# Seminars

## Seminar by Prof. Arvind Ayyer

Speaker: Arvind Ayyer
(Indian Institute of Science, Bangalore)

Date: 4th November 2019, Monday.
Time: 4:00 PM
Venue: MZ195, Committee Room, Department of Mathematics

Title: Factorization theorems for classical group characters

Abstract: Characters of classical groups appear in the enumeration of many interesting combinatorial problems. We show that, for a wide class of partitions, and for an even number of variables of which half are reciprocals of the other half, Schur functions (i.e., characters of the general linear group) factorize into a product of two characters of other classical groups. Time permitting, we will present similar results involving sums of two Schur functions. All the proofs will involve elementary applications of ideas from linear algebra. This is joint work with Roger Behrend (J. Combin. Theory Ser. A 165 (2019) 78-105).

## Seminar by Prof. Praveen Chandrashekar

Speaker: Praveen Chandrashekar
(TIFR Centre for Applicable Mathematics)

Date: 24 October 2019, Thursday.
Time:3:00 PM
Venue: MZ195, Committee Room, Department of Mathematics

Title: Divergence-free discontinuous Galerkin method for ideal
compressible MHD

Abstract:
Some PDE models like MHD and Maxwell's equations contain magnetic field as a dependent variable which must be divergence-free due to the non-existence of magnetic monopoles. This is an inherent constraint satisfied by the solutions of these PDEs due to their curl structure. Numerical schemes may not preserve this constraint unless they are specifically designed for this purpose. A staggered storage of variables is useful to satisfy such constraints by a numerical scheme. In this talk, I will describe a discontinuous Galerkin method which automatically satisfies the divergence constraint. The numerical flux used in such DG methods must satisfy a consistency condition between the 1-D and multi-D Riemann solvers, and we construct HLL-type schemes for MHD that exhibit such consistency. Some form of limiter is required to control spurious numerical oscillations especially for MHD and this is achieved by a divergence-free reconstruction scheme. I will show some results for MHD and Maxwell's equations.

## Seminar by Prof. Somnath Jha

Date: 22 October 2019, Tuesday.

Time:4:00 PM

Venue: MZ195, Committee Room, Department of Mathematics

Title: p^r Selmer companion modular forms

Abstract

## Seminar by Prof. Swadesh Kumar Sahoo

Speaker: Prof. Swadesh Kumar Sahoo, IIT Indore.

Venue: MZ 195, Committee room

Time: 17th September at 3.30pm.

Abstract

## Seminar by Prof. Ravi Prakash

Venue: MZ 195
Time: 3:00 pm
Date: September 11, 2019.

Title: Topological Derivatives and Its Applications

Abstract:

In this talk, we discuss topology optimization problem arises from inverse problem set up. We quickly review the concept of topological derivatives and it’s use in topology optimization. To be more precise, It is well known that a huge class of inverse problems can be written in the form of overdetermined boundary value problems. Such
a difficulty can be overcome by rewriting the inverse problem in the form of an optimization problem.The basic idea of this presentation consist in minimizing a functional
measuring the misfit between a given data and a weak solution with respect to the parameters under consideration. The topological derivative concept is used. In
particular, the objective functional is expanded and then truncated up to the second order term, leading to a quadratic and strictly convex form with respect to the parameters under consideration. Finally, a trivial optimization step will lead to a non-iterative second order reconstruction algorithm which does not depend on any initial guess. As a result, the
reconstruction process will become very robust with respect to noisy data.

## Colloquium and seminar by Professor Eknath Ghate

[1] Seminar on 13th August 2019

Date: 13.08.2019 (Tuesday)
Time: 3:30pm
Venue: MZ 195, Committee Room, Department of Mathematics

Title: P-adic families of modular forms.
Abstract: We explain some background on p-adic families of cusp forms. This will be an elementary talk for non-experts.

[2] Colloquium on 14th August 2019
Date: 14.08.2019 (Wednesday)
Time: 3:30pm
Venue: MZ 195, Committee Room, Department of Mathematics

Title: Reductions of Galois Representations and the theta operator
Abstract: Galois representations arise in many problems in number theory. For some years, my coauthors and I have been engaged in studying the reductions of local Galois representations, using various Langlands correspondences. Now that these reductions are known in many cases of small slopes, one might ask if there are some general principles which are beginning to emerge. In this talk I would like to explain one such general principle involving the theta operator, which was discovered recently (jointly with A. Kumar). The principle allows one to deduce the shape of some of the reductions in slope (v + 1) from the shape of the reductions in slope v.

## Colloquium by Professor GD Veerappa Gowda

Venue: MZ 195, Committee Room,

Department of Mathematics Time: 3:30pm

date: 15.04.2019 (Monday)

Speaker: GD Veerappa Gowda

Title: A Family of Godunov-type Solvers for the Pressureless Gas Dynamics and Related Models.

Abstract

## Seminar series by Prof. Nitin Nitsure

Seminar 1

Venue: LH623
Time: 5-6:30 pm
Date: 8th April 2019.

Title: Differential calculus via commutative algebra.

Abstract: In this talk, we will see how to use the tools of commutative algebra to get algebraic definitions and results inspired by usual differential calculus. This is of importance in algebraic geometry, algebraic groups and in modern number theory

Seminar 2

Venue: LH-310 (in Lecture hall complex)
Time: 4pm
Date: 10.04.2019 (Wednesday)

Speaker: Nitin Nitsure,
(School of Mathematics, TIFR, Mumbai)

Title: A glimpse into the Foundations of Mathematics.

Abstract: What is Mathematics about? What does it mean to say that some mathematical objects exist? What is the meaning of `truth' in mathematics? What is a proof? Why should we believe in the resulting theorems?

Foundational questions such as these have intrigued common people, as well as mathematicians and philosophers, for ages. In this talk, we will take a look at these questions, and at some of their suggested answers from ancient to modern times. Most of the talk will be understandable by undergraduate students of all subjects, who have had some exposure to mathematics.

Seminar 3

Speaker: Professor Nitin Nitsure
(School of Mathematics, TIFR, Mumbai)
Venue: MZ 195, Committee Room, Department of Mathematics
Time: 9:30-11:00 am
Date: 12th April 2019.

Title: The implicit function theorem in algebraic geometry.

Abstract: The implicit function theorem is a cornerstone of differential calculus as applied to manifolds. We will talk about its analogue in algebraic geometry, which led to important historical developments such as algebraic spaces and etale cohomology.

## Seminar by Professor Michael Karow

Venue: MZ 195, Committee Room, Department of Mathematics
Time: 4pm
Date: 26.03.2019 (Tuesday)

Speaker: Professor Michael Karow
(Department of Mathematics, TU Berlin, Germany)

Title: Projection Lemma and the Cyclic Decomposition Theorem
Abstract:
One of the fundamental results of Linear Algebra is the Cyclic Decomposition Theorem. Let $A:X o X$ be a linear operator on a finite dimensional vector space $X$ over a field $F$. The theorem states that $X$ is a direct sum of $A$ invariant subspaces which are generated by a single vector. The special case that $F$ is the field of complex numbers yields the Jordan Canonical Form. We present a short proof of the Cyclic Decomposition Theorem using a result on projections.

## Seminar by Siddhartha Pratim Chakrabarty

Title: Pricing of Passport Option
Time and Date: 12 noon, 20th March 2019,
Venue: Committee Room

Abstract:
The problem of pricing the passport option, whose contingent claim is dependent on the balance of a trading account, is considered. For the European passport option, a closed form solution exists for the symmetric case, when the risk-free rate is identical to the cost of carry. However, in absence of an explicit solution for the non-symmetric case, we need to use numerical methods in order to solve the corresponding pricing partial differential equation. In addition, we derive the Greeks, namely, Delta and Gamma for the symmetric case, since the optimal holding strategy is dependent on them. The key result is the improvement in the pricing of the option, as well as estimation of these Greeks, with significantly better results being observed near zero accumulated gain (in the symmetric case), by using the three time level scheme, which is then extended to estimate the price and the Greeks in the non-symmetric case. For the American passport option, the pricing is done by presenting the free boundary problem as a sequence of linear complementarity problems, with the numerical implementation being carried out using the three time level scheme. The key result is the usage of lesser number of grid points as compared to the numerical approaches used previously for this problem, while maintaining the accuracy of the option prices obtained.

## Seminar by Dr. Divyum Sharma

Speaker: Dr. Divyum Sharma;
Date: 29th March, 2019 (Friday);
Time: 12 noon;
Venue: Committee Room, Department of Mathematics.

Abstract: Let $F$ be an irreducible homogeneous polynomial in two variables with integer coefficients and with degree at least 3. Consider the equation $F(x,y) = h$ for some fixed non-zero integer $h$. In a pioneering work in 1909, Thue proved that this equation has only finitely many integral solutions. Much effort has been made to obtain upper bounds
for the number of solutions of these equations which are independent of the size of the coefficients of $F$. In this talk, we discuss the upper bounds predicted by some of the central conjectures of this area and present some partial contributions in that direction.

## Semianr by Dr. Pratyusha Chattopadhyay

Date: 22th March, 2019 (Friday);
Time: 12 noon;
Venue: Committee Room, Department of Mathematics.

Title: Equality of transvection groups.

Abstract: Hyman Bass introduced transvection groups to establish certain "classical" results on Serre's problem. These are special type of subgroups of the automorphism group of finitely generated projective modules. Transvection groups are important in the study of projective modules and their K-theory. Another interesting aspect of these groups are
that they can be visualized as the generalization of classical groups in the set up of projective modules. In this talk, we will recall the definitions of linear, symplectic, and orthogonal transvection groups and discuss some results regarding equality of transvection group and elementary transvection group in the relative case with respect to an ideal of the ring.

## Seminar by Dr. Sudhansu Sekhar Rout

Speaker: Dr. Sudhansu Sekhar Rout
Date: 20th March, 2019 (Wednesday);
Time: 4:30 PM;
Venue: Committee Room, Department of Mathematics.

Title: Sums of $S$-units in recurrence sequences

Abstract: In this talk, we give various finiteness results concerning terms of recurrence sequences $U_n$ representable as a sum of $S$-units with a fixed number of terms. First, we discuss that under certain (necessary) conditions, the number of indices $n$ for which $U_n$ allows such a representation is finite and can be bounded in terms of the
parameters involved. In this generality, our result is ineffective, i.e. we cannot bound the size of the exceptional indices. We also give an effective result, under some stronger assumptions.

## Seminar by Dr. Shreedevi K Masuti

Speaker: Dr. Shreedevi K Masuti;
Date: 19th March, 2019 (Tuesday);
Time: 12 Noon;
Venue: Committee Room, Department of Mathematics.

Title: Hilbert functions of Gorenstein Algebras.

Abstract: Hilbert function is an important numerical invaraint associated to an affine or a projective variety. It is a usual philosophy that the Hilbert function reflects the additional structure of the variety. Classification of the Hilbert functions of algebras with additional properties (like Gorenstein, level or complete interesection) is a challenging problem in commutative algebra. Recently, jointly with M. E. Rossi, we classified the possible Hilbert funcions of Gorenstein (more generally, level) algebras in some cases (Artinian algebras of socle degree 4). In this talk we will discuss these new developements.

## Seminar by Dr. Saurabh Kr Singh

Speaker: Dr. Saurabh Kr Singh;

Date: 18th March, 2019 (Monday);

Time: 12 Noon; Venue: Committee Room,

Department of Mathematics.

Title:Sub-convexity problems: Some history and recent developments;

Abstract

## Seminar by Dr. Arpan Kabiraj

Speaker: Dr. Arpan Kabiraj
Date: 13th March, 2019 (Wednesday)
Time: 12 Noon;
Venue: Committee Room, Department of Mathematics.

Title:Center of the Goldman Lie algebra

Abstract: In 1980s Goldman introduced a Lie algebra structure on the free vector space generated by the free homotopy classes of oriented closed curves in any orientable surface. This Lie bracket is known as the Goldman bracket and the Lie algebra is known as the Goldman Lie algebra. In this talk I will define Goldman Lie algebra and discuss a conjecture of Chas and Sullivan about the center of the Goldman Lie algebra. I will explain the relation between Goldman Lie algebra and character varieties of surface groups. If time permits, I will also show how techniques from geometric group theory could be used to compute center of the Goldman Lie algebra. I will mention some open problems related to Goldman Lie algebra.

## Seminar by Dr. Prangama Sarkar

Speaker: Dr. Prangama Sarkar.

Title: Mixed multiplicities, Minkowski inequalities and Rees' theorem for
filtrations.

Date: 12th March, 2019 (Tuesday);
Time: 12 Noon.
Venue: Committee Room, Department of Mathematics.

Abstract: We define mixed multiplicities of (not necessarily Noetherian) filtrations of $\mathfrak m$-primary ideals in a Noetherian local ring $(R,\mathfrak m)$, generalizing the classical theory for $\mathfrak m$-primary ideals. We construct a real polynomial whose coefficients give the mixed multiplicities. Many of the classical theorems for mixed multiplicities of $\mathfrak m$-primary ideals hold for filtrations (not necessarily Noetherian). In this talk we mainly focus on the famous Minkowski inequalities of Teissier and Rees' Theorem on multiplicity.

## Seminar by Dr. Lakshmi Kanta Patra

Speaker: Dr. Lakshmi Kanta Patra;
Date: 11th March, 2019 (Monday);
Time: 12 Noon;
Venue: Committee Room, Department of Mathematics.

Title: Estimating a function of scale parameter of an exponential
population with unknown location.

Abstract: We have considered the problem of estimating a function of scale parameter $\ln \simga$ of an exponential distribution under an arbitrary location invariant bowl-shaped loss function, when location parameter $\mu$ is unknown. Various improved estimators are proposed. Inadmissibility of the best affine equivariant estimator (BAEE) of
$\ln\sigma$ is established by deriving a Stein-type estimator. This improved estimator is not smooth. We derive a smooth estimator improving upon the BAEE. Further, the integral expression of risk difference (IERD) approach of Kubokawa is used to derive a class of improved estimators. To illustrate these results, we consider two specific loss functions: squared error and linex loss functions, and derive various estimators improving upon the BAEE. Finally, a simulation study has been carried out to numerically compare the risk performance of the improved estimators.

## Seminar by Prof. Arnab Mitra from IISER Tirupati

Date: 01/02/2019 (Friday)
Time: 3pm
Venue: MZ 195, Committee Room, Department of Mathematics, IIT Delhi.

Title: Periods and distinction problems

Abstract: Let G be a topological group and H a closed subgroup of G. An irreducible representation of G is said to be H-distinguished if it admits a linear form that is H-invariant. Given a pair (G,H) it is a natural question to classify all irreducible H-distinguished representations of G. I will begin the talk by describing why such distinction questions are interesting in representation theory. After that we will see some recent classification results for certain specific "symmetric" pairs (G,H).

## Seminar by Professor Ramesh Gangolli from University of Washington

Date: 12/02/2019
Time: 3pm
Venue: MZ 195, Committee Room, Department of Mathematics, IIT Delhi.

Title: Some Unpublished work of Harish-Chandra

## Seminar by Dr. Biswarup Biswas

Title and Abstract

Date: 16/01/19

Time: 11 am

Venue: Committee Romm, Department of Mathematics

## Seminar by Dr. Md Abu Talhamainuddin Ansary

Title and Abstract

Date: 09/01/19

Time: 11 am

Venue: Committee room

## Seminar by Dr. Arnapurna Panda

Date: 04/01/19
Time: 12 noon
Venue: Committee room

Title : Solving dynamic multi-objective optimization problems using nature inspired metaheuristics and their real life applications

Abstract : The dynamic multi-objective optimization problems (DMOPs) basically deal with objectives that are conflicting with each other and they change over time or environments. Thus a non-dominated solution with time becomes dominated and vice versa. In constrained scenarios, at times the constraint may also change with time. Thus a feasible solution may become infeasible and the reciprocal is also possible. This uncertain scenario need investigation and requires development of new strategies to
deal with these problems. One of the potential application is Railway Junction Rescheduling Problem. Ex. Suppose a train get delayed due to a disturbance, which leads to miss its scheduled time table. This results in conflict with another train scheduled to use that same track. To avoid the conflict a train dispatcher may have to delay other trains competing for the same track, which will propagate the delay throughout the network. Rescheduling is more difficult to deal with than scheduling (making a perfect schedule for the trains at a juncrion) because it involves rapid decision making within a time frame.

## Seminar by Dr. Pratibha Shakya

Title and Abstract

Date: 04/01/19

Time: 11 am

Venue: MZ 195, committee room, Department of Mathematics

## Seminar by Dr. Rajni Rohila

Title: Numerical Solutions of Some Linear and Nonlinear Diffusion Equations by Cubic B-spline Collocation Method

Abstract: Many phenomena in various scientific fields are mathematically expressed by using the well-known evolution equations. The diffusion equation is one of them. We aim to develop new numerical methods to study diffusion equations. Significant literature can be found over second order approximations for cubic B-spline collocation method. The fourth order method is never studied for numerical solutions of partial differential equations. We have developed fourth order cubic B-spline collocation method and a B-spline ADI method to solve partial differential equations.

Date: 02/01/19
Time: 3 pm
Venue: MZ 195, committee room, Department of Mathematics

## Seminar by Dr. Ajoy Jana

Title: REGULARIZATION OF ILL-POSED NONHOMOGENEOUS PARABOLIC PROBLEMS

Abstract:
Two types of ill-posed problems are studied, namely, parabolic final value problem (FVP) and abstract source identification problem. We define a mild solution for parabolic FVP and prove some properties of the mild solution. Truncated spectral regularization method and quasi-reversibility method are considered as regularization method. We derive error estimates for exact as well as noisy data and obtain estimates under a priori parameter choice strategies. Obtained estimates include many results in the literature.

Date: 13/12/2018
Time: 11 am
Venue: MZ 195, committee room, Department of Mathematics

## Seminar by Dr. Tapas Pandit, Postdoctoral fellow, IISC Bangalore

Speaker: Dr. Tapas Pandit, Postdoctoral fellow, IISC Bangalore

Date and Time: 30/11/2018 (Friday) at 11 AM

Venue: MZ 195, Committee room, Department of Mathematics

Title: Signcryption in a quantum world.

Abstract:
Post-quantum cryptography deals with cryptosystems that run on conventional computers and are secure against attacks by potential quantum computers. Quantum security is an ultimate goal in the race of modern cryptographic designs. This will ensure the security against quantum adversary even if the protocols run in the quantum computers.
Signcryption is an important public key cryptographic primitive which provides the functionality of encryption and signature, i.e., both confidentiality and authenticity of data. In the classical setting, An, Dodis and Rabin (Eurocrypt, 2002) proposed generic constructions of signcryption schemes based on three paradigms, viz., encrypt-then-sign
(EtS), sign-then-encrypt (StE) and commit-then-encrypt-and-sign (CtE&S). In this talk, we first explain a brief overview of post-quantum and quantum security of cryptographic protocols. Then, we discuss syntax, security definition and different paradigms (EtS, StE and CtE&S) of signcryption. Finally, we briefly illustrate the security of these paradigms in a quantum world.

## Seminar by Prof. Jacques Giacomoni from , Laboratory of Mathematics and their Applications (LMAP), Universite de Pau et des pays de l’adour, Pau, France.

Speaker: Prof. Jacques Giacomoni, Laboratory of Mathematics and their Applications
(LMAP), Universite de Pau et des pays de l’adour, Pau, France.

Date and Time: 22/11/2018 (Thursday) at 11 AM

Venue: MZ 194, Seminar Room, Department of Mathematics

Title: Global and blow-up radial solutions for quasilinear elliptic systems with gradient terms

## Seminar by Prof. Debdip Ganguly, IISER Pune

Speaker: Prof. Debdip Ganguly, IISER Pune

Date and Time: 20/11/2018 (Tuesday) at 11 AM

Venue: MZ 194, Seminar room, Department of Mathematics

Title: On the equivalence of heat Kernels.

Abstract: Let P be a second-order, symmetric, and nonnegative elliptic operator with real coefficients defined on noncompact Riemannian manifold M, and let V be a real-valued function which belongs to the class of small perturbation potentials with respect to the heat kernel of P in M. We prove that under some further geometric assumptions the
positive minimal heat kernels of P-V and of P on M are equivalent. This is a joint work with Yehuda Pinchover.

## Seminar by Prof. Krishna Maddaly, Faculty of Mathematics, Ashoka University

Speaker: Prof. Krishna Maddaly, Faculty of Mathematics, Ashoka
University

Date and Time: 26/10/2018 (Friday) at 3:30 PM

Venue: MZ 195, Committee Room, Department of Mathematics

Title: Spectral Theory of Random operators

Abstract: In this talk, I will give a overview of problems addressed in the spectral theory of random operators in Quantum Mechanics.

## Seminar by Prof. Alexander Volfovsky, Department of Statistical Science, Duke University

Speaker: Prof. Alexander Volfovsky, Department of Statistical Science,
Duke University

Date and Time: 05/10/2018 (Friday) at 4:00 PM

Venue: MZ 194, Seminar Room, Department of Mathematics

Title: Machine learning methods for causal inference from complex
observational data

Abstract: A classical problem in causal inference is that of matching treatment units to control units in an observational dataset. This problem is distinct from simple estimation of treatment effects as it provides additional practical interpretability of the underlying causal mechanisms that is not available without matching. Some of the main
challenges in developing matching methods arise from the tension among (i) inclusion of as many covariates as possible in defining the matched groups, (ii) having matched groups with enough treated and control units for a valid estimate of average treatment effect in each group, (iii) computing the matched pairs efficiently for large datasets, and (iv) dealing with complicating factors such as non-independence among units. We propose the Fast Large-scale Almost Matching Exactly (FLAME) framework to tackle these problems for categorical covariates. At its core this framework proposes an optimization objective for match quality that captures covariates that are integral for making causal statements while encouraging as many matches as possible. We demonstrate that this framework is able to construct good matched groups on relevant covariates and further extend the methodology to incorporate continuous and other complex covariates.

## Seminar by Prof. Krishna Athreya, Distinguished Professor Emeritus, Departments of mathematics and statistics, Iowa State University, USA.

Speaker: Prof. Krishna Athreya, Professor Emeritus, Departments of
mathematics and statistics, Iowa State University, USA.

Date and Time: 23/8/2018 (Thursday) at 3:30 PM

Venue: MZ 195, Committee Room, Department of Mathematics

Title: Standard Brownian Motion

Abstract: In this talk, an explicit construction of standard Brownian motion (SBM) using N(0,1) random variables and Haar functions will be described. We shall also discuss the Paley-Wiener-Zygmund(1933) theorem on the support of SBM by non-differentiable paths. An ergodic theorem of Kallianpur and Robbins will also be described.

## Seminar by Prof. Ravindra Bapat, Indian Statistical Institute, New Delhi

Speaker: Prof. Ravindra Bapat, Indian Statistical Institute, New Delhi

Date and Time: 04/04/2018 (Wednesday) at 4:00 PM

Venue: MZ 195, Committee Room, Department of Mathematics

Title: Cayley-Hamilton Theorem: Proof Techniques and Extensions

Abstract: Cayley-Hamilton Theorem is a well-known result in linear algebra, usually covered in a first course. We survey the history of this result and outline various proof techniques that have been used. Straubing gave a graph-theoretic proof of the Cayley-Hamilton Theorem. A readable exposition of the proof was given by Zeilberger. We describe this proof. We then turn to recent joint work with Souvik Roy where we have used the same technique to obtain an extension of the Cayley-Hamilton Theorem to mixed discriminants.

## Seminar by Prof. Krishnan Rajkumar, Jawaharlal Nehru University, New Delhi

Speaker: Prof. Krishnan Rajkumar, Jawaharlal Nehru University, New Delhi

Date and Time: 15/3/2018 (Thursday) at 4:00 PM

Venue: MZ 195, Committee Room, Department of Mathematics

Title: Generalized factorials in several variables

Abstract: The discovery by M. Bhargava (1997), of generalized factorials in Dedekind domains, unified past work as well as answered questions in the fields of integer valued polynomials, polynomial mappings over finite abelian groups and fixed divisors of polynomials. The first part of the talk will be a historical account of these developments. In the second part, we will focus on attempts by M. Bhargava (2000) and S. Evrard (2012) to define the notion of generalized factorials in several variables. We will then outline a joint work with D. Prasad and A. S. Reddy, where this notion is further developed.

## Seminar by Prof. Ved Prakash Gupta, Jawaharlal Nehru University, New Delhi

Speaker: Prof. Ved Prakash Gupta, Jawaharlal Nehru University, New Delhi

Date and Time: 15/2/2018 (Thursday) at 3:00 PM

Venue: MZ 195, Committee Room, Department of Mathematics

Title: IDEALS AND LIE IDEALS OF CERTAIN NORMED ALGEBRASAbstract: Every associative algebra inherits a canonical Lie algebra structure and there exists a deep relationship between ideals and Lie ideals of such algebras. This relationship extends to the category of normed algebras as well. After providing a quick overview of objects of interest, we will discuss some recent developments made in this direction. Some part of this talk will be based on joint works with Ranjana Jain and Bharat Talwar.

## Seminar by Prof. Apala Majumdar from University of Bath, United Kingdom

Speaker: Prof. Apala Majumdar (Reader in Applied Mathematics, University of Bath, United Kingdom)

Date and Time: 31/1/2018 (Wednesday) at 4:00 PM

Venue: MZ 195, Committee Room, Department of Mathematics

Title:  Multistability for Liquid Crystal SystemsAbstract: Nematic liquid crystals are classical examples of mesophases intermediate between solids and liquids, with anisotropic or direction-dependent optical and electro-magnetic properties. We review two popular continuum theories for nematic liquid crystals: the Oseen-Frank and the Landau-de Gennes theories. We illustrate how these theories can be applied to liquid crystal devices, with the Planar Bistable Nematic device as a case study. We model the Planar Bistable Nematic Device in terms of problems in the calculus of variations and theory of elliptic partial differential equations. We use tools from singular perturbation theory, topology, functional analysis and numerical methods to study the multiple solution branches as a function of the geometry, boundary conditions, temperature and material properties. We provide a semi-analytic description of a previously unreported Well Order Reconstruction solution in this planar device.

## Seminar by Prof. Ajay Kumar, Department of Mathematics, University of Delhi

Speaker: Prof. Ajay Kumar, Department of Mathematics, University of Delhi

Date and Time: 24/1/2018 (Wednesday) at 4:00 PM

Venue: MZ 194, Seminar Room, Department of Mathematics

Title: Uncertainty Principles on locally compact groups

Abstract: We discuss uncertainty principles like Hardy’s theorem, Qualitative uncertainty principle, Beurling‘s theorem and Heisenberg inequality for locally compact groups such as R^n, abelian groups, Heisenberg group, nilpotent Lie groups and several other classes of non-abelian groups

## Seminar by Prof. Rajendra Bhatia, ISI Delhi & Ashoka University, Haryana.

Speaker: Prof. Rajendra Bhatia, ISI Delhi & Ashoka University, Haryana.

Date and Time: 15/1/2018 (Monday) at 3:00 PM

Venue: MZ 194, Seminar Room, Department of Mathematics

Title:  Diagonals of matrices

Abstract: Everyone knows that the trace of a matrix is the sum of its diagonal entries as well as the sum of its eigenvalues. A lot more can be said, and leads to much interesting mathematics., some of which will be discussed in the talk.