker:**Prof. Ananthnarayan Hariharan :**Affiliation:**IIT Bombay**Title:**Boij-Soderberg Theory over Standard-Graded Rings**Abstract:**The Boij-Soderberg conjectures, which appeared in 2008, signified a paradigm shift in the study of Betti numbers of graded modules over polynomial rings. In this talk, we identify questions arising out of these conjectures, that are relevant over standard graded k-algebras, and some attempts to resolve them.

- Time:
- 11:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Ph.D. Defence Seminar**Monday, 17 April, 2023 at 11 am

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

**Venue:**Ramanujan Hall**Host:**Sandip Singh**Speaker:**Shashank Vikram Singh**Affiliation:**IIT Bombay**Title:**Arithmeticity and Thinness of Some Hypergeometric Groups

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Number Theory Seminar**Monday, 17/04/2023 at 4 pm

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

**Venue:**Ramanujan Hall**Host:**Sandip Singh**Speaker:**C. S. Rajan**Affiliation:**Ashoka University**Title:**Classical Branching Laws**Abstract:**We consider the classical branching laws; for example, that of understanding the decomposition of the highest weight representation of GL(n) to that of GL(n-1), or restriction from odd orthogonal to even orthogonal and symplectic branching laws. We outline an approach via the Weyl character formula. This is joint work with Sagar Srivastava.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Geometry Seminar**Tuesday, 18 April, 2023 at 11.30 am

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

**Venue:**Ramanujan Hall**Host:**Sudarshan Gurjar**Speaker:**Nitin Nitsure**Affiliation:**TIFR (Retd)**Title:**The cotangent complex

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**IPDF Seminar**Tuesday, 18 April 2023, 2.30 pm

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

**Venue:**Ramanujan Hall**Host:**Rekha Santhanam**Speaker:**Navnath Daundkar**Affiliation:**IIT Bombay**Title:****Topological Complexity of fibre bundles, lower bounds on higher topological complexity and its Applications****Abstract:**For a path-connected space, Farber introduced a numerical homotopy invariant called topological complexity. Farber gave an additive upper bound on the topological complexity of product spaces. In the first part of this talk, we show that fibre bundles have such an upper bound under certain conditions. As an application, we obtain a tight upper bound on the topological complexity of higher-dimensional Klein bottles. This is based on the joint work with Prof. Soumen Sarkar. In the next part of this talk, we study a higher analogue of topological complexity. Here we improve the usual cohomological lower bound by introducing the concept of higher TC-weights. Then we use this to show that nth topological complexity of Seifert fibre manifolds is either 3n or 3n+1. This is based on joint work with Prof. Rekha Santhanam and Soumyadip Thandar.

- Time:
- 4:00pm
- Location:
- Room No 215, Department of Mathematics
- Description:
**Algebraic Groups seminar**Tuesday, 18 April 2023, 4 pm

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

**Venue:**Room 215**Host:**Shreepad Garge**Speaker:**Dibyendu Biswas**Affiliation:**IIT Bombay**Title:**Diagonalizable groups

- Time:
- 4:00pm
- Location:
- Room No 215, Department of Mathematics
- Description:
**CACAAG Seminar**Thursday, 20 April 2023, 4 pm

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

**Venue:**Room 215**Host:**Madhusudan Manjunath**Speaker:**Saurav Bhaumik**Affiliation:**IIT Bombay**Title:**The Hard Lefschetz theorem - second talk**Abstract:**We will state and prove the hard Lefschetz theorem.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Geometric Group Theory Learning Seminar**21 April 2023 at 11:30 AM

**Host:**Rekha Santhanam**Venue:**Ramanujan Hall**Speaker:**Radhika Gupta (TIFR)**Affiliation:**TIFR, Mumbai**Title:**“Growth of Groups.”

- Time:
- 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**PDE seminar**Monday, April 24, 3:30 pm

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

**Venue:**Ramanujan Hall**Host:**Saikat Mazumdar**Speaker:**Mitesh Modasiya**Affiliation:**IISER Pune**Title:**Fine boundary regularity results for fully nonlinear mixed local

nonlocal problems**Abstract:**In this talk, I will consider Dirichlet problems for fully nonlinear mixed local-nonlocal non-translation invariant operators. I will start by the discussion on global Lipschitz regularity for such problems. Later I will move on to the fine boundary regularity which will require careful construction of appropriate sub/super solutions and a weak version of Harnack inequality. If time permits, I will talk about an overdetermined problem for linear mixed local-nonlocal operators.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**IPDF Seminar**Tuesday, 25 April 2023, 11.30 pm

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

**Venue:**Ramanujan Hall**Host:**Sudarshan Gurjar**Speaker:**Arusha C**Affiliation:**TIFR, Mumbai**Title:**Vector Bundles and Parabolic Bundles on Nodal Curves**Abstract:**A great deal is known about vector bundles and parabolic bundles in the case of smooth curves but a similar study on singular curves has been relatively slow.

Interestingly, the results for irreducible nodal curves are very similar to those for smooth curves; however, the proofs are different and much more difficult as there are torsion free

sheaves on a nodal curve that are not locally free unlike the smooth case. Ramanan proved in the 70s that a universal family (also called a Poincar ́e bundle) exists for the moduli problem vector bundles on smooth curves if and only if the rank and degree are coprime. One of the key elements in the proof is the computation of the Picard group of the moduli space. First, we prove the non-existence of a Poincar ́e bundle for the moduli problem of vector bundles on nodal curves when the degree and rank are not coprime closely following that of Ramanan. When the degree is sufficiently high, the pushforward of a Poincar ́e bundle to the moduli space is a vector bundle, called the Picard bundle. Although the existence of Poincar ́e bundles (hence Picard bundles) depend on the rank and degree being relatively prime, there always exists a Poincar ́e family of projective bundles called the projective Poincar ́e bundle. Similarly, there is a projective Picard bundle. Next, we discuss the stability of these bundles. Finally, we move from vector bundles to parabolic bundles. Mehta-Seshadri theorem gives a one to one correspondence between irreducible unitary representations of the fundamental group of a punctured compact Riemann surface and stable parabolic bundles on the compact Riemann surface with a parabolic structure at the punctures. We prove that such a correspondence does not hold for nodal curves.

- Time:
- 4:30pm
- Location:
- Room 105, Mathematics Department
- Description:
**Algebraic Groups seminar**Tuesday, 25 April 2023, 4.30 pm

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

**Venue:**Room 105**Host:**Shreepad Garge**Speaker:**Dibyendu Biswas**Affiliation:**IIT Bombay**Title:**Study of diagonalizable groups

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Geometry seminar:**Thursday, 26 April at 11.30 am.==========================================

**Host:**Sudarshan Gurjar :**Venue:**Ramanujan Hall**Speaker:**Nitin Nitsure :**Affiliation:**TIFR (retd)**Title:****Derived Categories and derived functors: a first look-2**

**Abstract:**

greater ease.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**GGT Seminar**Date and time: 28th April 2023, at 11:30 AM

Venue: Ramanujan Hall.

Host: Rekha Santhanam

Speaker: Soumyadeb Samanta

Affiliation: IIT Bombay

Title: Lamplighter groups

Abstract: In this talk, we shall discuss about the Lamplighter groups, mostly Lamplighter group L_2, it's group operation and presentation. Then we will move on to give an efficient formula for calculating the word length of elements of L_2 and have a look at the Cayley graph of L_2. I shall end with a short discussion on which contexts Lamplighter groups appear in Mathematics.