Colloquium

   

 


Abstract:


How would you strategize in a game with say, 50 players ? If the game were repeated many times, and you saw that your neighbour was doing well in several previous rounds, would you be tempted to imitate the neighbour in the next round ? Would that be {\em rational} on your part ?  In games with a large number of players, outcomes are associated not with the actual tuple of strategies chosen by players but with the distribution of what fraction of players choose which move. The pattern of reasoning in such games is different from those in which all players know each others' types. We discuss Nash equilibria, and some logical / automata theoretic formulations of stability in such games.


About the speaker:


Professor R. Ramanujam from The Institute of Mathematical Sciences, Chennai. 

 


Abstract:


Urn models are one of the basic models studied in stochastic processes. It has nearly a century long history dating back to the works of Polya and Eggenberger. It has useful applications in modelling spread of contagious diseases, prey-predator analysis, diffusion of gases, reinforced learning, database management, analysis of algorithms - to name a few only. It is also useful in clinical trials, but in that case it is important to assume the replacement matrix to be random. Bai and Hu (2005) provided a detailed analysis of such models using martingale techniques under the assumption of existence of $(2+\epsilon)$ moments with $\epsilon>0$. Laruelle and Pages (2013) improved upon the results using stochastic approximation by relaxing the moment assumptions to existence of second moment alone. We relax the moment conditions further by careful application of stochastic approximation technique. The presentation will provide a brief overview of stochastic approximation technique in the current context. This is a joint work with Ujan Gangopadhyay.


About the speaker:


Professor Krishanu Maulik from Indian Statistical Institute, Kolkata. 

 


Abstract:


The classical Wierstrass approximation theorem of a   continuous function  from [0,1]  to R by polynomials in uniform norm will be proved using the weak law of large numbers for coin tossing. This will be generalised to continuous functions on the unit simplex and the unit cube in higher dimensions. The approximation by convolution  to produce smooth functions will also be discussed. Finally, Stirlings formula will be proved using Fourier analysis and the local clt for the Poisson distribution.


About the speaker:


Professor Athreya obtained his Phd. in mathematics from Stanford University, California USA in 1967. He returned to India in 1971 and was a professor of mathematics at the Indian Institute of Science from 1971 to 1980. He was a professor at Iowa State University from 1980 till 2013. He is currently a professor emeritus at Iowa State University. He was given the title of professor in the College of Liberal arts and Sciences, Iowa State University, in 1998.


His fields of interest are Probability Theory, Mathematical Statistics, Mathematical Analysis and Mathematical Modelling. He is a Fellow of the Indian Academy of Sciences. He is a Fellow of the Institute of Mathematical Statistics, USA.


He is an elected member of the International Statistics.
He has authored two books published by Springer Verlag  and written a number of research papers in mathematics and statistics. He is deeply interested in teaching mathematics at all levels.  His hobbies include listening to Indian classical and folk  music. 

 


Abstract:


Among the many contributions of George Polya in Mathematics, "Polya's Theorem on Polynomials", stands out for being a surprising result and for its beauty of proof. So much so that it has been favorite to Paul Erdos. We present this wonderful result and its astoundingly beautiful and simple proof.


About the speaker:


Professor Harish Chandra is from the Department Of Mathematics Institute of Science, Banaras Hindu University. 

 


Abstract:


Riemann surfaces or complex structures on surfaces are ubiquitous in mathematics. I shall introduce some other associated geometric structures like hyperbolic and projective structures, and talk of their deformations. The study of their moduli spaces involves an interplay of topology, geometry and analysis, and I will highlight some of that interaction in the context of my own work.


 Abstract:


We explore the entropy solution framework for scalar conservation laws that are perturbed by multiplicative Levy noise. The primary focus of this talk is to establish existence and uniqueness of entropy solutions of conservation laws with multiple spatial dimensions that are driven by jump processes. The entropy inequalities are formally obtained by Ito-L´evy chain rule. The issue of multidimensionality requires generalized ´ interpretation of entropy inequalities to accommodate Young measure valued solution. We first establish the existence of entropy solution in the generalized sense via vanishing viscosity approximation, and then establish the L1-contraction principle which also requires vanishing viscosity regularization. Finally, the L1 contraction principle is used to argue that the generalized entropy solution is indeed the classical entropy solution.
Based on joint works with K. H. Karlsen, U. Koley and A. K. Majee. 

 


Abstract:


In 1927, Van der Waerden proved that if the set of natural numbers is partitioned into two sets, one of them will have arbitrarily long arithmetic progressions. Generalizing, Erdos conjectured that one could partition any sufficiently dense infinite set S of numbers into two, and one of the parts will contain arbitrarily long arithmetic progressions. This was proved in a celebrated result by E. Szemeredi in 1975, using combinatorial techniques.In 1978, H. Furstenberg provided an ergodic theoretic proof of Szemeredi's result. The talk will cover the topological dynamical approach to questions on arithmetic progressions on integer sets using Furstenberg's approach. We will briefly mention some effective versions of Furstenberg's result, obtained in a recent joint work of the speaker with Rod Downey and Andre Nies.As a minor digression, we will also mention a "proof from the book" by H.
Furstenberg, which sheds some light on the connection between topology and number theory. About the speaker:


Satyadev Nandakumar is an assistant professor in computer science and engineering at IIT Kanpur. He received his Ph. D from Iowa State University in 2009.

 


Abstract:


In this talk we discuss a proof of the result that the surfaces of revolution that are geodesically conjugate to the flat cylinder are isometric to it. This is a joint work with H. A. Gururaja.


About The Speaker:


Professor C.S. Aravinda finished M.Sc. in 1985 from Central College, Bangalore and Ph.D. in Mathematics in 1995 from TIFR, University of Mumbai. His research interests are in Geometry, Topology and Dynamics in negative curvature.He was a faculty in Chennai Mathematical Institute from 1997-2007, and has been at TIFR-CAM since 2007.Professor Aravinda has translated the biography "The Man Who Knew Infinity" of Ramanujan from English to Kannada. Also he has been conducting workshops for college and university teachers and has been in the Editorial board of RMS newsletter, Mathematics Student, Hardy-Ramanujan Journal.

 


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.


About The Speaker:


Prof. K. Sandeep is a faculty at TIFR-CAM, Bangalore. His research interests lie in Variational Methods of PDEs, including PDE posed on hyperbolic spaces, and nonlinear Functional Analysis. He completed his Ph.D. from TIFR, Bangalore centre in 2002. He received the Shanti Swarup Bhatnagar Prize for Mathematical Sciences in 2015.


 


Abstract:


Every one knows Fermat's Last Theorem was proved by Andrew Wiles in 1994. But not many are aware that some 10 years before that Gerd Faltings had made substantial progress towards proving the theorem. In fact Faltings proved a very general result (known as Mordell's conjecture) which asserts in particular that for a large class of homogeneous polynomials with coefficients in the rational number field $\Q$, the set of zeros in $\Q^3$ is finite upto scaling by $\Q^x$. This class includes the Fermat polynomials $x^n+ y^n + z^n$ for $n > 4$. In this talk I will formulate and explain the statement of Falting's theorem and add some general comments. I will say nothing about the proof (which I am not adequately familiar with).


 


Abstract:


We consider certain lower order perturbations of polyharmonic operators and prove uniqueness of recovery of the perturbations from the knowledge of full and partial boundary Neumann data. Time permitting, we will prove stability estimates for the recovery of zeroth order perturbation of the biharmonic operator from full and partial boundary Neumann data as well.


 


Abstract:


Width (resp. height) for a subgroup of a group roughly measures the pairwise (resp. total) intersection of conjugates of the subgroup. In this talk, after going through some basics of Hyperbolic Geometry, I will prove width and height of quasiconvex subgroups of closed hyperbolic surface groups to be finite. This proof is due to R.Gitik, M.Mitra, E.Rips and M.Sageev. They have proved it in more general case: quasiconvex subgroups of hyperbolic groups have finite height and width..


 


Abstract:


One simple approach to visualize and summarize complex curve/image data is to extend the classical boxplot to the functional setting. This necessitates to develop a ranking of the functions. A first possibility is to use the notion of band depth that produces an ordering from the center outward. A second possibility is to use a tilting approach to assessing the influence that functional data have on the value of a statistic, and to rank the data in terms of that influence. We describe the computational aspects of those two approaches, explore their properties by simulations, and illustrate their application to data from climate science and brain imaging.


 


About The Speaker:


We shall review the general expectation that in Anderson Model describing disordered systems, it is expected and proved that the local eigenvalue statistics is Poission in the localized regime. However we show in this work that this is special to the rank one tight binding model and in general the statistics can only be Compound Poisson in the localized regime.


 


About The Speaker:


Prof. B. V. Rao is a an eminent mathematicians of the country. He obtained his PhD from ISI Kolkata in 1970 and after spending few years at UC Berkeley he was associated with ISI till 2010. Presently he is a Professor at CMI Chennai. His research contributions has been admired all over the world. He has motivated generations of mathematicians in the country through his teaching. He is a role model for many teachers in the country.


 


Abstract:


Matrix groups are ubiquitous in mathematics - Lie theory, Arithmetic groups, Number theory, Representation Theory, K-theory, are areas where different aspects are considered. We consider certain questions on factorizations of groups into special types of subgroups that give rise to some unexpected implications on the ambient group.


About The Speaker:


Professor Sury had received his PhD from TIFR, Mumbai and currently a Professor at ISI, Bangalore. He works in Algebra and Number Theory, and is well known for his contribution on congruence subgroup problem. He is actively involved in editorial responsibilities of Resonance, Proceedings of IAS and Indian Journal of Pure and Applied maths as well as mathematical training programs in the country. He is an excellent expositor of the subject.


 


Abstract:


In the 18th century, while dealing with astronomical and geodesic measurements, the scientists were confronted with a statistical problem, which in those days was described as "the problem of combining inconsistent equations". People who worked on this problem and contributed towards its solutions include Euler, Laplace, Gauss and Legendre among many others. I shall discuss the history of the problem and how it eventually led to the invention of the method of least squares.


About The Speaker:


Prof. Probal Chaudhuri did his undergraduate and post-graduate studies at the Indian Statistical Institute (ISI), and received his PhD in Statistics from the University of California at Berkeley. Before returning to India to join ISI, he was a faculty member of the University of Wisconsin at Madison. He has received the Shanti Swarup Bhatnagar Award for Mathematical Sciences in 2005, is an elected fellow of all three national science academies in India and an invited speaker at the International Congress of Mathematicians (ICM) 2010.


 


Abstract:


We discuss various ways of constructing higher dimensional spaces and studying them. This leads us into two approaches to higher dimensional spaces one due to Grothendieck and the other due to Kan and Quillen.


About The Speaker:


Prof. Kapil H. Paranjape is a well known mathematician and famous for his outstanding contributions in the field of algebraic geometry, especially the theory of algebraic cycles. He is an alumnus of our department. Currently he is a professor at IISER, Mohali. He has worked at University of Chicago, University of Paris-Sud and University of Warwick, ISI Banagalore, and IMSc Chennai. He has received Shanti Swarup Bhatnagar Award for Mathematical Sciences; he is a Fellow of all three Academies of Sciences, and is a recipient of the J.C. Bose Fellowship.


 


Abstract:


The algebraic Riccati equation occurs naturally in optimal control problems with infinite time horizon. In this talk, we will discuss the existence of a solution to the degenerate algebraic Riccati equation. Under suitable conditions on the control system, we can select a solution which will provide a feedback control law to stabilize the system. We will discuss the finite dimensional case in detail and indicate extensions to infinite dimensions especially to certain cases where the control operator is unbounded.


About The Speaker:


Prof. S. Kesavan is a Professor at the Institute of Mathematical Sciences, Chennai. He obtained his Docteur-es-Sciences Mathematiques from Universite Pierre et Marie Curie (Paris VI) in 1979, under the supervision of Profs. J. L. Lions and P. G. Ciarlet. His research interests are rested in Elliptic PDEs, Symmetrisation and Isoperimetric inequalities for PDEs and Homogenization. In addition to his research publications, he has four books to his credit. He is a fellow of various academies and recipient of several awards.


 


Abstract:


We will start with a review of the results on the arithmetic nature of the values of the Riemann zeta function at integers. In particular, we will focus on Apéry's 'miraculous' proof of the irrationality of ζ(3). We will then present a proof of Apéry's theorem that originates from a continued fraction due to Ramanujan and discuss the claim that this was the original motivation of Apéry's constructions.


About The Speaker:


Prof. Krishnan did his integrated MSc at IIT Kanpur. He had joined Infosys Tech after his degree and worked there for 7 years before deciding to work in Number Theory. He had finished his PhD from IMSc, Chennai and currently a Professor at Shiv Nadar University.


 


Abstract:


Heterogeneities and the associated Microstructures are present in materials whether they are natural or man-made.It is of great interest in applications to know how they influence the behaviour of materials.The main aim of this talk is to highlight various mathematical issues involved in the study of this problem and progress made.Efforts will be made to make the talk widely accessible and to explain various phenomena to non-specialists by treating simple models.


 


Abstract:


The chromatic polynomial is a classical invariant of a graph, which counts the number of ways of colouring the vertices of the graph such that vertices connected by an edge get different colours. A Lie algebra is a vector space equipped with a commutator bracket operation. We will describe how Lie algebras can be associated to graphs and how chromatic polynomials can be obtained purely in terms of Lie theoretic data.


About The Speaker:


Prof. Viswanath currently working at IMSc, Chennai. He is an alumni of IITK. He has finished his Ph.D from University of California, Berkeley in 2004. He works in Lie algebra.


 


Abstract:


Groups and representation theory plays a fundamental role in modern arithmetic. I will try to give a flavor of the role of representation theory in arithmetical questions.


About The Speaker:


Prof. Rajan is a professor at School of Mathematics, TIFR Mumbai and works in arithmetic geometry, automorphic forms and representation theory. He is a fellow of Indian Academy of Sciences as well as of INSA. He is an illustrious alumni and has many notable publications.


 


Abstract:


We consider iid random environments at the vertices of a tree of fixed even degree. The environment probabilities are independent over the vertices and identically distributed according to the action of a free group. The tree in question is the Cayley graph of this free group. Given the environment, a random walk following these probabilities will be shown to be transient. The proof relies on the connection between electrical conductance and random walks. Certain issues related to the speed of the random walk will also be discussed. 


 


Abstract:


After discussing preliminaries on hyperbolic geometry and Teichmuller spaces, we shall discuss two interrelated results of Maryam Mirzakhani:


a) Asymptotics, as L tends to infinity, of the number of simple closed geodesics on a hyperbolic surface with length
less than L.


b) A recursive formula for the volume of moduli space (of Riemann surfaces) equipped with the Weil-Petersson metric.

 


About The Speaker:


Mahan Maharaj is an alumnus of our Department at IITK. He changed to Mathematics after first joining B. Tech. in EE, and graduated with a Masters in Mathematics in 1992. Subsequently he went on to do a PhD at University of California, Berkeley with Andrew Casson as his advisor. He received the prestigious Sloan Fellowship for 1996–1997. He worked briefly at the Institute of Mathematical Sciences in 1998, and then joined the Ramakrishna Math as a renunciate. He is currently Professor of mathematics at the Ramakrishna Mission Vivekananda University at Belur Math.
In 2011 Mahan Maharaj received the Shanti Swarup Bhatnagar Award and JCBOSE fellowship in 2015.


"I am enjoying being a monk as much as I enjoy my mathematics"

 

   Abstract:Robust regression techniques are seen as alternative to traditional ordinary least squares regression when data is contaminated with heavy tailed noise or the dataset contains atypical observations. In
this talk, we discuss the problem of robust M-estimation of parameters of nonlinear signal Processing models. Asymptotics in such a scenario may be under a fixed model order setup or when the model order may itself be a function of sample size. For the fixed model dimension case, we
investigate the conditions under which M-estimators are consistent for convex and non-convex penalty functions and a wide class of additive noise scenarios, contaminating the actual transmitted signal. We further explore the conditions under increasing dimensionality setup when M-estimators are consistent. 
 


Abstract:


There is an intricate connection between the orbit structure of the geodesic flow associated with the modular surface and values of binary quadratic forms on integral pairs. In this talk I will describe some codings of the geodesic flow in terms of various continued fraction expansions and discuss how they are used to study the values of binary quadratic forms.


About The Speaker:


Prof. Dani is a well known mathematician and an excellent expositor. He retired as a Distinguished Professor at TIFR, Mumbai and presently a Distinguished Professor at IIT Mumbai. His areas of interest are dynamics and ergodic theory of flows on homogeneous spaces and its applications to various areas OF mathematics. He has received several awards including Shanti Swarup Bhatnagar, TWAS prize and the Ramanujan Medal. He was an invited speaker at ICM 1994. Apart from being a brilliant mathematician Prof. Dani is involved in development of mathematics in India very actively, he was Chairman of NBHM and was also Chairman of Commission for Development and Exchange (CDE) of International Mathematical Union.

 

   Abstract:The first is a construction of a planar set, within which a unit line segment can be turned around 360 degrees, and which has minimal area. The second is a result about convergence of Spherical partial sums of Fourier series in dimension > 1, where unlike the one dimension, these partial sums do not converge in the L^p norm, unless p=2.
 


Abstract:


We will try to have glimpses of works by an extra ordinary geniu Grothendieck. Possibly among the French school of analysts he was too much of an exception - so was his approach to Functional Analysis.


 


Abstract:


Epistemic logic is the modal logic of knowledge, and dynamic epistemic logic is the modal logic of change of knowledge. Knowledge is formalized with a modality for every knowing agent, and change of knowledge is formalized with a dynamic modality, for example, for the consequences of a public announcement. Over the past 10 years this two-types-of-modality approach of dynamic epistemic logic has been used in other areas of interest in computer science and in artificial intelligence: situation calculus, belief revision, planning, epistemology, theory of mind, topology; maybe even security. More theoretical results, such as on model checking and satisfiability, have also become available. We will give an overview of the area over the past 25 years.


About The Speaker:


Hans van Ditmarsch heads the section (equipe) called CELLO (for: Computational Epistemic Logic in LOrraine) at LORIA (Laboratoire Lorrain de Recherche en Informatique et ses Applications), Nancy. His research is on the dynamics of knowledge, information-based security protocols, modal logics for belief revision, proof tools for epistemic logics, combinatorics, and computer and information science education. He has written several books on logic, and is active in logic education. He is also an enthusiastic cello player, and has performed in many concerts.