2:30pm» Prafullkumar Tale, IISER Bhopal- 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 Weyl algebra A_n(K). We give application to local cohomology modules of K[X_1,...., X_n]
- 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.