- Time:
- 2:30pm
- Location:
- Google Meet
- Description:
Combinatorics and TCS Seminar

Wednesday, 3rd January 2024, 2.30 pm

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

Venue: Google Meet (https://meet.google.com/ctv-ynac-gjt)

Host: Sudhir R. Ghorpade

Speaker: Prafullkumar Tale

Affiliation: IISER Bhopal

Title: Parameterized Complexity and Some New Lower Bounds for Problems in NP

Abstract: In this talk, we briefly introduce Parameterized Complexity and some graph theoretical NP complete problems. We then look at the usual conditional lower bounds in this domain, most of which are single (or almost single) exponential.

Our results, for the first time, derive double-exponential lower bounds for natural, important, and well-studied NP-complete graph problems when parameterized by structural parameters. Specifically, we design a technique to obtain such lower bounds and show its versatility by applying it to three different problems: Metric Dimension, Strong Metric Dimension, and Geodetic Set. This techniques use for the lower bounds uses a novel yet simple technique based on the Sperner families of sets.

- Time:
- 4:00pm
- Location:
- Room No 105, Department of Mathematics
- Description:
Algebraic Groups seminar

Friday, 5 January, 4.00-5.15

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

Venue: Room 105

Host: Dipendra Prasad

Speakers: Dibyendu Biswas, Chayan. Karmakar and Mohammed Saad

Affiliation: IIT Bombay

Abstract: We will discuss a variety of topics in Algebraic groups through reading some of the papers that have become classics in the subject. The first few seminars will be on the paper by Robert Steinberg, Regular elements of semi-simple algebraic groups Publications mathématiques de l’I.H.É.S., tome 25 (1965), p. 49-80

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Analysis and PDE seminar

Monday, 8th Jan, 4 pm—5 pm==================

Venue: Ramanujan Hall

Host: Saikat Majumdar

Speaker: Anusha Krishan, University of Münster

Title: Toral symmetries of homogeneous ancient Ricci flows

Abstract: Ricci flow solutions that are defined for all negative times, are called ancient, and have a special significance since they arise as blowup limits at singularities of the flow. Several instances in the literature suggest that ancient solutions to the Ricci flow have a higher degree of symmetry than initially assumed. In recent work (joint with F. Pediconi and S. Sbiti), we show that under certain assumptions, collapsed homogeneous ancient solutions to the Ricci flow have additional toral symmetry.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Algebraic Groups seminar

Tuesday, 9 January 2024, 4 pm

====================Venue: Ramanujan Hall

Host: Shripad M. Garge

Speaker: Shripad M. Garge

Affiliation: IIT Bombay

Title: Topological properties of morphisms

Abstract: We are following T. A. Springer's book on Linear Algebraic Groups, Chapter 5. In this lecture, we will study dominant morphisms between irreducible varieties.

- Time:
- 4:00pm - 5:30pm
- Location:
- Room No 215, Department of Mathematics
- Description:
Commutative Algebra Seminar

Tuesday, 9 Jan 2023, 4 pm-5:30 pm

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

Host: Tony Puthenpurakal

Venue: Room 215

Speaker: Tony J. Puthenpurakal

Affiliation: IIT Bombay

Title: Modules over Weyl algebras with application to local cohomology modules over polynomial rings

Abstract. Let K be a field of characteristic zero. We study finitely generated modules over the Weyl algebra A_n(K). We give application to local cohomology modules of K[X_1,...., X_n].

- Time:
- 4:00pm - 5:15pm
- Location:
- Room No 105, Department of Mathematics
- Description:
Algebraic Groups seminar

Friday, 12 January, 4.00-5.15

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

Venue: Room 105

Host: Dipendra Prasad

Speakers: Dibyendu Biswas, Chayan. Karmakar and Mohammed Saad

Abstract: We will discuss a variety of topics in Algebraic groups through reading some of the papers that have become classics in the subject. The first few seminars will be on the paper by ROBERT STEINBERG, Regular elements of semi-simple algebraic groups Publications mathématiques de l’I.H.É.S., tome 25 (1965), p. 49-80

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Mathematics colloquium

15 January, 2023, 4 pm

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

Venue: Ramanujan Hall

Host: Jugal Verma

Speaker: Sujatha Ramadorai

Affiliation: University of British Columbia, Vancouver, Canada

Title: Asymptotics of Rational Points of Elliptic curves

and Krull dimension

Abstract: Modules over power series rings occur naturally in

Number Theory and in concrete cases, certain asymptotics

arising from the study of such modules encode arithmetic information

related to the Krull dimension of the modules. We will discuss this

phenomena specifically for elliptic curves.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Algebraic geometry seminar

Tuesday, 16 January, 11.30 am

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

Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: Nitin Nitsure

Affiliation: TIFR, Mumbai (retd)

Title: Separated Morphisms and Proper Morphisms.

Abstract: Separated morphisms and proper morphisms are two very important classes of morphisms in algebraic geometry. In the next few lectures, we will study these for schemes, algebraic spaces, and algebraic stacks. The basic theory of such morphisms between schemes is given in Hartshorne's `Algebraic Geometry', Chapter 2, Section 4. After recalling the basics, we will go on to consider such morphisms between algebraic spaces and then between algebraic stacks. The first few lectures should be easily accessible to beginner students in algebraic geometry.

- Time:
- 3:00pm - 4:00pm
- Location:
- Room No 215, Department of Mathematics
- Description:
Commutative Algebra Seminar

Tuesday, 16 Jan 2023, 3 pm-4 pm

Note the unusual time

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

Host: Tony Puthenpurakal

Venue: Room 215

Speaker: Tony J. Puthenpurakal

Affiliation: IIT Bombay

Title: Modules over Weyl algebras with application to local cohomology modules over polynomial rings-2

Abstract. Let K be a field of characteristic zero. We study finitely generated modules over the Weyl algebra A_n(K). We give application to local cohomology modules of K[X_1,...., X_n]

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Algebraic Groups seminar

Tuesday, 16 January 2024, 4 pm

====================Venue: Ramanujan Hall

Host: Shripad M. GargeSpeaker: Shripad M. Garge

Affiliation: IIT BombayTitle: Finite morphisms and normal varieties

Abstract: We introduce the notion of normal varieties and prove the following version of Zariski's main theorem: A bijective and birational morphism of irreducible varieties, \phi: X Y, is an isomorphism if Y is normal.

- Time:
- 4:00pm - 5:00pm
- Description:
Number Theory seminar

Tuesday, January 16, 16:00 - 17:00

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

Venue: Room 105

Host: Ravi Raghunathan

Speaker: Surya Ramana

Affiliation: Harish-Chandra Research Institute

Title: An Improved Bound for the Additive Energy of Large Sets of Prime Numbers

Abstract: When A and B are subsets the integers, the additive energy of A and B is the quantity E(A,B) defined by E(A,B) = | { (x_1,x_2,y_1, y_2) \in A\times A \times B \times B\, | x_1 +y_1 = x_2 +y_2 } | Additive energy is a basic notion in additive number theory and additive combinatorics. Given $\alpha$ in $(0,1)$ and $\lambda >0$ and a large enough integer $N$, we obtain an essentially optimal upper bound for the additive energy $E(A,B)$ of any subsets $A$ and $B$ of the prime numbers in the intervals $[1, N]$ and $[1, \lambda N]$ respectively, when $A$ satisfies $|A| \geq \alpha N$. This is based on work with K. Mallesham and Gyan Prakash.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Mathematics colloquium

Wednesday, 17 January, 2023, 4 pm

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

Venue: Ramanujan Hall

Host: Ravi Raghunathan

Speaker: R. Balasubramanian

Affiliation: Institute of Mathematical Sciences, Chennai

Title: Product of three primes in an arithmetic progression

Abstract. Linnik proved that there exists a positive constant c such that the set {p: p is a prime ≤ q c} contains all invertible residue classes mod q. The original value of c was very large. The best known is c = 5 . It is expected to be true for any c > 2. We ask an analogous question What is the value of c for which we can claim that the set {p_1p_2p_3: p_i ≤ q c for i = 1, 2, 3} covers all invertible residue classes mod q . We shall explain how additive combinatorics naturally enters into the proof. This is a joint work with Ramare and Priyamvad Srivastav.

- Time:
- 2:30pm - 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Combinatorics seminar

Monday, 22 January 2024, 14:30-15:30 hrs

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

Venue: Ramanujan Hall

Host: S. Krishnan

Speaker: Hiranya DeyAffiliation: Indian Institute of Science, Bengaluru

Title: On the sum of the entries in the character table of a finite groupAbstract: In 1961, Solomon proved that the sum of all the entries (total sum) in the character table of a finite group does not exceed the cardinality of the group. In this

talk, we will see that for symmetric groups, the total sum is asymptotically the same as

the first column sum. We will also prove that similar results hold for hyperoctahedral

groups and demihyperoctahedral groups. We will also see the generating function for total

sum for generalized symmetric groups which uses Flajolet's work on continued fractions.

This is a joint work with Arvind Ayyer and Digjoy Paul.

- Time:
- 9:30am - 10:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Annual Progress Seminar

Tuesday, January 23, 2024, 9.30-10.30

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

Venue: Ramanujan Hal

Host: S. Krishnan

Speaker: Umesh ShankarAffiliation: IIT Bombay

Title: Bijective approach to enumerating permutation statistics

- Time:
- 11:30am
- Location:
- Room No. 105, Department of Mathematics
- Description:
Lecture series on algebraic stacks

Tuesday, 23 January 2024, 11:30 AM

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

Venue: Room 105

Host: Sudarshan GurjarSpeaker: Nitin Nitsure

Affiliation: Bhaskaracharya Pratishthana, PuneTitle: Separated and proper morphisms of schemes

Abstract: The basic theory of separated and proper morphisms of schemes, developed by Grothendieck, is explained in Hartshorne's book `Algebraic Geometry' chapter 2 section 4. We will look at it from the perspective of functors of points. The functorial point of view is essential for Artin's extension of the theory of such morphisms first to algebraic spaces and then to algebraic stacks, which are going to be our next topics.

- Time:
- 4:00pm - 5:30pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
**Commutative Algebra Seminar**Tuesday 23 Jan 2024, 4.00-5:30 pm

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

**Venue:**Room 215**Host:**Tony J. Puthenpurakal**Speaker :**Tony J. Puthenpurakal**Affiliation:**IIT Bombay**Title:**Modules over Weyl algebras with application to local cohomology modules over polynomial rings-III**Abstract:**Let $K$ be a field of characteristic zero. We study finitely generated modules over the

- Time:
- 2:30pm - 3:30pm
- Location:
- Room No 105, Department of Mathematics
- Description:
Seminar on control theory

Wednesday, 24 January, 2.30-3.30

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

Venue: Room 105, Dept. of Mathematics

Host: Sudhir Ghorpade

Speaker: Chandrajit Bajaj

Affiliation: University of Texas at Austin, USA

Title: Optimized Decision-Making via Active Learning of Stochastic Hamiltonians

Abstract: A Hamiltonian represents the energy of a dynamical system in phase space with coordinates of position and momentum. Hamilton’s equations of motion are obtainable as coupled symplectic differential equations. In this talk, I shall show how optimized decision-making (action sequences) can be obtained via a reinforcement learning problem wherein the agent interacts with the unknown environment to simultaneously learn a Hamiltonian surrogate and the optimal action sequences using Hamilton dynamics, by invoking the Pontryagin Maximum Principle. We use optimal control theory to define an optimal control gradient flow, which guides the reinforcement learning process of the agent to progressively optimize the Hamiltonian while simultaneously converging to the optimal action sequence. Extensions to stochastic Hamiltonians leading to stochastic action sequences and the free-energy principle shall also be discussed.

This is joint work with Taemin Heo, Minh Nguyen

Brief Bio: Professor Chandrajit Bajaj is a Computational Applied Mathematics Chair in Visualization at the Department of Computer Science and the Oden Institute of Computational Engineering and Sciences at the University of Texas at Austin, USA. He is a Fellow of AAAS, ACM. IEEE and SIAM. More information about him is available at: http://www.cs.utexas.edu/~bajaj

- Time:
- 3:00pm - 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Probability and Statistics seminar

Wednesday, 24 January, 3.00-4.00 pm

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

Venue: Ramanujan Hall

Speaker: Hira Koul

Affiliation: Professor, Department of Statistics and Probability, Michigan State University

Distinguished Visiting Professor, Department of Mathematics, IIT Bombay

Title: A signed-rank estimator in nonlinear regression models when covariates and errors are dependent

Abstract: This talk will describe the asymptotic uniform linearity of a signed rank statistic of the residuals in a class of nonlinear parametric regression models when regression errors are possibly dependent on the covariates. This result is used to prove the asymptotic normality of a signed rank estimator of the regression parameter vector in the given nonlinear regression model where covariates and regression errors are dependent. The latter result in turn is used to derive the asymptotic distribution of this signed rank estimator in the errors in variables linear regression model. The asymptotic relative efficiency of this SR estimator relative to the bias-corrected least squares estimator is shown to increase to infinity, as the measurement error variance increases to infinity, thereby establishing another robustness property of this estimator.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Venue: Ramanujan Hall

Host: Sudhir R Ghorpade

Speaker: S K Jain

Affiliation: Ohio University, Athens, OH, USA

DATE: Wednesday, January 24 at 4 pm.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Algebraic Geometry Seminar

Tuesday, 30 January 2024, 11:30 am========================

Host: Sudarshan Gurjar

Venue: Ramanujan Hall

Speaker: Nitin Nitsure

Affiliation: Bhaskaracharya Pratishthana, PuneTitle: Separated and proper morphisms of schemes

Abstract: The lecture will begin with closed and universally closed morphisms of schemes. We will prove, following B Poonen, that any scheme that is universally closed over Spec k (where k is any field) is quasi-compact. This will be followed by some basics of quasi-compact morphisms, preparing the way to study separated and proper morphisms via specialization of points. The lecture will be easily accessible to students that have looked at section 4 of Chapter 2 of Hartshorne's “Algebraic Geometry”

- Time:
- 2:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Analysis Seminar

Tuesday, 30 Jan. 2 pm

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

Venue: Ramanujan hall

Host: Sourav Pal

Speaker: Himadri Halder

Affiliation: IIT Bombay

Title: Bohr's theorem for the polydisc and the symmetrized polydisc

Abstract: In this talk, we will discuss Bohr's theorem for the family of holomorphic functions in the polydisc and symmetrized polydisc. We obtain several new estimates of the multidimensional Bohr radius for polydisc. Moreover, we will also study Bohr's zone for the symmetrized polydisc. In addition, we will answer certain open questions related to the exact values of multidimensional Bohr radius by using the concept of arithmetic Bohr radius for vector-valued holomorphic functions defined in complete Reinhardt domains in \mathbb{C}^n. Our discussion will include several interesting earlier results as well as our recent works on Bohr's theorem problem.

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Analysis Seminar**Tuesday, 30 Jan. 2:30 pm

**=================****Venue:**Ramanujan hall**Host:**Sourav Pal**Speaker:**Swapan Jana**Affiliation:**IIT Bombay**Title:**Positive definite functions and a generalized Naimark theorem**Abstract:**We study the operator-valued positive definite functions on a group and characterize them in terms of positive block matrices. We present a generalization of a theorem of Naimark which states that the positive definite functions and unitary representations are in one-to-one correspondence. We discuss an alternative proof of Brehmer's positivity for doubly commuting operators. We classify all commuting unitary representations over a finite group and present a structure theorem. In the end, we show that the power of a positive-definite function and a unitary representation need not be a positive definite function and a unitary representation respectively. We also present a characterization of such a class of functions.

- Time:
- 3:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Analysis Seminar**Tuesday, 30 Jan. 3 pm

**===============****Venue:**Ramanujan hall**Host:**Sourav Pal**Speaker:**Nitin Tomar**Affiliation:**IIT Bombay**Title:**Operators associated with the pentablock and their relations with biball and symmetrized bidisc**Abstract:**We discuss properties of commuting operator triples for which the closed pentablock is a spectral set. An explicit dilation for such a triple is obtained. Also, we show the interactions of such an operator triple with the operator pairs associated with the biball and the symmetrized bidisc.

- Time:
- 4:00pm - 5:30pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
Commutative Algebra Seminar

Tuesday 30 Jan 2024, 4.00-5:30 pm

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

Venue: Room 215

Host: Tony J. Puthenpurakal

Speaker : Samarendra Sahoo

Affiliation: IIT Bombay

Title: The Eisenbud operator and complexity of modules

Abstract: The Eisenbud Operator is an important tool for studying the behavior of infinite free resolution of a module. In this talk, we discuss Eisenbud Operator and its properties as well as how the Betti numbers are related to the complexity of modules.

- Time:
- 4:00pm - 5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Algebraic Groups seminar

Tuesday, 30 January 2024, 4 pm -- 5.30 pm

============================Venue: Ramanujan Hall

Host: Shripad M. GargeSpeaker: Shripad M. Garge

Affiliation: IIT BombayTitle: Finite morphisms and normal varieties

Abstract: We introduce the notion of normal varieties and prove the following version of Zariski's main theorem: A bijective and birational morphism of irreducible varieties, \phi: X \to Y, is an isomorphism if Y is normal.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Mathematics Colloquium

Wednesday, 31 Jan. 4 pm

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

Venue: Ramanujan Hall

Host: Prachi Mahajan

Speaker: Debraj Chakrabarti

Affiliation: Central Michigan University, Mt. Pleasant, MI

Title: Convexity conditions and complex analysisAbstract: The global geometric properties of a space affect the properties of functions that can be defined on it: for example, on a connected topological space a locally constant function is constant. In complex analysis, complex convexity properties such as pseudo convexity play a crucial role in the construction and properties of holomorphic functions and other analytic objects. These conditions become very important in several complex variables since in domains in the plane the required convexity conditions are automatically satisfied.

After introducing classical complex convexity conditions, we discuss partial convexity conditions, which lead to the vanishing of Dolbeault cohomology in specified degrees. At the end, we will introduce some new geometric conditions that allow us to prove the vanishing of Dolbeault cohomology in domains in complex manifolds.

This is ongoing joint work with Phil Harrington and Andy Raich of the University of Arkansas.

We will try to make the talk accessible to a wide audience.