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Profile Book 2017 MATH MEMBERS A. Raghuram Debargha Banerjee Neeraj Deshmukh Sneha Jondhale Abhinav Sahani Debarun Ghosh Neha Malik Soumen Maity Advait Phanse Deeksha Adil Neha Prabhu Souptik Chakraborty Ajith Nair Diganta Borah Omkar Manjarekar Steven Spallone Aman Jhinga Dileep Alla Onkar Kale Subham De Amit Hogadi Dilpreet Papia Bera Sudipa Mondal Anindya Goswami Garima Agarwal Prabhat Kushwaha Supriya Pisolkar Anisa Chorwadwala Girish Kulkarni Pralhad Shinde Surajprakash Yadav Anup Biswas Gunja Sachdeva Rabeya Basu Sushil Bhunia Anupam Kumar Singh Jyotirmoy Ganguly Rama Mishra Suvarna Gharat Ayan Mahalanobis Kalpesh Pednekar Ramya Nair Tathagata Mandal Ayesha Fatima Kaneenika Sinha Ratna Pal Tejas Kalelkar Baskar Balasubramanyam Kartik Roy Rijubrata Kundu Tian An Wong Basudev Pattanayak Krishna Kaipa Rohit Holkar Uday Bhaskar Sharma Chaitanya Ambi Krishna Kishore Rohit Joshi Uday Jagadale Chandrasheel Bhagwat Makarand Sarnobat Shane D'Mello Uttara Naik-Nimbalkar Chitrabhanu Chaudhuri Manidipa Pal Shashikant Ghanwat Varun Prasad Chris John Manish Mishra Shipra Kumar Venkata Krishna Debangana Mukherjee Milan Kumar Das Shuvamkant Tripathi Visakh Narayanan Debaprasanna Kar Mousomi Bhakta Sidharth Vivek Mohan Mallick Compiling, Editing and Design: Shanti Kalipatnapu, Kranthi Thiyyagura, Chandrasheel Bhagwat, Anisa Chorwadwala Art on the Cover: Sinjini Bhattacharjee, Arghya Rakshit Photo Courtesy: IISER Pune Math Members 2017 IISER Pune Math Book WELCOME MESSAGE BY COORDINATOR I have now completed over five years at IISER Pune, and am now in my sixth and possibly final year as Coordinator for Mathematics. I am going to resist the temptation of evaluating myself as to what I have or have not accomplished as head of mathematics, although I do believe that it’s always fruitful to take stock, to become aware of one’s strengths, and perhaps even more so of one’s weaknesses, especially when the goal we have set for ourselves is to become a strong force in the international world of Mathematics. The math personnel are now around 80 strong, including faculty, postdocs, PhD, Integrated PhD, 5th year BS-MS students, teaching assistants, and staff. Our numbers are steadily growing each year. Our post-doc program is getting very strong; this year we went international(!); with some luck, by Fall 2017, we might have around 10 postdocs in Mathematics. We have had continuing success in our BS-MS students getting placed in excellent PhD programs around the world. For example, of our current 5th year students, we have Papia Bera with an offer from Maryland, and Deeksha Adil with several offers from universities such as UC San Diego and Toronto; from our previous batch we had Abhishek Shukla who is now pursuing his PhD at UBC, Vancouver. It’s an absolute pleasure to see our students going places! In the year 2015-2016, we were selected for a grant under the FIST program that gives us about 1.5 Cr for a high performance computer cluster, a computer lab, and some funds to supplement our library. We have started using these funds in phases; the library has procured many volumes, including several collected works of great mathematicians. Let me add that in a few moments our library will be named as the Srinivasa Ramanujan Library! Our computer lab is getting set-up and very soon we will have a grand inauguration and a series of workshops on computational mathematics are in the offing. I have had a personal success recently: I was offered a membership at the Institute for Advanced Study at Princeton. This is one of the biggest things that happened to me and I am very excited about my visit to the IAS in the spring and summer of 2018. But, this also goes beyond me, as it bodes well for IISER and also Indian Mathematics to get greater exposure in such exalted centers of Mathematics. All in all, IISER Pune is doing well and has positioned itself to be an important center for Mathematics in India. But, on a damp note, I feel that we are not yet an international force to reckon with. We have a long way to go in increasing both the quality and quantity of papers in Mathematics. It is my hope that we make it into a place to be well known in international circles as the place that proves great theorems! A. RAGHURAM COORDINATOR, MATHEMATICS, IISER PUNE AMIT HOGADI Associate Professor [email protected] Amit Hogadi received PhD from Princeton University, USA in 2007. He was at Tata Institute of Fundamental Research (TIFR), Mumbai, India before joining IISER Pune in December 2013. ALGEBRAIC GEOMETRY One can describe algebraic geometry as the study of varieties, which are spaces defined by vanishing of polynomial equations. I have been interested in moduli spaces which are special types of varieties which parametrize geometric objects. In the last couple of decades, people have succeeded in applying ideas from topology, especially homotopy theory, to the study of algebraic varieties. This interplay between homotopy theory and algebraic geometry has been one of my latest fascinations. Currently, I am working on problems which are sometimes clubbed under the title homotopical algebraic geometry and have applications to K-theory, motivic cohomology and also classical topics like Brauer groups. SELECTED PUBLICATIONS With Indranil Biswas. Fundamental group of quotient singularities. To appear in International Mathematics Research Notices. Esnault, H. and Hogadi, A. (2012). On the algebraic fundamental group of smooth varieties in characteristic p>0. Transactions of the American Mathematical Society 364:2429-2442. Hogadi, A. and Mehta, V. (2011). Birational invariance of the S-fundamental group scheme. Pure and Applied Mathematical Quarterly 7(4):1361- 1370. Hogadi, A. and Pisolkar, P. (2011). On the cohomology of Witt vectors of p-adic integers and a conjecture of Hesselholt. Journal of Number Theory 131(10):1797-1807. Hogadi, A. and Xu, C. (2009). Degenerations of rationally connected varieties. Transactions of the American Mathematical Society 361(7):3931-3394. 2017 IISER Pune Math Book 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 Goswami, A., Patel, J. and Sevgaonkar, P. (2016). A system of non-local parabolic PDE and application to option pricing. Stoch. Anal. Appl. 34(5):893- 905. Goswami, A. and Nandan, S. (2016). Convergence of estimated option price in a regime switching market. Indian Journal of Pure and Applied Mathematics 47(2), 169-182 Goswami, A. and Saini, R.K. (2014). Volterra equation for pricing and hedging in a regime switching market. Cogent Economics & Finance 1(2):1-11. Atar, R., Goswami, A. and Shwartz, A. (2014). On the risk-sensitive cost for a Markovian multiclass queue with priority. Electronic Communications in Probability 19(11):1-13. Atar, R., Goswami, A. and Shwartz, A. (2013). Risk-sensitive control for the parallel server model. SIAM Journal on Control and Optimization 51:4363- 4386. 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 University of Mumbai in 2007. Following this, she held postdoctoral positions at the Institute of Mathematical Sciences (IMSc), Chennai; Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy; and 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 Moving Plane Method for a differential equation defined on the variable domain. punctured ball on the unit sphere We have solved some shape optimization problems for a class of doubly connected domains over Rank-one symmetric spaces of non-compact type.
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