Speaker:Dr. Sasmita Barik, School of Basic Science, IIT Bhubaneswar. Venue: Committee Room, Department of Mathematics Time and Date: 3PM, 19th March 2018. Title: On the Spectra of MultidigraphsAbstract:We define adjacency matrix as well as Laplacian matrix of a multidigraph in a new way and study the spectral properties of some bipartite multidigraphs. It is well known that a simple undirected graph is bipartite if and only if the spectrum of its adjacency matrix is symmetric about the origin (with multiplicity). We show that the result is not true in general for multidigraphs and supply a class of non-bipartite multidigraphs which have this property. We describe the complete spectrum of a multi-directed tree in terms of the spectrum of the corresponding modular tree. In case of the Laplacian matrix of a multidigraph, we obtain a necessary and sufficient condition for which the Laplacian matrix is singular. Finally, it is proved that the absolute values of the components of the eigenvectors corresponding to the second smallest eigenvalue of the Laplacian matrix of a multi-directed tree exhibit monotonicity property similar to the Fiedler vectors of an undirected tree.Speaker: Prof. Andreas Brandstadt, University of Rostock, Germany Title : On Dually Chordal Graphs, Strongly Chordal Graphs and Leaf Powers Date and Time: 22nd February 2018 (Thursday), 3 PM Venue: Committee room, Department of Mathematics Abstract: Strongly chordal graphs, as a subclass of chordal graphs as well as of dually chordal graphs, are one of the main topics in algorithmic graph theory. In this talk, we will first mention some of the aspects of of chordal and dually chordal graphs and then focus on strongly chordal graphs and its proper subclass of leaf powers coming from phylogenetic trees. For leaf powers and its variants, various problems such as recognition and characterization are still open.Speaker:Taufiquar R Khan, Professor, Department of Mathematical Sciences. Director of Global Engagement Initiatives, College of Science, Clemson University O-201 Martin Hall, 220 Parkway Title: Electrical Impedance Using Sparsity Constraints and Statistical RegularizationAbstract:The complete electrode model for the inverse problem in Electrical Impedance Tomography (EIT) is presented. The appropriate function spaces and regularization required to solve these ill-posed inverse problems are described. The Bayesian statistical inversion using Markov Chain Monte Carlo method is used for image reconstruction. We also present some preliminary results using EIT data for damage detection in concrete. Venue: Committee Room MZ 195 Time and date: 4PM, 6th Feb 2018 (Tuesday).Speaker:Anisa Chorwadwala, IISER Pune. Title : An eigenvalue optimization problem over a family of planar punctured disks where the puncture has a dihedral symmetry. Time: 4 PM Date: 30th January 2018 (Tuesday) Venue: Committee room, Department of MathematicsAbstract:We deal with the following eigenvalue optimization problem: Given a bounded open disk $B$ in a plane, how to place an obstacle $P$ of fixed shape and size within $B$ so as to maximize or minimize the fundamental eigenvalue $\lambda_1$ of the Dirichlet Laplacian on $B\setminus P$. This means that we want to extremize the function $\rho \rightarrow lambda_1(B \setminus \rho(P))$, where $rho$ runs over the set of rigid motions such that $rho(P) \subset B$. We answer this problem in the case where $P$ is invariant under the action of a dihedral group $D_{2n}$, and where the distance from the center of the obstacle $P$ to the boundary is monotonous as a function of the argument between two axes of symmetry. The extremal configurations correspond to the cases where the axes of symmetry of $P$ coincide with a diameter of $B$. The maximising and the minimising configurations are identified.Speaker: Prof. Chris Rodger, Don Logan Endowed Chair in Mathematics, Auburn University, USA. Title : Fair colorings of graph decompositions Time: 11 AM Date: 12th January 2018 (Friday) Venue: Committee room, Department of MathematicsAbstract: Fairness notions in graph theory have been of interest for many years, attempting to distribute objects of interest evenly among different groups. Edge-coloring results include attempts to share edges equally amongst color classes, amongst edges at each vertex, and amongst edges between pairs of vertices (in the case of multigraphs). A graph decomposition of G is a partition of the edges of G into sets, each of which induces something interesting, such as an isomorphic copy of some graph H. Coloring these copies of H, while ensuring such notions of fairness are satisfied, provides a generalization of the expectations in the edge-coloring setting. Fair and extreme distributions of vertices associated with these block colorings have also been addressed. In this talk, several such results will be presented, focusing on recent work in the area.Speaker:Prof. Paola Tardelli, Department of Industrial and Information Engineering and Economics, University of L’Aquila Monteluco di Roio, Italy. Title : HEDGING OF A DEFAULTABLE CLAIM DRIVEN BY HAWKES PROCESSES Time: 2 PM Date: 12th January 2018 (Friday)Venue:Committee room, Department of Mathematics Abstract: This article presents the problem of hedging a defaultable claim in a Markovian framework. The underlying assets are assumed to be driven by mutually exciting Hawkes process. Perfect replication is not possible since the market is incomplete. Hence, a maximization of the mean value of exponential utility from the terminal wealth is considered. The value processes of the optimal investment problem and indifference prices are represented in terms of solutions to Backward Stochastic Differential Equations (BSDEs). Since the value function is characterized as the largest solution to a suitable BSDE with a non-Lipschitz generator, a result of uniqueness is is also presented.Speaker:Prof. Pong-Ping ZHU, School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia Title: A new integral equation formulation for American put options Time and Date: 17th Jan, 2018 (Wednesday) at 10.30 A.M. Venue: Committee Room, Dept. Math. .Abstract:In this talk, a completely new integral equation for the price of an American put option as well as its optimal exercise price is presented. Compared to existing integral equations for pricing American options, the new integral formulation has two distinguishable advantages; i) it is in a form of one-dimensional integral, and ii) it is in a form that is free from any discontinuity and singularities associated with the optimal exercise boundary at the expiry time. These rather unique features have led to a significant enhancement of the computational accuracy and efficiency as shown through some examples.Speaker:Prof. Biswa Nath Datta, IEEE Fellow, Distinguished Research Professor, Northern Illinois University DeKalb, Illinois 60115 USA, dattab@math.niu.edu Title: Computational and Optimization Methods for Quadratic Inverse Eigen Value Problems Arising in Mechanical Variation and Structural Dynamics: Linking Mathematics to Industry. Time and Date: 4th Jan, 2018 (Thursday) at 10:30AM Venue: Committee Room .Abstract:The Quadratic Eigenvalue Problem is to find eigenvalues and eigenvectors a quadratic matrix pencil of the form $P(\lambda) = M\lambda^2+ C\lambda+ K$, where $M, C,$ and $K$ are square matrices. Unfortunately, The problem has not been widely studied because of the intrinsic difficulties with solving the problem in a numerically effective way. Indeed, the state-of-the-art computational techniques are capable of computing only a few extremal eigenvalues and eigenvectors, especially if the matrices are large and sparse, which is often the case in practical applications. The inverse quadratic eigenvalue problem, on the other hand, refers to constructing the matrices M, C, and K, given the complete or partial spectrum and the associated eigenvectors. The inverse quadratic eigenvalue problem is equally important and arises in a wide variety of engineering applications, including mechanical vibrations, aerospace engineering, design of space structures, structural dynamics, etc. Of special practical importance is to construct the coefficient matrices from the knowledge of only partial spectrum and the associated eigenvectors. The greatest computational challenge is to solve the partial quadratic inverse eigenvalue problem using the small number of eigenvalues and eigenvectors which are all that are computable using the state-of-the-art techniques. Furthermore, computational techniques must be able to take advantage of the exploitable physical properties, such as the symmetry, positive definiteness, sparsity, etc., which are computational assets for solution of large and sparse problems. This talk will deal with two special quadratic inverse eigenvalue problems that arise in mechanical vibration and structural dynamics. The first one, Quadratic Partial Eigenvalue Assignment Problem (QPEVAP), arises in controlling dangerous vibrations in mechanical structures. Mathematically, the problem is to find two control feedback matrices such that a small amount of the eigenvalues of the associated quadratic eigenvalue problem, which are responsible for dangerous vibrations, are reassigned to suitably chosen ones while keeping the remaining large number of eigenvalues and eigenvectors unchanged. Additionally, for robust and economic control design, these feedback matrices must be found in such a way that they have the norms as small as possible and the condition number of the modified quadratic inverse problem is minimized. These considerations give rise to two onlinear unconstrained optimization problems, known respectively, as Robust Quadratic Partial Eigenvalue Assignment Problem (RQPEVAP) and Minimum Norm Quadratic Partial Eigenvalue Assignment Problem (MNQPEVAP). The other one, the Finite Element Model Updating Problem (FEMUP), arisingin the design and analysis of structural dynamics, refers to updating an analytical finite element model so that a set of measured eigenvalues and eigenvectors from a real-life structure are reproduced and the physical and structural properties of the original model are preserved. A properly updated model can be used in confidence for future designs and constructions. Another major application of FEMUP is the damage detections in structures. Solution of FEMUP also give rises to several constrained nonlinear optimization problems. I will give an overview of the recent developments on computational methods for these difficult nonlinear optimization problems and discuss directions of future research with some open problems for future research. The talk is interdisciplinary in nature and will be of interests to computational and applied mathematicians, and control and vibration engineers and optimization experts.Speaker:Prof. Anant Shastri tomorrow Venue: LH510 Time: Dec 5, 2017, 5PM. Title: Proof the Fundamental Theorem of Algebra via Linear Algebra.

** Speaker:** DAVID LEVIN, School of Mathematical Sciences, Tel Aviv University, Israel

Venue: Committee Room, Department of Mathematics

Time and Date: 3:30PM, 1^{st} December 2017.

Title: ATTRACTORS OF SEQUENCES OF FUNCTION SYSTEMS

AND THEIR RELATION TO NON-STATIONARY SUBDIVISIONAbstract:Iterated Function Systems (IFSs) have been at the heart of fractal geometry almost from its origin, and several generalizations for the notion of IFS have been suggested. Subdivision schemes are widely used in computer graphics and attempts have been made to link fractals generated by IFSs to limits generated by subdivision schemes. With an eye towards establishing connection between non-stationary subdivision schemes and fractals, in this talk we introduce the notion of “trajectories of maps defined by function systems” which may be considered as a new generalization of the traditional IFS. The significance and the convergence properties of ‘forward’ and ‘backward’ trajectories will be discussed. Unlike the ordinary fractals which are self-similar at different scales, the attractors of these trajectories may have different structures at different scales. Speaker: Dr. Samir Shukla, Visiting Scientist ISI Bangalore. Title: NEIGHBORHOOD COMPLEXES OF SOME EXPONENTIAL GRAPHS Time and Date: 3:30 PM, 22nd November 2017 (Wednesday) Venue: Committee Room, Dept Mathematics Abstract: See the abstract attached. Title: Biological Networks Speaker: Prof. S Arumugam, Kalasa Lingam University, TamilNadu Date and Time: 11th October 2017, 3 PM Venue: MZ194 Speaker: Dr. Satya Prakash, University of Haifa, Israel (Post Doctoral Fellow). Venue: Committee Room, Department of Mathematics Time and Date: 3PM, 10th October 2017. Title: Some issues in the design of experiments with ordered experimental treatments. Abstract: There are many situations where one expects an ordering among K>2 experimental groups or treatments. Although there is a large body of literature dealing with the analysis under order restrictions, surprisingly very little work has been done in the context of the design of experiments. Here, we provide some key observations and fundamental ideas which can be used as a guide for designing experiments when an ordering among the groups is known in advance. Designs maximizing power as well as designs based on single and multiple contrasts are discussed. The theoretical findings are supplemented by numerical illustrations. 14. Speaker: Prof. Christian Klingenberg, University of Wurzberg, Germany Title: Multi-species kinetic and fluid models and applications Time: 3:00 PM, 3rd October 2017 Venue: Committee Room, Mathematics Department. Abstract: We consider a multi component gas mixture. This mixture is modelled by a system of kinetic BGK equations. Consistency of the model is proven, also existence, uniqueness and the positivity of solutions. We can extend our model to an ES-BGK model and to polyatomic mixtures. By taking moments, this allows us to derive macroscopic two-species conservation laws. We present numerical simulations using an adaptive kinetic-fluid models for plasma simulations. This is joint work with Marlies Pirner (Wuerzburg University, Germany) and Gabriella Puppo (Universita Insubria, Italy).

Speaker: William Mcghee, Global Head of Quantitative Analytics, Royal Bank of Scotland. Title - Investment Banking & Quants Abstract: The speaker will talk about: What an investment bank does; Trading business and its future challenges; Role of a quant team in investment banking; Academic background of quants. Time and Date: 2:30 PM – 4 PM on 20th September 2017. Venue: LH 308

Speaker: K. Takao, Wuhan University in China,

Time: 3PM, 18^{th}August, 2017 Venue: Committee Room, Department of Mathematics. Title: Bernoulli-Carlitz and Caucy-Carlitz numbers related to hypergeometric functions Abstract: The hypergeometric-like Bernoulli-Carlitz and Cauchy-Carlitz numbers in function fields are defined as analogues of hypergeometric Bernoulli numbers and hypergeometric Cauchy numbers in real numbers, and as extensions of Bernoulli-Carlitz numbers and the Cauchy-Carlitz numbers in function fields. These numbers can be expressed explicitly in terms of incomplete Stirling-Carlitz numbers. Several analogues of hypergeometric functions in real numbers have been considered in the function fields. In this talk, we give several arithmetical properties of such numbers.

Speaker: Dr. Punit Sharma, Department of Mathematics and Operational Research, University

of Mons, Belgium.

Title: Eigenvalue backward errors of structured polynomial eigenvalue

problems

Time: 3:30 PM, Aug 17, 2017.

Abstract: Structured matrix polynomials have occurred in many engineering applications and have

been studied widely for the last two decades. Structured eigenvalue-eigenpair backward

error analysis of structured matrix polynomials is important in order to know the

backward stability of algorithms that compute them without losing the structure of of matrix

polynomials that have Hermitian and related structures, like skew-Hermitian, ∗-even, ∗-odd.

This involves a reformulation of the original problem of computing eigenvalue backward

error into an equivalent problem of minimizing the maximum eigenvalue of a

parameterized Hermitian matrix. Numerical experiments show that there is a

significant difference between the backward errors with respect to perturbations that

preserve structure and those with respect to arbitrary perturbations.

Speaker: Prof. K Parthasarathy, Ramanujan Inst. Adv study in Math (retired). Title: Groups and Analysis Time and Date: 3 PM, 20th April 2017 (Thursday) Venue: Committee Room, Dept of Math. Abstract: We will look at a few instances where groups are involved in analysis. Speaker: Dr. Divyum Sharma, Title: Thue equations with few coefficients, Time and Date: 3:30 PM, 28th April (Friday), Venue: Committee Room, Abstract: Let $F(X,Y)\in\mathbb{Z}[X,Y]$ be a form of degree $r\geq 3$, irreducible over $\mathbb{Q}$ and having at most $s+1$ non-zero coefficients. Let $h$ be a non-zero integer. Siegel proposed that the number $N_F(h)$ of integer solutions of the Thue inequality $|F(X,Y)|\leq h$ may be bounded only in terms of $s$ and $h$. Mueller and Schmidt showed that \[ N_F(h)\ll s^2h^{2/r}(1+\log h^{1/r}). \] Further, they conjectured that $s^2$ may be replaced by $s$. In this talk, we present some instances when $s^2$ may be improved. This is joint work with N. Saradha.

Speaker:Prof. Eknath Ghate, School of Mathematics, TIFR Mumbai.Title:Generalized Schwarz triples, Hypergeometric functions and Monodromy.Time:3 PM 29^{th}April 2016Venue:Committee room MZ 168Abstract:We give a classification of all generalized Schwarz tuples, using elementary number theory and group theory. This recovers Schwarz's classical 1873 results showing there are 15 families of 3-tuples (exactly the triplets for which the associated Gauss Hypergeometric function is algebraic). We deduce some results on the finiteness of certain monodromy representations. This is joint work with T. N. Venkataramana.

Speaker:Prof. Jon Aaronson, Dept. Of Mathematics, Tel-Aviv University, ISRAEL.Time:3PM – 4:30PM on 28^{th}April 2016Title:Rational ergodicity of "discrepancy" skew products and the asymptotics of affine random walks.Abstract:It is not hard to show that if (X(n): n=1,2,..) is given by a RAT (=random affine transformation) of the form X(n+1)=a(n+1)X(n)+b(n+1) where {(a(n),b(n)):n=1,2,...} are iid rvs taking values in {-1,+1} x R with E(b)=0 & E(b^2) finite, then X(n) satisfies both central and local limit theorems. We'll establish a ``weak, rough, local limit theorem" for certain non-stationary, multidimensional versions of this and use this to show rational ergodicity of "discrepancy" skew products T:X=[0,1) x Z--> X by T(x,z)=(x+A mod 1, z+D(x)) where A is irrational and the "discrepancy function" D=1 on [0,1/2) and D=-1 on [1/2,1). For each A there is a RAT sequence depending on the "minus-sign" continued fraction expansion of A. For badly approximated A, this RAT sequence satisfies the ``weak, rough, local limit theorem", whence bounded rational ergodicity of T_A.

**Speaker:** K. Sandeep.

**Title : **Moser-Trudinger and Adams Inequalities.

**Venue : **Committe room.

**Time: **4PM, April 18, 2016.

**Abstract :** Embeddings of Sobolev spaces play an important role in the

analysis of partial differential equations. We will discuss some of these sharp embeddings known as Moser-Trudinger and Adams Inequalities and

present some of the recent results obtained.

Speaker:Prof. Carlos Escudero, Departamento de Matem ́aticas Universidad Aut ́onoma de Madrid, email: carlos.escudero@uam.esTime:4PM on 6^{th }April 2016Title:On a “rather critical” “boundary value problem”Abstract:This talk is devoted to the analysis of a higher order semilinear elliptic problem. In particular, we consider a polyharmonic operator acting on the solution equal to the k-Hessian of the solution plus some datum. We pose the problem in the whole of the N-dimensional space and look for solutions with certain decay at infinity. We will first state our general existence result and then move to the possibly most interesting case: for a critical value of N the problem becomes especially hard as usual tools in nonlinear analysis seem to fail in the search for an existence proof. In order to build such a proof we develop an abstract tool consisting in a topological fixed point theorem. Existence of at least one solution to our differential problem follows from the combination of this theorem and a refinement of the classical critical Sobolev embedding. Regularity issues will also be discussed and, if time allows, we will extend our arguments to the nonlocal setting

Speaker:Dr Anish Ghosh, School of Mathematics, TIFR MumbaiTitle:Diophantine approximation andhomogeneous dynamicsTime:12 PM (NOON) 26^{th}Feb 2016Venue:Committee room MZ 168.Abstract:I will discuss the interplay between number theory and theergodictheory of group actions on homogeneous spaces of algebraic groups.Speaker:Prof. Jacques Giacomoni, LMAP (UMR CNRS 5142), Universite de Pau, Pau, FranceTitle:Uniqueness results by p(x)-extension of Diaz-Saa Inequality.Time:12 PM (Noon), 25^{th}Feb 2016.Venue:Committee room MZ 168.Abstract:I will present a new extension of the well-known inequality by Dıaz and Saa which, in our case, involves an anisotropic operator, such as the p(x)- Laplacian, ∆p(x)u ≡ div(|∇u|^{p(x)−2}∇u). Our present extension of this inequality enables us to establish some new results on the uniqueness of solutions and comparison principles for some anisotropic quasilinear elliptic and parabolic equations.

** Speaker: **J.-P. Raymond, Université Paul Sabatier Toulouse III & CNRS, Institut de Mathématiques de Toulouse 31062 Toulouse Cedex - France raymond@math.univ-toulouse.fr

**Title:** Local existence of strong solutions of fluid-structure models

**Time:** 3PM – 4PM on 22nd and 27th January 2016.

**Venue:** Committee or Seminar room (MZ168/ MZ163).

**Abstract:** We shall study a system coupling the incompressible Navier-Stokes equations with the Lam é system of linear elasticity. We prove the existence of strong solutions, local in time, when the fluid structure interface is flat. This is a joint work with M. Vanninathan. Next we shall see how we can adapt this analysis to the so-called immersed boundary method. This last part is a joint work in progress with Sylvain Ervedoza and Marc Savel.

** Speaker:** Prof. M. Vanninathan, TIFR, Center for Applicable Mathematics, Bangalore.

**Title:** Homogenization and Calculus of Variations

**Time:** 12 PM on 22nd and 27th January 2016.

**Venue:** Committee or Seminar room, (MZ 168 / MZ 163).

**Abstract:** Optimal Shape Problems form a subclass of problems of Calculus of Variations. Typically,they do not admit classical solutions. Hence relaxation of these problems is called for. Homogenization convergence offers a method to do it. Recently, another class of problems called "Optimal Oscillation Dissipation Problems" have been introduced. A new notion of convergence is required for the relaxation of this new problem. In my discussion, I plan to present main issues and ideas involved in the resolution of above problems.

** Speaker:** Biswa Nath Datta, IEEE Fellow, Distinguished Research Professor, Northern Illinois University, USA. Email: dattab@math.niu.edu

**Title:** COMPUTATIONAL AND OPTIMIZATION METHODS FOR QUADRATIC INVERSE EIGENVALUE PROBLEMS ARISING IN MECHANICAL VIBRATION AND STRUCTURAL DYNAMICS

**Time:** 11AM – 12PM on 15th January 2016.

**Venue:** Committee room MZ 168.

**Abstract:** The Quadratic Eigenvalue Problem is to find eigenvalues and eigenvectors a quadratic matrix pencil of the form P (λ) = M λ 2 + Cλ + K , where the matrices M, C, andK are square matrices. Unfortunately, The problem has not been widely studied because of the intrinsic difficulties with solving the problem in a numerically effective way. Indeed, the state-of-the-art computational techniques are capable of computing only a few extremal eigenvalues and eigenvectors, especially if the matrices are large and sparse, which is often the case in practical applications. The inverse quadratic eigenvalue problem, on the other hand, refers to constructing the matrices M, C, and K, given the complete or partial spectrum and the associated eigenvectors. The inverse quadratic eigenvalue problem is equally important and arises in a wide variety of engineering applications, including mechanical vibrations, aerospace engineering, design of space structures, structural dynamics, etc. Of special practical importance is to construct the coefficient matrices from the knowledge of only partial spectrum and the associated eigenvectors. The greatest computational challenge is to solve the partial quadratic inverse eigenvalue problem using the small number of eigenvalues and eigenvectors which are all that are computable using the state-of-the-art techniques. Furthermore, computational techniques must be able to take advantage of the exploitable physical properties, such as the symmetry, positive definiteness, sparsity, etc., which are computational assets for solution of large and sparse problems.

** Speaker:** **Prof. Paola Tardelli**, Department of Industrial and

Information Engineering and Economics, University of L'Aquila, Italy.

**Title:** Filtering for a Probabilistic Prediction of Credit

Ratings.

**Time:** 3PM – 4PM on 12 th January 2016.

**Venue:** Committee room MZ 168.

**Abstract: **To analyze the credit quality of firms, this note proposes a dynamical model. The population of firms is divided into a finite number of classes depending on their credit status. The cardinality of the population can increase during the time, since new firms can enter in the financial market. Due to changes in credit quality and to the defaults, each firm can move from a class to another, or can go to the class of the defaulted firms. Different rating agencies are considered, each of them defines its own partition of the population. Aim of this note is to find the probabilistic prediction of the actual partition of the population, and of the conditional distribution of the distance to defaults. In a partial observing setting, under some markovianity assumptions, this topic is discussed using stochastic filtering techniques.

Speaker: Prof Pramod Kanwar, Ohio University, Title: On some recent developments on clean elements in certain ring extensions. Time:11:30AM – 12:30PM.Venue:Committee room MZ 168.Abstract:An element a of a ring R is called clean if a = e + u for some idempotent e and some unit u in R. A ring is called clean if each of its elements is clean. Among other things, we discuss clean elements in certain group algebras and also in certain polynomial rings. It is shown that if the group algebra of a finitely generated solvable is clean then G is a finite group. We also obtain the set of clean elements in a polynomial ring and give conditions under which clean elements in a polynomial ring form a subring. It is shown that for a ring R, the set Cl(R[x]) of clean elements of R[x] forms a subring of R[x] if and only if Cl(R) is a subring of R and Cl(R[x]) = Cl(R) + N(R)[x] (where N(R) is the upper nil radical) and that a positive solution to the Köthe’s problem is equivalent to for any clean ring R, the set Cl(R[x]) of clean elements of R[x] forms a subring of R[x] if and only if R/N(R) is a reduced ring. (This is a joint work with Andre Leroy and Jerzy Matczuk.)

**Speaker: Dr. Prem Prakash Pandey.**

**Title: Square free values of polynomials**

** Date and Time:** 4PM – 5PM on 17th Nov and 11AM-12 PM 18th Nov.

**Venue:** Classroom MZ-158.

**Abstract:** It is conjectured that all the separable polynomials with integers coefficients, under some local conditions, take infinitely many (in fact positive density) square free values on integer arguments. But not a single polynomial of degree greater than $3$ is proven to exhibit this property. In this article we will study some properties of roots of unity, which separate a primitive $m^{th}$ root of unity with $1$, and use them to generate polynomials of degree $m-1$ which take square free values at infinitely many arguments, in fact on positive density of arguments. A very widely talked polynomial, in this direction, is $X^4+2$. In this article we prove that $X^4+2$ takes infinitely many square free values. The ideas of this article give some new openings, in particular, towards the conjecture.

**Speaker: Prof. K. R. Parthasarathy, ISI Delhi.**

**Title: What is quantum computation?**

**Date & Time:** 3PM – 4PM on 2nd and 9th November 2015.

**Location:** MZ 168, Committee Room, Mathematics Department..

**Abstract:**

This subject may be of interest to students of mathematics, computer science and electrical engineering. In these two lectures we shall cover the following elementary ideas leading to the notion of a quantum computer and circuits for algorithms on a quantum computer.

1. Logic gates in a classical computer and the universality theorem.

2. n-qubit Hilbert space, states, unitary transformations as gates, measurements, dirac notation.

3. Elementary gates: 1-qubit, Pauli, CNOT,Toffoli, Swap gates, universality theorem.

4. Circuits for algorithms, two examples: addition of n-bit numbers, Fourier transform in the group {0,1,2,…, n-1} with addition modulo n.

**Speaker: Dr. Shanta Laishram, ISI Delhi.**

**Title: On some Diophantine equations involving terms of binary recurrence sequences.**

**Date & Time:** 22nd September 2015, 3:00 PM.

**Location:** MZ 163, Department of Mathematics.

**Abstract:**

Fibonacci and other binary sequences come up in number theory and many other areas of mathematics. They have interesting properties and have been well studied. Most of the properties and problems in integers have an analogue in binary recurrence sequences. In this talk, I will discuss about some Diophantine equations involving terms of binary recurrence sequences. I will also report on some recent results on a joint work with P. Das. The talk will be accessible to general mathematical audience.

**Speaker: Prof. Krishna B. Athreya, Iowa State University, USA.**

**Title: Introduction to Markov Chain Monte Carlo methods.**

**Date & Time:** 17th July 2015, 11:00 AM.

**Location:** MZ 168, Committee Room, Mathematics Department.

**Speaker: Prof. Gerald Beer, Emeritus Professor at California State University, Los Angeles.**

**Talk 1: On locally Lipschitz functions.**

**Date and Time:** 21st April 2015, 11:00 AM to 12 noon.

**Talk 2: Uniform continuity of the product of real functions.**

**Date and Time:** 23rd April 2015, 11:00 AM to 12 noon.

**Location:** MZ 168, Committee Room, Mathematics Department.

**Speaker: Dr. Christopher Anand, McMaster University, Canada**

**Title: High Performance Medical Image Reconstruction. What could go wrong?**

**Date & Time:** 1st April 2015, 3:00 PM.

**Location:** MZ 168, Committee Room, Mathematics Department.

**Speaker: Dr. Sanjiban Santra, Faculdade de Matematica, Universidade ****Federal do Para 66.075-110 – Belem – Para – Brazil.**

**Title: On some fourth order problems associated to Physics.**

**Date & Time:** 31th March 2015, 4:00 PM.

**Location:** MZ 168, Committee Room, Mathematics Department.

**Abstract:**

We consider a fourth order traveling wave equation associated to the Suspension Bridge Problem (SBP). This equations are modeled by the traveling wave behavior on the Narrows Tacoma and the Golden Gate bridge. We prove existence of homoclinic solutions when the wave speed is small. We will also discuss the associated fourth order Liouville theorem to the problem and possible link with the De Giorgi’s conjecture. This is an attempt to prove the McKenna-Walter conjecture which is open for the last two decades.

**Speaker: Dr. Gautam Borisagar, Zakir Husain Delhi College.**

**Title : Iwahori-Hekce model for supersingular representation for GL2(Qp).
**

Iwahori-Hekce model for supersingular representation for GL2(Qp)

- See more at: http://sms.niser.ac.in/news/seminar-27#sthash.evWcPUUe.dpu

Iwahori-Hekce model for supersingular representation for GL2(Qp)

- See more at: http://sms.niser.ac.in/news/seminar-27#sthash.evWcPUUe.dpuf**.**

**Date & Time:** 17th March 2015, 3:00 PM.

**Location:** MZ 168, Committee Room, Mathematics Department.

**Speaker: Prof. M. L. Chaudhry, Royal Military College of Canada, Ontario, Canada.**

**Title: Roots, Stochastic Processes and Computers.
**

**Date & Time:** 10th March 2015, 3:00 PM.

**Location:** MZ 168, Committee Room, Mathematics Department

**Abstract: **

Roots of equations involving high degree polynomials and transcendental functions play an important role in many stochastic processes such as queueing, reliability and random walks. Several researchers have expressed concerns regarding the evaluation of such roots. Kendall (1964) states that interesting features of queueing theory are obscured by “the Laplacian Curtain”. Kleinrock (1975) states in his book “one of the most difficult parts of this method of spectrum factorization is to solve for the roots.” Neuts states in a paper by Shaler Stidham “In discussing matrix-analytic solutions, I had pointed out that when the Rouché roots coincide or are close together, the method of roots could be numerically inaccurate.” In a recent paper, while dealing with a complex batch service queueing system with batch size dependent service, Bar-Lev et al. state that, in practice, the general solution of their problem requires calculation of roots of a complicated equation which, in practice, can result in numerical inaccuracies when the decision variable assumes a large value. The purpose of this talk will be to trace the history of root finding and respond to above questions as well as show how easily and accurately the roots can be found using recent advances in computer science and software packages provided enough precision, which is readily available on such packages, is used. If time permits, we will discuss how roots are used in inverting probability generating functions and Laplace transforms.

**Speaker: Dr. Manoj Verma, Post-doctoral fellow, IMSc, Chennai.**

**Title: On a form of degree $d$ in $2d+1$ variables.**

**Date & Time:** 25th Feb 2015, 3:45 PM.

**Location:** MZ 168, Committee Room, Mathematics Department

**Abstract: **

The square-root barrier implies that the circle method is unlikely to give an asymptotic formula for the number of representations of zero by a form of degree $d$ if the number of variables is less than $2d+1$. Such asymptotic formulas are known in case of some cubic forms in seven variables but no example of such an asymptotic formula for a form of degree $d$ in $2d+1$ variables with $d\geq 4 $ seems to exist in literature. For each $d\geq 4$, we derive such an asymptotic formula for a particular form of degree $d$ in $2d+1$ variables.

**Speaker: Dr. Durga Prasad Challa, Postdoctoral researcher, INHA University, South Korea.**

**Title: Wave propagation by sound-soft small bodies.**

**Date & Time:** 19th Feb 2015, 3:00 PM.

**Location:** MZ 168, Committee Room, Mathematics Department

**Abstract: **

In this talk, we discuss the time harmonic wave propagation by the collection of small bodies embedded in a homogeneous acoustic medium in R^3. We model the small scatterers as impenetrable obstacles of arbitrary shapes. We assume no periodicity nor randomness in distributing the small scatterers. This collection of small scatterers is characterized by their number ‘M’, maximum among their diameters ‘a’ and the minimum distance between them ‘d’. The goal is to derive the asymptotic expansion of the scattered fields by taking into account all the 3 parameters ‘M; a and d’. The leading term appearing in this approximation is nothing but the exact formula derived, using Foldy-Lax method, for the far-field associated to the scattering by the point-like scatterers located on the locations of small scatterers where the scattering coefficients are replaced by the capacitances of the small scatterers. Finally, as an application to our result we we will discuss the corresponding inverse problem of locating the scatterers, recovering their capacitances and then to estimate their sizes. We will also discuss, in the case that the number of obstacles is very large, the problem of reconstructing the coefficients which models the equivalent effective medium.

**Speaker: Prof. Krishna Athreya, Iowa State University, USA.**

**Title: Introduction to Probability Theory.**

**Date & Time:** 29th January 2015, 3:00 PM.

**Location:** MZ 168, Committee Room, Mathematics Department.

**Abstract:**

Probability theory provides the mathematical basis for the study of random phenomena. First one identifies the set of all possible outcomes,called the sample space, followed by a collection of subsets of the sample space called the events collection and finally a function mapping the event collection into the interval [0,1]. This triplet consisting of the sample space, event collection and the probability function is an example of a measure space. We illustrate this with examples when the sample space is finite, countable, the real line, the Euclidean space, the sequence space of real numbers, the function space of continuous functions and many more. We also introduce the concepts of random variables, random vectors, random functions and random fields. We also describe the basic law of large numbers and the central limit theorem.

Ref. Probability Theory TRIM series Vol 41.

**Speaker: Professor Roberta Musina, Department of Mathematics, Università degli Studi di Udine, Italy**

**First talk:** 20th January at 11:30 AM

**Title of talk: A survey lecture on the classical obstacle problem**

**Second talk:** 23rd January at 11:30 AM

**Title of talk: The Dirichlet and Navier Fractional Laplacians**

**Location for both talks:** MZ 168, Committee Room, Mathematics Department.

**Speaker: Dr. Bhargab Chattopadhyay, Univ of Texas at Dallas, USA.**

**Title : Fixed-Width Confidence Interval for Gini Index.**

**Date & Time:** 9th January 2015, 3:00 PM.

**Location:** MZ 168, Committee Room, Mathematics Department.

**Speaker: Prof. Bong Dae Choi, Sungkyunkwan University, Seoul, Korea.**

**Title : Performance Analysis of MAC Protocol of EDCA on Common Channel and Reservation On Service Channels for IEEE 802.11p/1609.4 WAVE.**

**Date & Time:** 24th December 2014, 11:00 AM.

**Location:** MZ 168, Committee Room, Mathematics Department.

**Dr. Debajyoti Nandi, Rutgers University, USA**

**Title : Combinatorial identities arising from representation theory of ****affine Lie algebras using vertex-operator-theoretic techniques.**

**Date & Time:** 25th November 2014, 3:00 PM

**Location:** MZ 168, Committee Room, Mathematics Department.

**Abstract:**

Lepowsky-Wilson’s remarkable vertex-operator-theoretic proof of the classical Rogers-Ramanujan identities initiated a fruitful area of “algebraic combinatorics” relating partition identities to the representation theory of vertex algebras. In this talk I will give a brief historic overview of this area and a few examples of such partition identities, including my recent discovery of a new set of (conjectured) partition identities arising from the standard level 4 representations of the affine Lie algebra $A_2^{(2)}$. These new partition identities have exciting new features that were not seen in any of the previous examples of this type. My result follows from a construction of a spanning set using certain “vertex operators” acting on a highest weight vector. I will also talk about how “experimental mathematics” can be used to gain insight into such problems.

**Dr. Dhanya Rajendran, Post-Doctoral fellow, IISc, Bangalore.**

**Title : A three solution theorem for singular nonlinear elliptic boundary value problems.**

**Date & Time:** 18th November 2014, 12:00 Noon.

**Location:** MZ 168, Committee Room, Department of Mathematics.

**Abstract (PDF)**

**Dr. Lakshmi Sankar, University of West Bohemia, Czech Republic**

**Title : Semipositone Problems on Unbounded Domains**

**Date & Time: **17th November, 2014, 12:00 Noon

**Location: **MZ 168, Committee Room, Mathematics Department

**Abstract (PDF)
**

**Dr. Shrishendu Chaudhuri, TIFR, Centre for Applicable Mathematics, Bangalore**

**Title : Controllability of Linearized Compressible Navier Stokes equations.**

**Date & Time: **14th November 2014, 3:00 PM

**Location: **MZ 168, Committee Room, Mathematics Department.

**Abstract:**

Then we consider compressible Navier-Stokes equations in one dimension, linearized around a constant steady state $(Q_0,V_0)$, with $Q_0 > 0,V_0\geq 0$. It is a coupled system involving both transport and parabolic effects. We study the controllability of this linearized system in bounded interval $(0,L)$. We find that the properties of the two semigroups $(e^{tA})_{t\geq0} $ (the one when $V_0 = 0$ and the one when $V_0> 0$) and the spectrum of $A$ are completely different where $A$ is the corresponding linearized operator. We obtain several interesting positive and negative results for the null controllability and approximate controllability of the system using interior or boundary control in both the cases $V_0 =0$ and $V_0>0$.

Joint works with Mythily Ramaswamy, Jean-Pierre Raymond, Debanjana Mitra and Michael Renardy.

**Dr. Sutanu Roy, Visiting Scientist, ISI Kolkata**

**Title: A brief introduction to braided multiplicative unitaries**

**Date & Time: **October 17, 2014, 11:00 AM.

**Location:** MZ 168 Committee Room, Mathematics Department.

**Abstract**

**Dr. Krishan Gahalaut (Postdoctoral fellow), King Abdullah University of Science and Technology, Saudi Arabia**

**Title of the talk: Isogeometric Analysis: Condition Number Estimates and Multigrid Methods**

**Date & Time: **October 13, 2014, 3:00 PM.

**Location:** MZ 168 Committee Room, Mathematics Department.

**Abstract (PDF)**

**Professor S. S. Sritharan, Director, Center for DECISION, RISK, CONTROLS & SIGINT (DRCSI), Naval Postgraduate School, Monterey, California, USA.**

**Title: The Three Astras of Tosio Kato: Harmonic Analysis Methods for Nonlinear PDEs of Fluid Dynamics & Physics**

**Date & Time: **11th Sept. 2014 at 3:00 PM

**Location: **Committee Room, Mathematics Department.

**Abstract:**

In this talk we will give an exposition of three powerful weapons utilized effectively by Tosio Kato in the solvability theory of important nonlinear partial differential equations such as the Navier-Stokes equations, Nonlinear Schrodinger equations, the Maxwell-Dirac equations of relativistic quantum theory, the Einstein field equations, etc. The three tools are linear and nonlinear accretive operators, commutator estimates and logarithmic Sobolev inequality. In this talk we will work out one or two specific nonlinear PDEs mentioned above to demonstrate how these tools come together.

**Dr. Ashish K. Srivastava, Associate Professor, Saint Louis University, USA**

**Title: Modules invariant under automorphisms of their covers and envelopes.**

**Date & Time: **21st August 3:00 PM

**Location: **Committee Room (MZ 168)

**Abstract:**

**Dr. Prosenjit Roy, TIFR-CAM, Bangalore**

**Title: Eigenvalue Problems with Dirichlet-Neumann Type Boundary Conditions on Large Cylinders**

**Date & Time:** 12th May 2014 at 4 PM

**Abstract: **We will consider eigenvalue problems with mixed (Dirichlet on some part and Neumann on the remaining part of the boundary) boundary type conditions. The domains (dimensions > 1) under consideration will be of cylindrical types, which will tend to become unbounded in one direction. We will study the asymptotic behavior of the eigenmodes of such problems. I will show how these problems are connected to “Problems of Dimension Reduction”.