Profile Book 2013

mathematics 2013 Anindya Goswami Manasi Mahapatra Anisa Chorwadwala Manidipa Pal Ankur Paliwal Neha Prabhu Anupam Kumar Singh Parthasarathi R Ashwin T A N Prabhat Kushwaha Ayan Mahalanobis Prahlad Shinde Baskar Balasubramanyam Pranay Goel Chandrasheel Bhagwat Rabeya Basu Debraj Roy Raghuram A Diganta Borah Rama Mishra Gaurav Prabhakar Sawant Rashmi Kulkarni Gunja Sachdeva Rohit Joshi Hardik Gajera Soumen Maity Hitesh Raoundal Sreekar Sastry Jatin Majithia Steven Spallone Jayant Deshpande Sudhir Pujahari Jeeten Patel Sushil Bhunia Kaneenika Sinha Vivek Mallick Kumar Vasumitra Singh Yasmeen Shameem Makarand Sarnobat Compiling and Editing Photography Printing Anisa Chorwadwala IISER Pune students and staff Anson Advertising and Marketing, Pune Chandrasheel Bhagwat Pratima Videotech, Pune A Raghuram Shanti Kalipatnapu WELCOME MESSAGE I joined IISER Pune on December 26, 2011, as the Coordinator for Mathematics. Since that date it has been one exhilarating journey in heading a young and growing group of dedicated practitioners of Mathematics. In my first year here, the faculty strength in Mathematics has grown from 14 to 18, and the number of PhD students has grown from 4 to 14. An aggressive hiring policy is being pursued to bring in other areas of expertise, to complement and strengthen existing areas, and to build inter-disciplinary areas with a strong mathematical component. We had a major overhauling of the undergraduate courses being offered in Mathematics. We also set up courses for all the new PhD students. These courses have been based on an ideological framework stemming from the didactic dictum that most of Mathematics comes under one of these five mutually indistinguishable subjects: Algebra, Analysis, Geometry & Topology, Discrete Mathematics, and Applicable Mathematics. We had some very famous mathematicians visit us and give IISER Pune Colloquia; for example: Professor John Coates, the then Sadleirian Professor of pure mathematics at Cambridge University, UK; Professor Jean-Marc Fontaine, University of Paris-Sud at Orsay, Paris, France; Professor Benedict Gross, former Dean of Harvard College, Harvard University, USA. It was a great pleasure and a rare honor for me, and indeed all of us at IISER Pune, to host such important mathematicians. In July 2012, we had an international workshop on the “Bloch-Kato conjecture for the Riemann zeta function at odd positive integers.” This was followed by the “Pan Asian Number Theory” conference, held in India for the first time, and indeed it was held in IISER Pune. In September 2012 we organized an “Indo-French conference on Automorphic Forms, Galois Representations and L-functions.” All these events have announced the arrival of IISER Pune as an important center for Mathematics both on the national and the international stage. Mathematics at IISER Pune is now well-defined, vibrant and happening! A Raghuram Professor and Coordinator, Mathematics IISER Pune Anindya Goswami Assistant Professor [email protected] Anindya Goswami received his PhD from Indian Institute of Science (IISc), Bangalore, India in 2008. Following this, he held postdoctoral positions at the Universiteit Twente in Enschede, The Netherlands; INRIA in Rennes, France; and Technion in Haifa, Israel before joining IISER Pune in 2011. STOCHASTIC CONTROL – GAME THEORY, MATH FINANCE, QUEUING NETWORKS, RENEWAL PROCESSES I am exploring various topics in Applied Probability. Those include generalization of Black-Sholes-Merton PDE for options in semi-Markov modulated market, Föllmer Schweizer decomposition of an unattainable contingent claim, equilibrium of non-cooperative semi-Markov game under ergodic cost, optimal control under risk sensitive cost, portfolio optimization, large deviation limit, fluid limit in queuing network, PDE techniques in stochastic control and differential games etc. I use Markov models, filtering techniques, stochastic calculus, infinitesimal generator for semigroup of operators, mild solution technique for parabolic equations, viscosity solution method for HJB/HJI equations, stability analysis of numerical schemes for solving PDE or IE., convergence of value iteration schemes, marginalization technique in rare event simulation for hybrid processes, martingale formulation for Markov processes etc. SELECTED PUBLICATIONS Atar, R., Goswami, A. and Shwartz, A. Risk-sensitive control for the parallel server model (Submitted). Basak, G.K., Ghosh, M.K. and Goswami, A. (2011). Risk minimizing option pricing for a class of exotic options in a Markov modulated market. Stochastic Analysis and Applications 29:259-281. Ghosh, M.K., Goswami, A. and Kumar, S.K. (2010). Portfolio optimization in a Markov modulated market: Chapter in Modern Trends In Controlled Stochastic Processes: Theory and Applications. Luniver Press, pp. 181-195. Ghosh, M.K., Goswami, A. and Kumar, S.K. (2009). Portfolio optimization in a semi-Markov modulated market. Applied Mathematics & Optimization 60:275-296. Ghosh, M.K. and Goswami, A. (2009). Risk minimizing option pricing in a semi-Markov modulated market. SIAM Journal on Control and Optimization 48:1519-1541. Ghosh, M.K. and Goswami, A. (2008). Partially observable semi-Markov games with average payoff. Journal of Mathematical Analysis and Applications 345:26-39. Anisa M H Chorwadwala Assistant Professor [email protected] Anisa Chorwadwala received her PhD from the University of Mumbai in 2007. Following this, she held postdoctoral positions at the Institute of Mathematical Sciences (IMSc), Chennai; The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy; and the Tata Institute of Fundamental Research (TIFR), Mumbai. She has been on the faculty of IISER Pune since April 2011. SHAPE OPTIMIZATION PROBLEMS My research work falls mainly in the following two branches of Mathematics: Partial differential equations and Riemannian geometry. I work on shape optimization problems including isoperimetric problems. A typical shape optimization problem is to find a shape which is optimal in the sense that it minimizes a certain cost functional while satisfying given constraints. In many cases, the functional being minimized depends on the solution of a given partial differential equation defined on the variable domain. We have solved some shape optimization problems for a class of doubly connected domains over Rank-one Moving Plane Method for a punctured ball symmetric spaces of non-compact type. Here the functionals on the unit sphere to be optimized were the energy functional and the principal frequency associated with the Dirichlet boundary value problem and the Dirichlet Eigenvalue problem respectively, for both linear as well non-linear operators, namely the Laplacian and the p-Laplacian. SELECTED PUBLICATIONS Anisa M. H. C. and Mahadevan, R. A shape optimization problem for the $p$-Laplacian (Submitted). Anisa, M.H.C. and Vemuri, M.K. (2012). Two functionals connected to the Laplacian in a class of doubly connected domains on rank one symmetric spaces of non-compact type. Geometriae Dedicata DOI: 10.1007/s10711-012-9800-7. Anisa, M.H.C. and Aithal, A.R. (2012). Convex polygons and the isoperimetric problem in simply connected space forms $M_κ^2$. The Mathematical Intelligencer (Accepted for Publication). Anisa, M.H.C. and Aithal, A.R. (2005). On two functionals connected to the Laplacian in a class of doubly connected domains over space forms. Proceedings of the Indian Academy of Sciences (Math. Sci.) 115:93-102. Ayan Mahalanobis Assistant Professor [email protected] Ayan Mahalanobis obtained his PhD from Florida Atlantic University, Boca Raton, USA in 2005. He was then a Visiting Assistant Professor at the Stevens Institute of Technology, New Jersey, USA for a few years before joining IISER Pune in 2009. PUBLIC KEY CRYPTOGRAPHY I work at the intersection of pure mathematics (group theory) and public key cryptography. Cryptography, especially public key cryptography, is the backbone of a modern society. It serves us with the required tools for online transactions and trading, i.e., online commerce. My research aims to find new cryptograhic primitives and to build secure protocols from that. We look for groups in which the discrete logarithm problem is secure. My recent work has shown that the group of non-singular circulant matrices over a finite field has some properties that make them attractive over the discrete logarithm problem on a finite field. This new finding has opened a new avenue in research of public key cryptography. SELECTED PUBLICATIONS Shah, J. and Mahalanobis, A. A new guess-and-determine attack on the A5/1 stream cipher (Submitted). Mahalanobis, A. The ElGamal cryptosystem over circulant matrices (Submitted). Mahalanobis, A. The MOR cryptosystem and extra-special p-groups (Submitted). Mahalanobis, A. The automorphism group of the group of unitriangular matrices over a field (Submitted). Mahalanobis, A. (2012). A simple generalization of the ElGamal cryptosystem to non-abelian groups II. Communications in Algebra 40:3583-3596. Mahalanobis, A. (2010). The discrete logarithm problem in the group of non-singular circulant matrices. Groups Complexity Cryptology 2:83-89. Baskar Balasubramanyam Assistant Professor [email protected] Baskar Balasubramanyam completed his PhD from Brandeis University, USA in 2007. In 2007- 08, he was a postdoctoral fellow at the Center for Advanced Study in Mathematics at the Ben- Gurion University of the Negev in Israel. Following this, he was a Bateman Instructor at California Institute of Technology,

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