**Speaker:** Professor M. K. Kadalbajoo

**Affiliation:** LNMIIT

**Date:** April 21, 2022 (Thursday)

**Time:** 4:00 PM

**Venue:** LT-16

**Title:** The Mysteries of Zero and Infinity

**Abstract:** Traversing very quickly through more than two millennia and from Greek philosophy (Archimedes, Aristotle, Ptolemy, Pythagoras) to Indian discovery (Pingala, Bhaskara, Brahmagupta, Aryabhata), we shall unravel mysteries about the two fascinating and important Numbers-Zero and Infinity- including some very famous paradoxes, the Calculus of Newton & Leibnitz, some relevant fundamental and revolutionary notions given by Gauss, Riemann, Cantor… in discourse. In the latter part of the lecture (time permitting), we shall briefly mention the cross-over of Zero from Mathematics to Physics and talk very briefly about the revolutionary concepts of the last century, namely, the Relativistic Zero and the Quantum Zero and in passing the Black Holes. The quote “Zero will have the last laugh” would end the lecture.

**Guest Speaker:** Prof. M. K. Kadalbajoo

**Affiliation:** LNMIIT

**Date:** February 28, 2022 (Monday)(National Science Day)

**Time:** 4:00 PM

**Venue:** LT-16

**Google meet link:** meet.google.com/asi-mkfx-aut

**Title:** An optimal error estimate of an IMEX finite element method for some partial integro-differential equations arising in finance

**Abstract:** Over the past few decades, the growth of the derivative markets has been a major development in finance. Among the most popular derivatives, options are actively traded in the financial world. The price of a European option, under the Black-Scholes jump-diffusion model, is governed by a parabolic partial integro-differential equation (PIDE). The aim of this talk is to present a finite element method combined with an implicit-explicit (IMEX) time-stepping procedure for the aforementioned PIDE. Since the pay-off function (i.e., the final condition of the PIDE) is in general not smooth enough and hence, over the whole domain, the solution of the PIDE is also not smooth enough. Therefore, in the natural norm, one can not achieve an optimal rate of convergence of the numerical method. With realistic regularity assumptions on the data and without any severe step-size restrictions, an optimal error estimate for the proposed method will be provided under a certain weighted Sobolev norm. The theoretical findings and the efficiency of the proposed method will be demonstrated by some numerical experiments.

**About the Speaker:** Prof. M K Kadalbajoo is the retired professor from the department of Mathematics, IIT Kanpur. He is currently working as distinguished professor in the department of mathematics, The LNM Institute of Information Technology, Jaipur. He received his Ph.D. degree from IIT Bombay in 1976. His research area is Numerical analysis and parallel algorithms. He was awarded the C.L Chandna Mathematics Award for distinguished and outstanding contributions in Mathematics Research and Teaching (1998). He is the Fellow, National Academy of Sciences, India (1996). He worked as an expert member in many government committees.

**Guest Speaker:** Prof. Sudhir Ghorpade

**Affiliation:** IIT Bombay

**Date:** December 27, 2021(Monday)

**Time:** 11:30 AM

**Venue:** LT-5

**Title:** Number of common zeros of systems of polynomials over finite fields

**Google meet link:** https://meet.google.com/ube-tdnc-asb

**Abstract:** It is elementary and well-known that a polynomial in one variable of degree d with coefficients in a field F has at most d zeros in F. An analogue of this for homogeneous polynomials is that a homogeneous polynomial in two variables of degree d with coefficients in F has at most d non-proportional zeros in F 2 (excluding the origin). We note that d is a “good” bound in the sense that if F has at least d elements, then there are polynomials of degree d that attain this bound. When F is a finite field with q elements, it makes sense to ask similar questions for the number of common zeros of systems of multivariable polynomials of a given degree. A remarkable answer for the general case of r linearly independent polynomials of degree d in m variables over the field with q elements was given by Heijnen and Pellikaan in 1998. The analogous problem for systems of multivariable homogeneous polynomials turned out to be more challenging, and answers were known only in the case of a single polynomial or a system of two linearly independent polynomials, thanks to the work of Serre (1991) and Boguslavsky (1997). For the general case, there was an elaborate conjecture by Boguslavsky and Tsfasman that remained open for almost two decades. In this talk we will outline some recent progress on this conjecture as well as some newer developments. This is based on a joint work with M. Datta, and also with P. Beelen and M. Datta. Most of the talk should be accessible to anyone with undergraduate-level background in mathematics.

- An Invited Talk by Prof. Anish Ghosh, TIFR Bombay on “An invitation to ergodic theory”, December 22, 2021. (National Mathematics Day)
- An Invited Talk by Prof. Kadalbajoo, LNMIIT on “Remembering Srinivasa Ramanujan, A Legendary Mathematician of the 20th Century” December 22, 2021 (National Mathematics Day)

**Guest Speaker:** Prof. S. Kesavan

**Affiliation:** IIT Madras

**Date:** December 22, 2021(Wednesday) (National Mathematics Day)

**Time:** 11:30 AM

**Venue:** LT-5

**Title:** An invitation to ergodic theory

**Google meet link:** Meet - drx-soin-nbd (google.com)

**Abstract:** Ergodic theory is the mathematical study of "chaotic" systems. I will explain what this means and how it connects to an entirely different branch of mathematics, namely the study of numbers.

**Guest Speaker:** Prof. Anish Ghosh

**Affiliation:** TIFR Bombay

**Date:** December 22, 2021(Wednesday) (National Mathematics Day)

**Time:** 10:00 AM

**Venue:** LT-5

**Title:** From the triangle inequality to the isoperimetric inequality

**Google meet link:** Meet - drx-soin-nbd (google.com)

**Abstract:** Starting from the basic geometric result that the sum of the lengths of two sides of a triangle is greater than the length of the third side, we will look at a series of shape optimisation problems involving polygons and finally arrive at the classical isoperimetric inequality in the plane. The talk will be accessible to all persons familiar with high school geometry (triangles) and basic notions of analysis (like supremum, elementary limits).

**Guest Speaker:** Prof. M. K. Kadalbajoo

**Affiliation:** LNMIIT

**Date:** December 22, 2021(Wednesday) (National Mathematics Day)

**Time:** 12:30 PM

**Venue:** LT-5

**Title:** Remembering Srinivasa Ramanujan, A Legendary Mathematician of the 20th Century

**Google meet link:** Meet - drx-soin-nbd (google.com)

**Abstract:** The talk would very briefly traverse through the life of the great and legendary mathematician, Srinivasa Ramanujan, followed by a peep into some of his outstanding and phenomenal contribution that attracted and engaged the attention of several great mathematicians for over a century leading to exemplary advances in many branches of mathematics.

**Guest Speaker:** Prof. Bimal Roy

**Affiliation:** ISI Kolkata

**Date:** December 14, 2021(Tuesday)

**Time:** 11:30 AM

**Venue:** LT-5

**Title: ** On Recent Issues of Cryptology

**Google meet link:** meet.google.com/qym-diub-kaz

**Abstract:** The concepts like Data Obfuscation, Zero Knowledge Protocols, E-voting, Matroids in Secret Sharing etc. will be explained with illustrations and applications.

**Guest Speaker: ** Prof. Amitabha Tripathi

**Affiliation:** IIT Delhi

**Date:** November 25, 2019 (Monday)

**Time:** 3:00 PM

**Venue:** LT-5

**Title:** A Gentle Introduction to Ramsey’s Theorems.

**Abstract:** Two players sit in front of a hexagonal board with vertices labelled 1, 2, 3, 4, 5, 6. Player A has a red marker while player B has a blue marker. Player A goes first and draws a line joining any two vertices with his marker. Player B then selects a different pair of points and joins them with his marker. The two players take turns drawing lines between pairs of points hitherto unmarked. The player who first succeeds in having a triangle with all sides of his colour wins. Is it possible for the game to end in a draw? The answer is No! This leads to the determination of the Ramsey number R(3, 3). More generally, the determination of the (classic) Ramsey numbers R(m, n) for different pairs of positive integers m, n has been the central theme of Ramsey’s theorem.

**Guest Speaker:** Professor Marie-Françoise Roy

**Affiliation:** University of Rennes, France

**Date:** February 14, 2020 (Friday)

**Time:** 3:00 PM

**Venue:** LT-9

**Title:** Bernstein polynomials, computer-aided geometric design and real algebraic applications.

**Abstract:** Bernstein polynomials serve as the mathematical foundation for modern computer-aided geometric design (CAGD). Popular programs, like Adobe's Illustrator and Flash, and font imaging systems such as Postscript, utilize Bernstein polynomials to form what are known as Bézier curves. Introduced in the 1960's, Bézier curves were first implemented in automobile design but quickly gained popularity in other areas of CAGD with the expansion of the digital age. The Bernstein polynomials, however, came about long before the invention of computers and were introduced by the russian mathematician, Sergei Natanovich Bernstein, as a means to prove the Weierstrass Approximation Theorem. These polynomials are currently widely used in approximation theory, probability, but also provide certificates of positivity in real algebraic geometry.

**Guest Speaker:** Prof Carsten Carstensen

**Affiliation:** Humboldt-Universität zu Berlin, Germany

**Date:** March 5, 2020 (Thursday)

**Time:** 10:00 am

**Venue:** LT-5

**Title:** Challenges in Computational Calculus of Variations: 3 Examples in 1D.

**Abstract:** Three examples in the calculus of variations serve as master examples to illustrate what can go wrong in the minimization of a functional. The three disaster problems will be explained and illustrate the direct method in the calculus of variations and the success or failure of the simplest finite element approximation. Some illustrations for real-life applications will give an outlook at the computational calculus of variations.

**Guest Speaker:** Prof. A. S. Vasudeva Murthy

**Affiliation:** TIFR-CAM, Bangalore,

**Date:** November 1, 2019 (Friday)

**Time:** 4:00 PM

**Venue:** LT-5

**Title:** Far Field Boundary Conditions and their Approximation.

**Abstract:** Many PDE's are often formulated in unbounded domains. However for computing the solutions numerically we need to truncate it to a bounded domain. This introduces artificial boundaries and consequently artificial boundary conditions (ABC). The choice of ABC can be tricky and can lead to wrong solutions. We give a brief survey for ABC with some simple examples.

**Guest Speaker:** Prof G.K. Srinivasan

**Affiliation:** IIT Bombay

**Date:** September 13, 2018 (Thursday)

**Time:** 05:15 PM

**Venue:** LT-5

**Title:** Isoperimetric Inequalities.

**Abstract:** This is an old classical result with many modern ramifications. We shall give two proofs of this inequality and also discuss connections with other analytic inequalities such as the Sobolev inequality and the Coarea formula. We also discuss some further ramifications.

**Guest Speaker:** Prof. Manjul Gupta

**Affiliation:** IIT Kanpur

**Date:** November 5, 2019 (Tuesday)

**Time:** 4:00 PM

**Venue:** LT-5

**Title:** Matrix Transformations on Sequence Spaces.

**Abstract:** A finite matrix of order mn, defines a continuous linear transformation from a vector space of dimension n to a vector space of dimension m and vice-versa. The natural question is “what can we say about infinite matrices?” After giving brief introduction of sequence spaces, in this talk we consider this aspect of sequence space theory which dates back to the beginning of the last century in the work of G. Kothe and O. Toeplitz.

**Guest Speaker:** Dr. Charu Goel

**Affiliation:** IIIT Nagpur

**Date:** February 15, 2020 (Saturday)

**Time:** 9:00 AM

**Venue:** LT-5

**Title:** Positive Polynomials and Sums of Squares.

**Abstract:** Sums of squares representations of polynomials is of fundamental importance in real algebraic geometry. Determining the positivity of a polynomial in more than one variable is computationally difficult in general. Writing a polynomial as a sum of squares, on the other hand, provides a computationally tractable certificate of positivity. The study of these two notions goes back to the 1888 seminal paper of Hilbert, where he gave a full characterization of all pairs (n, d) for which every nonnegative (positive) polynomial of a fixed degree d in a given number of variables n is a sum of squares of polynomials. Ninety years later, Choi and Lam asserted that this characterization remains unchanged for symmetric forms. In this talk first some key observations and problems related to Hilbert’s the- orem will be discussed. We then complete the above assertion of Choi-Lam. Along the way, we shall also discuss briefly how test sets for positivity of symmetric polynomials play an important role in establishing this assertion.

**Guest Speaker:** Prof. MK Kadalbajoo

**Affiliation:** distinguished professor at LNMIIT

**Date:** November 14, 2019 (Thursday)

**Time:** 5:00 PM

**Venue:** LT-8

**Title:** Some Fundamental Principles of Numerical Computations.

**Abstract:** Some fundamental principles of numerical computations and challenges to solve mathematical models to real world phenomena will be discussed

**Guest Speaker:** Mr. Shankar Veerabathiran

**Affiliation:** Research Scholar at Ramanujan Institute for Advanced Study in Mathematics, University of Madras.

**Date:** Oct 12, 2018 (Friday)

**Time:** 5:00 PM

**Venue:** LT-4

**Title:** An invariant subspace theorem.

**Abstract:** Beurling-Lax-Halmos theorem says that any shift invariant subspace of a vector valued Hardy Hilbert space is given by an isometric (or partially isometric) image of a vector valued Hardy space. Completely contractive covariant representations on sub product systems are important since they provide a unified approach to study commuting as well as non-commuting tuples of operators on Hilbert spaces. In this talk we investigate a Beurling-Lax-Halmos type invariant subspace theorem for completely contractive covariant representations on standard sub product systems. The notion of curvature is also explored which generalizes earlier definitions of curvature due to Arveson, Popescu and Muhly-Solel. This is a joint work with J.Sarkar and Harsh Trivedi.

**Guest Speaker:** Prof. Jaydeb Sarkar

**Affiliation:** ISI Bangalore

**Date:** November 02, 2018 (Friday)

**Time: ** 12:00 Noon

**Venue:** LT-7

**Title:** Fibonacci sequence

**Abstract:** The Fibonacci sequence is the number sequence 0, 1, 1, 2, 3, 5, 8, 13..... Note that 1 = 1 + 0, 2 = 1 + 1, 3 = 2 + 1, 5 = 3 + 2, 8 = 5 + 3 etc. This talk will be an elementary and modest introduction to the theory of Fibonacci sequence. We will also recall some ideas of Euclid (of Alexandria) and the (geometric/archeological) Concept of ``Golden ratio''. The talk will be aimed at a general audience and is accessible for B.Tech. Students.

**Guest Speaker:** Prof. S. Kumaresan

**Affiliation:** University of Hyderabad

**Date:** January 28, 2019 (Monday)

**Time:** 4:00 PM

**Venue:** LT-5

**Title:** From Coordinates to Manifolds: A setting for Modern Differential Geometry.

**Abstract:** In this talk, He will start with the genesis of coordinate systems. Then he moves on to a practical definition of a manifold, the basic notions of tangents and transformation laws.

**Guest Speaker:** Prof. S. Kumaresan

**Affiliation:** University of Hyderabad

**Date:** January 29, 2019 (Tuesday)

**Time:** 4:00 PM

**Venue:** LT-5

**Title:** Function Spaces

**Abstract:** This will be an overview of various results scattered throughout courses in analysis and studied in isolation. The talk will emphasize the recurring themes which exhibit unifying principles of these results. It may be considered as a Global view of analysis.

**Guest Speaker:** Prof G.K. Srinivasan

**Affiliation:** IIT Bombay

**Date:** September 15, 2018 (Saturday)

**Time:** 09:30 AM

**Venue:** LT-5

**Title:** The Gamma Function: An Eclectic tour

**Abstract:** The ubiquitous gamma function was introduced in analysis by Leonard Euler in a letter to Goldbach nearly 300 years ago. Since its inception it has attracted the attention of almost every eminent mathematician of the eighteenth and nineteenth century and continues to interest the mathematicians of the present generation. The talk will be an expository in which some important historical signposts of the nineteenth century will be discussed. We shall touch upon several diverse approaches to the study of this special function with a sampling of a few proofs (off the beaten track) of some known results and also a discussion of certain less known identities. The talk would conclude with some recent results.

**Guest Speaker:** Prof. M.K.Kadalbajoo

**Affiliation:** LNMIIT

**Date:** October 20, 2018 (Saturday)

**Time:** 4:00 PM

**Venue:** LT-4

**Title:** Mathematics Everywhere.

**Abstract:** This is an introductory talk without giving mathematical details but describing some of the important and emerging areas where mathematical thinking and maturity finds its presence and we shall start with derivative pricing and end with quantum chaos.

A career counselling Seminar on Cyber Security by Dr. Dheerendra Mishra

**Guest Speaker:** Chirag Goyal, Director

**Affiliation:** Bulwark Cyberx

**Date:** March 17, 2018 (Saturday)

**Time:** 9:30 AM

**Venue:** LNMIIT

**Title:** Cyber Security

**Abstract:** Chirag Goyal is Certified Ethical Hacker & cyber security and Forensics Consultant. Has worked for the Ministry Of Defence and many other institutions as a Cyber security trainer and forensics investigator.

**Guest Speaker:** Dr. V.C.V. Rao

**Affiliation:** C-DAC, Pune

**Date:** March 21, 2018 (Wednesday)

**Time:** 11:00 PM

**Venue:** LT-7

**Title:** Challenges in Computational Mathematics (High Performance Computing Perspective

**Abstract:** his talk would be of interest to the general audience, mainly students (both UG & PG), having a background of the broad area of Scientific Computing.

**Guest Speaker:** Prof. M.K.Kadalbajoo

**Affiliation:** LNMIIT

**Date:** September 07, 2017 (Thursday)

**Time:** 3:00 PM

**Venue:** LT-7

**Title:** Computational Mathematics - Some Challenges

**Abstract:** We shall give very rudimentary details of two very important sub-fields of Computational Mathematics, viz. Numerical Linear Algebra (NLA) and Computational Fluid Dynamics (CFD) and conclude with some major challenges that need attention.

**Guest Speaker:** Prof. Tirupathi Gudi

**Affiliation:** IISc Bangalore

**Date:** March 27, 2017 (Monday)

**Time:** 9:00 AM

**Venue:** LT-5

**Title:** On Quadratic Finite Element Methods for the Obstacle Problem

**Abstract:** The quadratic finite element method on simple meshes for two dimensional obstacle problems is known to converge with constraints at the midpoints of the edges. The convergence of analogous quadratic finite element methods is not known for three dimensional problems so far. In this talk, we will design a bubble enriched quadratic finite element and prove the convergence of the method. Further we will discuss numerical experiments to illustrate the theoretical results. This is a joint work with Gaddam Sharat.

**Guest Speaker:** Prof. Tirupathi Gudi

**Affiliation:** IISc Bangalore

**Date:** March 22, 2017 (Wednesday)

**Time:** 4:00 PM

**Venue:** LT-5

**Title:** Stabilization methods for convection-diffusion problem

**Abstract:** It is well known that the numerical solution of the convection dominated diffusion problem by the standard Galerkin method exhibits spurious oscillations. There were different remedies proposed in the literature to suppress those oscillations and further to enhance the accuracy of the solution by improved order of convergence. Examples are streamline diffusion method, local projection method, bubble stabilization technique, least square method and discontinuous Galerkin method, etc. In this talk, we will discuss on two newly designed methods based on patch-wise local projections by using the conforming finite element space and the nonconforming finite element space, respectively. These methods are defined on a single mesh and without enriching the finite element space. Some numerical examples illustrating the theoretical results will be presented. This is a joint work with Dr. Asha K. Dond.

An invited seminar by Prof. Nandini Nilakantan (IIT Kanpur) on “The KneserConjecture: A proof using the Borsuk Ulam Theorem” March 10, 2015

An invited seminar by Prof. Amber Habib (SNU Noida) on “Black-Scholes PDE in Finance” May 22, 2015.

Lecture series by Prof. Graeme Fair-weather (Colorado School of Mines, (USA) on “Alternating Direction Implicit Orthogonal Spline Collocation Methods for Time-Dependent Problems” March 26, 2014.

An invited seminar by Prof. Amiya K. Pani (IIT Bombay) on “Scientific Computing: A New Way of Looking at Mathematics” March 26, 2014 Lecture series by Prof. P.C. Das on “Inverse Problems” Feb. 7, 2014. An invited seminar by Prof. J.K. Verma (IIT Bombay) on “A recent proof of the fundamental theorem of Algebra” April 17, 2012.

A series of seminars on Partial Differential Equations by Prof. V. Raghavendra (IIT Kanpur) and Prof. Vasudev Murthy (TIFR Bangalore), November 3-4, 2011.