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A Raghuram Chitrabhanu Chaudhuri Milan Kumar Das Shiva Chidambaram Advait Phanse Debangana Mukherjee Mousumi Bhakta Soumen Maity Akash Krishna Debargha Banerjee Neha prabhu Steven Spallone Aman Jhinga Diganta Borah Nishad Mandlik Sudhir Pujahari Amit Hogadi Dipramit Majumdar Prabhat Kushwaha Supriya Pisolkar Anindya Goswami Girish Kulkarni Pralhad Shinde Sushil Bhunia Anisa Chorwadwala Gunja Sachdeva Pranay Goel Suvarna Gharat Anup Biswas Hitesh Raundal Preeti Tathagata Mandal Anupam Singh Jatin Majithia Rabeya Basu Tejas Kalelkar Ayan Mahalanobis Jyotirmoy Ganguly Rama Mishra Uday Jagadale Ayesha Fatima K Hariram Rashmi Kulkarni Uttara Naik-Nimbalkar Baskar Balasubramanyam Kalpesh Pednekar Reshma Chandrasekharan Vivek Mallick Bhagyalaxmi Kaneenika Sinha Rohit Joshi Yasmeen Akhtar Bhakti Bhushan Manna Krishna Kaipa Ronnie Sebastian Chaitanya Ambi Makarand Sarnobat Sanket Nandan Chandrasheel Bhagwat Manidipa Pal Shirish Kulhari

Compiling, Editing and Design: Anisa Chorwadwala and Shanti Kalipatnapu Photo Courtesy: Makarand Sarnobat, VS Rao, Anisa Chorwadwala, Stefan Friedl, and other contributors from IISER Pune

Cover Page: Pi value up to 10,000 digits taken from http://www.math.utah.edu/~pa/math/pi.html Welcome Message

I am now into my fourth year as Coordinator for Mathematics at IISER Pune, and life here, as always, is full of new beginnings. Starting this semester, all the mathematics personnel are now comfortably ensconced in the top floor of the Main Building at IISER Pune. Such beginnings invariably give a new energy and there is this feeling that in front of us is evolving a path that we were born to take… a path full of beautiful theorems and pretty lemmas just waiting to be proved by the eager minds of IISER Pune!

The last year has seen us consolidate our strengths. We are now 22 regular faculty members, 1 INSPIRE fellow, and 1 visiting professor, 2 post-docs with possibly two more joining us later this year. Our PhD program is now going very well, and it is a pleasure to see some of our students blossoming into mathematicians. From this coming fall semester we will be starting an integrated-PhD program. Our BS-MS students who graduated in 2014 got selected into top- quality programs around the world such as University of Michigan, USA; University of Washington at Seattle, USA; Essen University, Germany; INSEAD, France etc.

We have continued with our tradition of hosting high-profile events at IISER Pune. In June 2014, there was an international workshop on “p-adic Aspects of Modular Forms” followed by the “29th Annual Conference of the Ramanujan Mathematical Society.” The “Young Women and Mathematics” symposium in July capped off a very busy summer. And, later in December, we had “Advances in Mathematical Biology.” Events such as these go a long way in establishing IISER Pune as a vibrant center for Mathematics!

A Raghuram Professor and Coordinator Academic & Mathematics, IISER Pune Administrative Support

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.

Amit Hogadi Currently, I am working on problems which are sometimes clubbed under the title homotopical algebraic geometry and have applications to K-theory, motivic Associate Professor cohomology and also classical topics like Brauer groups. [email protected] Selected Publications Amit Hogadi received PhD from With Indranil Biswas. Fundamental group of quotient singularities. To appear in International Princeton University, USA in 2007. He was at Tata Institute of Mathematics Research Notices. Fundamental Research (TIFR), Esnault, H. and Hogadi, A. (2012). On the algebraic fundamental group of smooth varieties in Mumbai, India before joining IISER characteristic p>0. Transactions of the American Mathematical Society 364:2429-2442. Pune in December 2013. 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.

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 Anindya generator for semigroup of operators, mild solution technique for parabolic Goswami equations, viscosity solution method for HJB/HJI equations, stability analysis of numerical schemes for solving PDE or IE, convergence of value iteration Assistant Professor schemes, marginalization technique in rare event simulation for hybrid processes, [email protected] martingale formulation for Markov processes etc.

Selected Publications Anindya Goswami received his PhD from Indian Institute of Science Goswami, A. and Saini, R.K. (2014). Volterra equation for pricing and hedging in a regime switching (IISc), Bangalore, India in 2008. market. Cogent Economics & Finance 1(2):1-11. Following this, he held postdoctoral Atar, R., Goswami, A. and Shwartz, A. (2014). On the risk-sensitive cost for a Markovian multiclass positions at the Universiteit Twente queue with priority. Electronic Communications in Probability 19(11):1-13. in Enschede, The Netherlands; Atar, R., Goswami, A. and Shwartz, A. (2013). Risk-sensitive control for the parallel server model. INRIA in Rennes, France; and SIAM Journal on Control and Optimization 51:4363-4386. Technion in Haifa, Israel before Basak, G.K., Ghosh, M.K. and Goswami, A. (2011). Risk minimizing option pricing for a class of exotic joining IISER Pune in 2011. 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.

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 symmetric spaces of non-compact type. Among the Rank-one symmetric spaces of compact type, we dealt only with the case of Sn, the unit sphere in n+1 with the induced metric. In fact, we gave a Anisa M H uniform proof for all the three space forms. Here, the functionals to be optimized ℝ were the energy functional and the principal frequency associated with the Chorwadwala Dirichlet boundary value problem and the Dirichlet Eigenvalue problem respectively, for both linear as well non-linear operators, namely the Laplacian Assistant Professor and the p-Laplacian. [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. Moving Plane Method for a punctured ball on the unit sphere

Selected Publications Anisa, M.H.C. and Mahadevan, R. A shape optimization problem for the p-Laplacian. Proceedings of the Royal Society of Edinburgh (Accepted for Publication). Anisa, M.H.C., Mahadevan, R. and Toledo, F. (2015). On the Faber-Krahn inequality for the Dirichlet p-Laplacian. ESAIM: Control, Optimisation and Calculus of Variations DOI: 10.1051/cocv/2014017 Anisa, M.H.C. and Vemuri, M.K. (2013). Two functionals connected to the Laplacian in a class of doubly connected domains on rank one symmetric spaces of non-compact type. Geometriae Dedicata 167(1):11-21.

Stochastic Controls and Queuing Theory

My broad research area falls under Applied Probability. I am mainly interested in stochastic controls, small noise diffusion, asymptotics of queuing networks and many other related models.

In the last couple of years, I have worked on problems from queuing theory that involves measure-valued process. Such processes have proven powerful in modeling queuing networks with general service and reneging distributions. Another important area of queuing theory is scheduling control where one looks for a policy that optimizes certain cost associated to the model. I also work on Anup Biswas such control problems.

Assistant Professor Selected Publications [email protected] Arapostathis, A., Biswas, A. and Pang, G. Ergodic control of multi-class M/M/N+M queues in the Halfin-Whitt regime. To appear in Annals of Applied Probability. Anup Biswas received his PhD from Atar, R., Biswas, A. and Kaspi, H. Fluid limits of G/G/ 1+G queues under non-preemptive Earliest- TIFR-Centre for Applicable Mathematics, Bangalore, India in Deadline-First discipline. To appear in Mathematics of Operation Research. 2011. He held postdoctoral Biswas, A. (2014). Risk-sensitive control for the multiclass many-server queues in the moderate positions at Technion, Israel, and deviation regime. Mathematics of Operation Research 39(3):908-929. University of Texas, Austin, USA before joining IISER Pune. Atar, R. and Biswas, A. (2014). Control of the multiclass G/G/1 queue in the moderate deviation regime. Annals of Applied Probability 24(5).

Conjugacy Questions and Representation Theory of Groups

Conjugacy questions in group theory have been of interest for its connection with the representation theory and they have not been understood very well for Algebraic Groups over arbitrary field. Usually groups are difficult objects and one studies them via their representations to get better understanding.

Let G (e.g. GLn) be an algebraic group defined over a field k. We denote the k

points of G by G(k) (e.g. GLn(k), SLn(k) etc.). An element t of G(k) is said to be real if it is conjugate to its own inverse in G(k). I have been concerned with finding real elements in algebraic groups. Very interestingly often it relates to Anupam Kumar finding strongly real elements (the elements which are product of two involutions in G(k)). Singh Apart from studying structure of real elements in Algebraic Groups over k, I also Assistant Professor looked at many examples such as linear groups, orthogonal groups, symplectic [email protected] groups and the groups of type G2 to get better understanding of the problem. Finding real elements helps in the understanding of real characters of the group After doing MSc (Mathematics) which in turn give information about those complex representations of the group from Indian Institute of Technology which are either orthogonal or symplectic. (IIT) Kanpur, Anupam Singh worked for his doctorate at Harish Chandra Research Institute, Allahabad and Indian Statistical Institute (ISI), Selected Publications Bangalore, India and got PhD from Gates, Z., Singh, A. and Ryan Vinroot, C. Strongly real classes in finite Unitary groups of odd ISI in 2007. He held postdoctoral characteristic. To appear in the Journal of Group Theory. positions at Tata Institute of Kulshrestha, A. and Singh, A. (2011). Real elements and Schur indices of a group. The Mathematics Fundamental Research (TIFR), Student 80:73-84. Mumbai and Institute of Gill, N. and Singh, A. (2011). Real and strongly real classes in PGLn(q) and quasi-simple covers of Mathematical Sciences (IMSc), PSLn(q). Journal of Group Theory 14:461-489. Chennai, India before joining the Gill, N. and Singh, A. (2011). Real and strongly real classes in SLn(q). Journal of Group Theory faculty of IISER Pune in 2008. 14:437-459.

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 Ayan discrete logarithm problem on a finite field. This new finding has opened a new avenue in research of public key cryptography. Mahalanobis

Assistant Professor Selected Publications [email protected] Mahalanobis, A. The ElGamal cryptosystem over circulant matrices (Submitted). Mahalanobis, A. and Shah, J. (2014). A new guess-and-determine attack on the A5/1 stream cipher. Computer and Information Science 7(1):115-124. Ayan Mahalanobis obtained his PhD from Florida Atlantic Mahalanobis, A. (2013). Are matrices useful in public-key cryptography? International Mathematical University, Boca Raton, USA in Forum 8(39):1939-1953. 2005. He was a Visiting Assistant Mahalanobis, A. The MOR cryptosystem and extra-special p-groups. Proceedings of WCC 2012, Professor at the Stevens Institute of Castro Urdiales, Spain July 9-13, 2012 & To appear in Journal of Discrete Mathematics and Technology, New Jersey, USA for a Cryptography. few years before joining IISER Mahalanobis, A. (2013). The automorphism group of the group of unitriangular matrices over a field. Pune in 2009. International Journal of Algebra 7(15):723-733. 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.

Modular Forms and Galois Representations

My research interests are in Number Theory. A modular form is essentially a function defined on the complex upper half-plane (everything above the real axis) that behaves in a good way under transformations of certain 2x2 matrices with integer entries. The expansion at infinity of such a function gives us a power series whose coefficients have interesting arithmetic properties. An important example of numbers that arise in such a way is the Ramanujan Tau function τ(n). In order to understand these coefficients, it is useful to consider an object attached to it called the L-function (these are generalizations of the Riemann zeta function). Baskar A Galois group is a set of permutations of roots of an irreducible polynomial. For Balasubramanyam example, complex conjugation permutes the roots of x2+1. It is possible to represent such permutations by matrices. One of the problems in Number Theory Assistant Professor is to try and understand the Galois group by studying its representations. One [email protected] can also attach L-functions to Galois representations and in some cases modular

Baskar Balasubramanyam forms and Galois representations are related through their L-functions. completed his PhD from Brandeis University, USA in 2007. In 2007- 08, he was a postdoctoral fellow at Selected Publications the Center for Advanced Study in Balasubramanyam, B., Ghate, E. and Vatsal, V. (2013). On local Galois representations over totally Mathematics at the Ben-Gurion real fields. Manuscripta Mathematica 142:513-524. University of the Negev in Israel. Balasubramanyam, B. and Longo, M. (2010). ∧-adic modular symbols over totally real fields. Following this, he was a Bateman Commenterii Mathematici Helvetici 86:841-865. Instructor at California Institute of Technology, USA during 2008-10. Balasubramanyam, B. and Raghuram, A. Special values of adjoint L-functions and congruences for He has been with IISER Pune since automorphic forms on GL(n) over a number field (Submitted) September 2010.

Representation Theory, Analysis & Geometry of Locally Symmetric Spaces, Number Theory

The interplay between arithmetic, spectral theory and geometry was studied by mathematicians like Selberg, Maass, and Sunada among many others. From the last few years, I have been working on the study of arithmetic aspects of the spectral theory and geometry of symmetric spaces. My thesis work involved proving various analogues of the classical number theoretic results in the context of symmetric spaces. I am also interested in the study of analytic properties of the Zeta functions associated to a rank one locally symmetric space, which encode a lot of spectral and geometric data. They can be considered as the spectral counterparts of the Dedekind zeta functions associated to number fields. I would Chandrasheel like to look at some of the `inverse problems’ on locally symmetric spaces with Bhagwat the aid of the Zeta functions mentioned above. In a joint work with Prof CS Rajan and Dr Supriya Pisolkar, we have established Assistant Professor some results which relate the notions of weak commensurability (introduced by [email protected] Prasad and Rapinchuk) and representation equivalence of arithmetic lattices in Lie groups. These notions are in turn related to the geometry and spectral theory Chandrasheel Bhagwat obtained of the locally symmetric spaces defined by them. I am currently working (jointly Bachelor of Science in Mathematics from Fergusson College, Pune in with Dr Supriya Pisolkar) on some of the related problems on discrete subgroups 2003 followed by Master of of Lie groups. Mathematics at Indian Statistical Institute, Bangalore in 2005. He My joint work with Prof Raghuram establishes period relations for the tensor completed PhD in Mathematics product of motives which together with the celebrated Deligne’s conjecture; from Tata Institute of Fundamental Research (TIFR) Mumbai, India in predict the results of a similar nature about the special values of Rankin - Selberg 2011 and spent a few months as a L-functions and Dirichlet L-series. I am interested in working on some related postdoctoral fellow at IISER Pune. problems about special values for automorphic L-functions associated to He has received the DST-INSPIRE faculty award and research grant in representations of algebraic groups; using techniques like Cohomology of 2011 and has joined IISER Pune as sheaves and Langlands constant term theory. INSPIRE Faculty Fellow in March 2012. From December 1, 2014, he has been working as an Assistant Selected Publications Professor at IISER Pune. Bhagwat, C. (2015). On Deligne's periods for tensor product motives. Comptes rendus – Mathématique 353:191-195. Bhagwat, C., and Raghuram, A. (2013). Ratios of periods for tensor product motives. Mathematical Research Letters 20(4):615-628. Bhagwat, C., Pisolkar, S., and Rajan, C.S. (2013). Commensurability and representation equivalent arithmetic lattices. International Mathematics Research Notices (IMRN) doi:10.1093/imrn/rns282. Bhagwat, C. and Rajan, C.S. (2011). On a multiplicity one property for the length spectra of even dimensional compact hyperbolic spaces. Journal of Number Theory doi:10.1016/j.jnt.2011.05.009. Bhagwat, C. and Rajan, C.S. (2010). On a spectral analogue of the strong multiplicity one theorem. International Mathematics Research Notices doi:10.1093/imrn/rnq243.

Automorphic Forms and Arithmetic Geometry

In arithmetic geometry, we study the integral solutions of polynomial equations. In arithmetic geometry we usually work over non-algebraically closed fields (like rational numbers), and often in fields of non-zero characteristic (like finite fields), and we may even restrict ourselves even to rings that are not a field (like integers). We use the rich theory of modular forms (more generally, automorphic representations) to find these solutions.

Modular forms/ automorphic forms are generalizations of the periodic functions like sine or cosine. The theory of modular forms made major contributions in Debargha several important discoveries in modern mathematics, including the uniform boundedness of torsion point of elliptic curves.

Banerjee I am interested in understanding objects in geometry called “motives” and objects in analysis called automorphic representations. The overarching Assistant Professor bridge/conjecture of Langlands connects these two fairly faraway worlds. I am [email protected] interested in understanding the integral and $p$-adic bridges that connect these

Debargha Banerjee received his two beautiful universes. PhD degree from Tata Institute of Fundamental Research, Mumbai. In the automorphic universe, I wish to focus on modular symbols and special He earned his Master’s degree in values of L-functions (one of the main objects of study in the Langlands' Mathematics from Indian Statistical program). Motives can be described by different cohomology theories. I wish to Institute and BSc from St Xavier’s College, Kolkata. He got the understand and use different cohomology theories using modular symbols, which Australian Research council in turn give insights into special values of L-functions. Discovery postdoctoral fellowship for 2 years at the Australian In another work, I developed the theory of differential modular forms for Shimura National University, Canberra, curves over totally real fields. The differential modular forms were invented by Australia. He was a visiting scientist Buium and his collaborators. These work open the p-adic bridge of certain at the IMSC, Chennai, India and later a guest scientist at the Max automorpic forms. Planck institute of Mathematics, Bonn, Germany before joining IISER Pune in November 2013. Selected Publications Banerjee, D. (2014). A note on the Eisenstein elements of prime square level. Proceedings of the American Mathematical Society 142:3675-3686. Banerjee, D. (2014). Differential modular forms on Shimura curves over totally real fields. Journal of Number Theory 135:353-373. Banerjee, D. and Ghate, E. (2013). Adjoint lifts and modular endomorphism algebras. Israel Journal of Mathematics 195(2):507-543. Banerjee, D. and Ghate, E. (2011). Crossed product algebras attached to weight one forms. Mathematical Research Letters 18(1):139-149. Banerjee, D., Ghate, E. and Kumar, N. (2010). ∧-adic forms and the Iwasawa main conjecture. Iwasawa Theory of totally real Fields (Proceedings of a Workshop held at IIT Guwahati, published by Ramanujan Mathematical Society) 2010, No. 12. pp.15-47. Banerjee, D. and Krishnamoorthy, S. The Eisenstein elements inside the space of modular symbols (Submitted).

Banerjee, D. and A. Raghuram, p-adic L-functions for GLn (preprint, expository article)

Several Complex Variables

My research interests are in Several Complex Variables, Potential Theory and in Differential Geometry. In the past, I studied various properties of a Kahler metric, known as the Robin metric defined on bounded pseudoconvex domains in Cn, n>1. This metric was constructed by N. Levenberg and H. Yamaguchi using the Robin function that arises from the Green function associated to the standard Laplacian in C^n.

Currently, I am studying various questions related to the motion of critical points and the differential geometry of level lines of the Green function of a bounded Diganta Borah multiply connected domain in the complex plane. I am also investigating properties of the metric induced by the capacity function on such domains. Assistant Professor [email protected] Selected Publications Remarks on the metric induced by the Robin function III (Submitted). Diganta Borah received his PhD Borah, D. (2013). Remarks on the metric Induced by the Robin Function II. Michigan Mathematical from the Indian Institute of Science Journal 62(3):581-630. (IISc), Bangalore, India in 2010 and Borah, D. and Verma, K. (2011). Remarks on the metric induced by the Robin function. Indiana was a Research Associate there until 2011. He joined IISER Pune in University Mathematics Journal 60:751-802. January 2012.

Analytic Number Theory, Harmonic Analysis and Arithmetic Geometry

My primary research work is concerned with extremal functions in Fourier analysis, equidistribution of Fourier coefficients of modular cusp forms, Eichler- Selberg trace formula and arithmetic of modular curves. Modular forms play an extremely important role in number theory and their Fourier coefficients carry fundamental information about points of elliptic curves over finite fields, values of the partition function, class numbers and representations of integers by quadratic forms. They are essential tools in addressing many fundamental problems in Mathematics, like Fermat's Last Theorem. Modular forms are a special case of automorphic representations and lead to the Langlands program, a theme that Kaneenika Sinha drives much of the twenty first century research in number theory and representation theory. My research program focuses on the behavior of the Assistant Professor Fourier coefficients of normalized Hecke eigenforms and their connections with [email protected] Jacobian varieties of modular curves.

Kaneenika Sinha completed her My research program in number theory heavily draws ideas and techniques from PhD from Queen's University, various mathematical areas, like harmonic analysis and arithmetic geometry. The Canada in 2006. She has held postdoctoral fellowships at problems pursued by me are posed in the language of algebra and geometry, University of Toronto, University of where as the techniques used in resolving them come from harmonic analysis. Alberta and Mathematical Sciences Moreover, a comprehensive understanding of these questions necessitates Research Institute, Berkeley. She was an assistant professor in IISER approaching them from a representation-theoretic point of view. Kolkata before joining IISER Pune in December 2012. Selected Publications Bucur, A., David, C., Feigon, B., Lalín, M. and Sinha, K. (2012). Distribution of zeta zeroes of Artin- Schreier covers. Mathematical Research Letters. Lalín, M. and Sinha, K. (2011). Higher Mahler measure for cyclotomic polynomials and Lehmer's question. The Ramanujan Journal 26:257-294. Ram Murty, M. and Sinha, K. (2010). Factoring newparts of Jacobians of certain modular curves. Proceedings of the American Mathematical Society 138:3481-3494. Ram Murty, M. and Sinha, K. (2009). Effective equidistribution of eigenvalues of Hecke operators. Journal of Number Theory 129:681-714.

Algebraic Geometric Coding Theory

My recent work is about studying Error Correcting Codes from the viewpoint of projective geometry over finite fields. To give a flavour of the kind of questions I am working on currently, consider k by n matrices over a finite field with q elements (say q is odd) such that all k by k minors of this matrix are nonzero. Let us call such a matrix MDS.

Question: What can we say about 3 by q+1 MDS matrices? Segre showed that any such matrix is row equivalent to a matrix whose columns lie on the conic y^2 = xz. Krishna Kaipa Question: Do there exist k by q+2 MDS matrices when k

Krishna Kaipa obtained a BTech Selected Publications from IIT Bombay and an MS Kaipa, K. (2014). An asymptotic formula in q for the number of [n,k] q-ary MDS codes. IEEE degree from University of Maryland College Park, both in Mechanical Transactions on Information Theory 60(11):7047-7057. Engineering. He then pursued a With Harish Pillai (2013). Weight spectrum of codes associated with the Grassmannian G(3,7), IEEE PhD in Mathematics from University Transactions on Information Theory 59(2):986-993. of Maryland, College Park. He held With Sudhir Ghorpade (2013). Automorphism groups of Grassmann codes, Finite fields and its assistant professor positions at IIT Applications 23:80-102. Bombay and IISER Bhopal before With Peter Grinevich (2009). Multiscale limit for finite-gap Sine-Gordon Solutions and Calculation of moving to IISER Pune in 2014. Topological Charge using Theta-functional Formulae. Proceedings of Steklov Mathematical Institute 266(1):49-58.

Elliptic Partial Differential Equations

My research interest includes semilinear and quasilinear elliptic partial differential equations arising from geometry and physics. I study existence/nonexistence of positive/sign-changing solutions, qualitative properties of solutions, regularity properties etc using the techniques from nonlinear analysis.

One of my main research areas is studying the second order and fourth order semilinear and quasilinear elliptic equations with singularity. Such second order equations for example, Hardy-Sobolev type equations arise in astrophysics. Fourth order equations, for example, equations with biharmonic operator arise in Mousomi Bhakta continuum mechanics, bio-physics, geometry. In particular, in the modeling of thin elastic plates, clamped plates and in the study of the Paneitz-Branson equation Assistant Professor etc. [email protected] The other area of my research is studying the semilinear elliptic equations with measure data, generalized boundary trace and generalized boundary value Mousomi Bhakta received her PhD problems. from TIFR-Centre for Applicable Mathematics, Bangalore, India in August, 2011. After that she held visiting scientist position in ICTP, Selected Publications Trieste, Italy for two months. Next, Bhakta, M. A note on semilinear elliptic equation with biharmonic operator and multiple critical she had postdoctoral positions at nonlinearities. To appear in Advanced Nonlinear Studies. Technion, Israel for two years and University of New England, NSW, Bhakta, M. (2015). Entire solutions for a class of elliptic equations involving p-biharmonic operator Australia for one year before joining and Rellich potentials. Journal of Math Analysis and Applications 423(2). IISER Pune in August 2014. Bhakta, M and Marcus, M. (2014). Semilinear elliptic equations admitting similarity transformations. Journal of Functional Analysis 267(10). Bhakta, M. and Marcus, M.(2014). Reduced limit for semilinear boundary value problems with measure data. Journal of Differential Equations 256(8). Bhakta, M, and Musina, R. (2012). Entire solutions for a class of variational problems involving the biharmonic operators and Rellich potentials. Nonlinear Analysis 75(9). Bhakta, M. and Sandeep, K. (2012). Poincar’e-Sobolev equations in the hyperbolic space. Calculus of Variations and Partial Differential Equations 44(1-2). Bhakta, M, and Biswas, A. (2011). Hardy-Sobolev type equations for p-Laplacian, 1

Dynamical Systems Modeling of Multiscale Phenomena in Biology

Dynamical processes in biology naturally span several systems and multiple scales, both in space and in time. We are interested in studying the dynamical behavior of biological processes through mathematical modeling to complement experimental understanding. My research focuses primarily on theoretical neuroscience, cardiac dynamics and diabetes. Each of these areas is rich with issues that arise from a fundamental need to develop theoretical frameworks, and to handle multiscale dynamics within those.

Our understanding of glucose-stimulated insulin secretion from the pancreatic Pranay Goel endocrine tissue, the islets of Langerhans, has developed considerably over the last three decades. Much of my recent work has been related to analyzing some Assistant Professor newly proposed models of islet voltage oscillations (called “bursting”) that [email protected] implicate both ionic as well as metabolic activity as being jointly responsible for function. Simultaneously, we are also interested in modeling and analysis of data Pranay Goel received his PhD in collected from patients diagnosed with Type 2 diabetes. This is joint work with Physics at the University of researchers at the University of Pune and K. E. M. Hospital, Pune. Pittsburgh, USA. His postdoctoral work was carried out at the Although we are a dry lab, since such research is highly interdisciplinary in Mathematical Biosciences Institute, The Ohio State University, and at nature, we collaborate extensively with experimentalists. the Laboratory of Biological Modeling, NIDDK, National Institutes of Health, USA. He joined Selected Publications the Mathematics and Biology Goel, P. and Sherman, A. (2009). The geometry of bursting in the dual oscillator model of pancreatic faculty at IISER Pune in 2009. beta-cells. SIAM Journal on Applied Dynamical Systems (SIADS) 8:1664-1693. Goel, P., Sherman, A. and Friedman, A. (2009). Multiscale modeling of electrical and intracellular activity in the pancreas: The islet Tridomain equations. SIAM Multiscale Modeling and Simulation 7:1609-1642. Zhang, M., Fendler, B. Peercy, B., Goel, P., Bertram, R., Sherman, A., Satin, L. (2008). Long lasting synchronization of calcium oscillations by cholinergic stimulation in isolated pancreatic islets. Biophysical Journal 95:4676-4688. Higgins, E.R., Goel, P., Puglisi, J.L., Bers, D.M., Cannell, M. and Sneyd, J. (2007). Modeling calcium microdomains using homogenization. Journal of Theoretical Biology 247:623-644. Goel, P., Sneyd, J. and Friedman, A. (2006). Homogenization of the cell cytoplasm: The calcium bidomain equations. SIAM Multiscale Modeling and Simulation 5:1045-1062.

Classical Algebraic K-theory

My work is based on problems in classical K-theory which are related to Serre’s problem on projective modules, widedly known as Quillen-Suslin theorem. One of such problem is Quillen-Suslin’s local-global principle. This was one of the main ingredient for the proof of Serre’s problem. I work on the matrix version of this theorem introduced by A. Suslin to give a simpler proof of the theorem. There are many generalizations and variations of this local-global technique for different types of classical groups. I have worked for general quadratic and general Hermitian groups.

Rabeya Basu Another type of problems is stabilization of K1 functor and the structure of unstable K1 Groups. These problems are also studied for different types of Assistant Professor classical groups. Recently, I have studied the solvability property of the unstable [email protected] K1 group for the general Hermitian group.

Rabeya Basu received her PhD Our method of proof can be used uniformly for many other classical groups. In from Tata Institute of Fundamental my PhD thesis we have given the uniform treatment for general linear, symplectic Research (TIFR), Mumbai, India in and orthogonal groups. We have also deduced a module theoretic version of 2007. She then undertook postdoctoral work initially at Harish local-global principle which is useful to generalize results from the free case to Chandra Research Institute, the module case. At present I am working on this local-global principle for the Allahabad and later as an NBHM transvection subgroup of the general quadratic module. Fellow at the Indian Statistical Institute, Kolkata, India. She was in IISER Kolkata as an assistant Selected Publications professor before joining IISER Pune in 2010. Basu, R. Local-global principle for the general quadratic and the general Hermitian groups and the

nilpotence of KH1 (Submitted).

Basu, R. (2013). On elementary subgroup of GLn over rings. Ramanujan Mathematical Society Newsletter 24(3).

Basu, R. (2011). Absence of torsion for NK1(R) over associative rings. Journal of Algebra and its Applications 10:793-799. Basu, R. and Rao, R.A. (2010). Injective stability for K1of regular rings. Journal of Algebra 323:367- 377. Bak, A., Basu, R. and Rao, R.A. (2010). Local-global principle for Transvection groups. Proceedings of the American Mathematical Society 138:1191-1204. Basu, R. and Sridharan, R. (2007). An expository article: On Forster's conjecture and related results. Punjab University Research Journal.

Low Dimensional Topology

For a reasonably long period of time my research focused around the Polynomial representation of long knots. It was motivated by the issue of settling a long lasting conjecture of Abhayankar. We established the equivalence between polynomial isotopic classes of long knots with the ambient isotopic classes of classical knots. Thus the entire knot theory can be done over polynomial knot category. I am trying to compute some numerical knot invariants such as unknotting number through polynomial knot theory.

Quantum topology is one of the emerging research areas. Many knot invariants Rama Mishra naturally arise through nice matrix algebra representation of interesting quantum groups. They have been related to several models in statistical mechanics. I Associate Professor would like to explore some models that are related to Singular knot theory. [email protected] I am also interested in classical knot invariants and their application in Rama Mishra has obtained her PhD mathematics and biological sciences. My joint work with Prof Louis Kauffman on from Indian Institute of Technology (IIT) Bombay, India in 1994. She nodal parity invariants of knotted rigid vertex graphs discusses the application of spent a few years with Harish this invariant on protein folding classification. Chandra Research Institute, Allahabad and Indian Statistical Institute, Delhi as a postdoctoral Selected Publications fellow and then served as a faculty Mishra, R. (2014). Polynomial unknotting and singularity index. Kyungpook Mathematical Journal at IIT Kharagpur and IIT Delhi for several years. She worked as a 54(2):271-292. JSPS fellow at Osaka City Kauffman, L. and Mishra, R. (2013). Nodal parity invariants for knotted rigid vertex graphs. Journal of University, Japan for one year and Knot Theory and its Ramifications 22(4):1340002. as a visiting faculty at Boise State University, USA before joining Mishra, R. and Bhushan, S. (2012). Knot theory in understanding proteins. Journal of Mathematical IISER Pune. Biology 65:1187-1213. Prabhakar, M. and Mishra, R. (2009). Minimal degree sequence for torus knots of type (p,q). Journal of Knot Theory and its Ramifications 18:485-491. Prabhakar, M. and Mishra, R. (2009). Polynomial representation for long knots. International Journal of Mathematical Analysis 3:325-337. Mishra, R. (2006). Polynomial representations of strongly invertible knots and strongly negative amphicheiral knots. Osaka Journal of Mathematics 43:625-639. Prabhakar, M. and Mishra, R. (2006). Minimal degree sequence of 2–bridge knots. Fundamenta Mathematicae 3:190.

Number Theory, Representation Theory and Automorphic Forms

My group is currently studying the arithmetic properties of special values of automorphic L-functions.

The earliest prototype of a special value of an L-function is the classical formula by Euler which says that the sum ∑ 1/n^2 of reciprocals of squares of all positive integers is π^2/6. More generally, suppose M = {a_n} is a sequence of numbers coming from some interesting data, for example, a_p can be the number of solutions of an equation modulo a prime p, then a guiding principle in modern number theory says that to study the sequence M one should study the L-function A Raghuram L(s, M) = ∑ a_n/n^s. One can glean much information about the sequence M by studying first the analytic properties, and second the arithmetic properties of Professor and Coordinator L(s,M). [email protected] The Langlands program, considered by many as a grand unifying principle in After getting a BTech in Computer modern mathematics, bridges different areas of mathematics, like geometry Science and Engineering from (elliptic curves), number theory (Galois representations) and representation Indian Institute of Technology (IIT) Kanpur, Raghuram moved to theory (automorphic forms). The central theme making these bridges possible is Mathematics and got a PhD in the notion of an L-function. Mathematics in 2001 from the Tata Institute of Fundamental Research Our work uses the results and techniques of the Langlands program to prove (TIFR), Mumbai, India. He had theorems about special values of various L-functions. These values encode postdoctoral positions at University of Toronto, Canada and TIFR, within them a lot of arithmetic and geometric information of the objects to which Mumbai, India and visiting assistant the L-functions are attached. In earlier work stemming from my thesis, we have professorships at Purdue University also studied the representation theory and harmonic analysis of p-adic groups. and University of Iowa, USA. He joined Oklahoma State University, USA in 2006 as a tenure-track assistant professor and was Selected Publications and Editorial Work promoted to associate professor Critical values for Rankin-Selberg L-functions for GL(n) x GL(n-1) and the symmetric cube L-functions with tenure in 2011.Raghuram for GL(2). To appear in Forum Mathematicum. joined IISER Pune in December The Bloch – Kato Conjecture for the Riemann Zeta Function, Editors: John Coates, A. Raghuram, 2011 as a Professor and the Anupam Saikia and R. Sujatha. pp. 312 To be published by Cambridge University Press. Coordinator of Mathematics. His With Harald Grobner. On the arithmetic of Shalika models and the critical values of L-functions for research has been partially funded GL(2n). With an appendix by Wee Teck Gan. American Journal of Mathematics 136 (2014) 675- by the National Science Foundation, USA, and the 728. Alexander von Humboldt With Chandrasheel Bhagwat. Ratios of periods of tensor product motives. Mathematical Research Foundation, Germany. Letters 20 (2013) No. 4, 615-628. With Wee Teck Gan. Arithmeticity for periods of automorphic forms. To appear in the Proceedings of the International Colloquium on “Automorphic representations and L-functions,” held in TIFR Mumbai, January 2012. With Günter Harder. Eisenstein cohomology and ratios of critical values of Rankin-Selberg L- functions. C. R. Acad. Sci. Paris, Ser. I 349 (2011) 719-724. With Naomi Tanabe. Notes on the arithmetic of Hilbert modular forms. Journal of the Ramanujan Mathematical Society 26(3) (2011) 261-319. On the special values of certain Rankin-Selberg L-functions and applications to odd symmetric power L-functions. International Mathematical Research Notices (2010) No. 2, 334-372. Algebraic Geometry

My research so far has dealt with questions in algebraic geometry. More specifically, with problems related to cycles on abelian varieties and problems related to moduli of vector bundles on curves and surfaces. In cycles I have been interested in a conjecture of Voevodsky which says that smash equivalence is the same as numerical equivalence. This conjecture has some very nice consequences, for instance, it implies that numerical and homological equivalence coincide, which is suggested by the standard conjectures of Grothendieck. My work on moduli of vector bundles has focused on proving Torelli theorems and theorems on rationality of vector bundles. I am currently Ronnie Sebastian focusing on expanding my research to number theory.

INSPIRE Faculty Fellow [email protected] Selected Publications Sebastian, R. (2013). Smash nilpotent cycles on varieties dominated by products of curves. After a Masters’ in Mathematics and Compositio Mathematica 149(9):1511-1518. Scientific Computing from Indian Biswas, I. and Sebastian, R. (2013). On rationality of moduli spaces of vector bundles on real Institute of Technology (IIT) Kanpur, Hirzebruch surfaces. Proceedings of the Indian Academy of Sciences Mathematical Sciences Ronnie Sebastian did a PhD with V Srinivas and Indranil Biswas at Tata 123(2):213-223. Institute of Fundamental Research (TIFR), Mumbai. He then pursued postdoctoral research at the Institute of Mathematical Sciences, Chennai; Humboldt University, Berlin as an IMU Berlin Einstein Foundation Fellow; and at the Indian Statistical Institute, Bangalore before joining IISER Pune in May 2013.

Combinatorics − covering arrays,

and cryptography

I am mostly interested in combinatorial problems. More specifically, I have been working on covering arrays on hypergraphs, and construction of cryptographically important Boolean functions.

Covering Arrays on Hypergraphs: Covering arrays are combinatorial structures which extend the notion of orthogonal arrays and have applications in the realm of software and circuit testing. A covering array of strength three is an array with the property that any three rows are qualitatively independent. A covering array is optimal if it has the minimum number of columns among covering arrays with the Soumen Maity same number of rows. We work on upper and lower bounds on the size of covering arrays on hypergraphs based on hypergraph homomorphism. Associate Professor [email protected] Cryptography: Boolean functions are used as nonlinear combining functions in LFSR based stream ciphers. A Boolean function is said to be resilient if its output Soumen Maity received a PhD from the Theoretical Statistics & leaks no information about its input values. My research in this area presents Mathematics Unit at Indian some strategies to modify the bent functions, by toggling some of its outputs, in Statistical Institute, Kolkata, India in getting a large class of 1-resilient functions with very good nonlinearity and 2002. He has postdoctoral experience from Lund University autocorrelation. Sweden; Indian Institute of Management (IIM) Kolkata, India; Selected Publications and University of Akhtar, Y, Maity, S. and Chandrasekharan, R.C. Covering arrays of strength four and software Ottawa, Canada. Prior to joining IISER Pune in 2009, he was at testing. To appear in Springer Proceedings in Mathematics and Statistics. Indian Institute of Technology (IIT) Maity, S., Arackaparambil, C. and Meyase, K. (2013). A new construction of resilient Boolean Guwahati and Indian Institute of functions with high nonlinearity. Ars Combinatoria 109:171-192. Technology (IIT) Kharagpur, India. Maity, S. (2012). 3-Way software testing with budget constraints. IEICE Trans. Information & Systems E95-D (9): 2227-2231. Akhtar, Y. and Maity, S. (2012). Mixed covering arrays on hypergraphs. Communications in Computer and Information Science 305:327-338.

Representation Theory and Canonical Forms

A basic theme in representation theory for a topological group is the duality between the geometry of the group and its spectral theory. In one project, I study arithmetically interesting representations called “discrete series” using this duality. I attempt to write their multiplicities in terms of measures over conjugacy classes of p-adic groups.

In another project, I study representations of isometry groups of quadratic forms, notably those induced from a stabilizer P of a nondegenerate subspace. I show that relationships between such representations are illuminated by first Steven Spallone decomposing P into two subgroups M and N, and then byfinding canonical forms for the conjugation action of M on N. Associate Professor To introduce another project, consider square matrices, with entries modulo a [email protected] cubefree integer. I study the question of when two such matrices are conjugate. I

have also written some papers regarding when two germs of dynamical systems Steven Spallone received his PhD from the University of Chicago, fixing a point are conjugate, in the p-adic setting. USA in 2004. Afterwards he did postdoctoral work at the Max- Planck Institute in Bonn, at Purdue Selected Publications University, and at the University of Spallone, S. (2012). Stable trace formulas and discrete series representations. Pacific Math Journal Oklahoma, USA. He also visited the Tata Institute of Fundamental 256:435-488. Research (TIFR) Mumbai, India. He Jenkins, A. and Spallone, S. (2012). Local analytic conjugacy of semi-hyperbolic mappings in two joined the faculty of IISER Pune in variables, in the non-archimedean setting. International Journal of Mathematics 23:1250059. July 2012. Shahidi, F. and Spallone, S. (2010). Residues of intertwining operators for SO(6) as character identities. Compositio Mathematica 146:772-794. Spallone, S. (2008). Residues of intertwining operators for classical groups. International Mathematics Research Notices 056:37. Margalit, D. and Spallone, S. (2007). A homological recipe for pseudo-Anosovs. Mathematical Research Letters 14:853-863.

Number Theory, Galois Cohomology, Arithmetic Aspects of Symmetric Spaces

Broadly speaking, my area of research is number theory and I have been working on problems mostly related to local fields. My thesis deals with questions having a common theme of understanding behavior of norm maps in Galois extensions of local fields. As an application, I computed the Chow group of Zero-cycles of degree zero on Châtelet surfaces over local fields. This work relies on the work of Bloch, Swinnerton-Dyer, Colliot-Téllène, Sansuc.

In joint work with Dr A Hogadi, we proved a conjecture of Hesselholt which 1 predicts the vanishing of the cohomology group H (G(L/K),W(OL)) for a Galois Supriya Pisolkar extension of local fields L/K. This can be seen as an analogue of Hilbert theorem- 90. In the future, I would like to work on generalizations of this result. Assistant Professor Over the last couple of years I have also been fascinated by arithmetic aspects of [email protected] locally symmetric spaces which are special type of manifolds. The theory of

locally symmetric spaces is a beautiful amalgamation of theory of Lie groups, Supriya Pisolkar obtained her PhD degree from Harish Chandra algebraic groups, analysis, di erential geometry, representation theory. In a joint Research Institute, Allahabad, India work with Prof CS Rajan and Dr C Bhagwat we have studied questions related to ff in 2010. She was a postdoctoral commensurability type problems of these spaces. fellow at Tata Institute of Fundamental Research, Mumbai for Currently, I am interested in understanding the work of Gopal Prasad and about three years before joining IISER Pune in December 2013. Rapinchuk which establishes a connection between arithmetic and geometric aspects of these spaces, giving rise to series of questions in this area.

Selected Publications Bhagwat, C., Pisolkar, S. and Rajan, C.S. (2013). Commensurability and representation equivalent arithmetic lattices. International Mathematical Research Notices doi: 10.1093/imrn/rns282. Hogadi, A. and Pisolkar, S. (2013). An equicharacteristic analogue of Hesselholt’s conjecture on cohomology of Witt vectors. Acta Arithmetica 158(2):165-171. Hogadi, A. and Pisolkar, S. (2011). On the cohomology of Witt vectors of p-adic integers and a conjecture of Hesselholt. Journal of Number Theory 131(10):1797-1807. Pisolkar, S. (2008). The Chow group of zero-cycles on certain Châtelet surfaces over local fields. Indagationes Mathematicae 19(3):427-439.

Low Dimensional Topology

My area of research is low-dimensional topology. This is a very active area of research with several longstanding conjectures proved fairly recently, like Thurston’s Geometrization conjecture (which implies the Poincare conjecture) and the Virtual Fibering conjecture. Within low-dimensional topology I focus mainly on foliations, triangulations and Heegaard splittings of 3-dimensional manifolds.

A closed book looks like a solid 3-dimensional object, but on closer analysis is observed to consist of 2-dimensional pages stacked tightly together. Similarly, Tejas Kalelkar every 3-manifold can be built by stacking 2-dimensional surfaces tightly together into what is called a foliation. I am studying a special class of foliations called taut Assistant Professor foliations which tell us useful topological properties of the 3-manifold. [email protected] On cutting open a 3-manifold along a special embedded surface, called the

Heegaard-splitting surface, we end up with two simple pieces called After completing his MSc from Indian Institute of Technology, handlebodies. Every closed 3-manifold has such a splitting surface which may Bombay, Tejas Kalelkar got his not be unique. I am currently working on a structure for these splitting surfaces PhD from Indian Statistical Institute, when a 3-manifold has infinitely many of them. Bangalore in 2010. He was then a postdoctoral fellow at Institute of Every 3-manifold can be built by suitably sticking tetraheda together. Normal Mathematical Sciences, Chennai and a Chauvenet Postdoctoral surfaces are surfaces embedded particularly `nicely' with respect to such a Fellow at the Washington University triangulation. I have proved several results using normal surfaces, such as a in St Louis, USA. He joined IISER weak converse of Haken’s well-known result about normality of incompressible Pune in December 2013. surfaces with respect to every triangulation of the 3-manifold.

Selected Publications Kalelkar, T. and Roberts, R. Taut foliations in surface bundles with multiple punctures. arXiv:1211.3637, Pacific Journal of Mathematics 273:257-275. Gadgil, S. and Kalelkar, T. (2013). A Chain complex and Quadrilaterals for normal surfaces. Rocky Mountain Journal of Mathematics, 43(2):479-487. Kalelkar, T. (2009). Incompressibility and normal minimal surfaces. Geometriae Dedicata 142(1):61- 70. Kalelkar, T. (2008). Euler characteristic and quadrilaterals of normal surfaces. Proceedings of the Indian Academy of Sciences Mathematical Sciences 118(2):227-233.

Statistics

My research interests are in the areas of inference in stochastic processes, survival analysis reliability theory and statistics in finance. Currently I am working on two problems.

(i) Modeling and analysis of statistical dependence: for example, in load sharing systems the failure of a component may reduce (increase) the lifetimes of the surviving components resulting in dependence between their lifetimes. (ii) Hypothesis testing problems in competing risks with missing causes of failure: the failure of a unit is caused by one of the several risks acting on it. It is of interest to Uttara Naik- know whether some risk dominates the others but sometimes the actual cause of failure for some units is missing.

Nimbalkar Selected Publications Visiting Faculty [email protected] Sutar, S.S. and Naik-Nimbalkar, U.V. (2014). Accelerated failure time models for loadsharing systems. IEEE Transactions on Reliability 63(3):706-714. Uttara Naik-Nimbalkar joined IISER Deshpande, J.V., Dewan, I. and Naik-Nimbalkar, U.V. (2010). A family of distributions to model load in February 2015. She has about sharing systems. Journal of Statistical Planning and Inference 140(6):1441-1451. thirty years of teaching and research experience at the Lam, K.F., Deshpande, J.V., Lau, E.H., Naik-Nimbalkar, U.V., Yip, P.S. and Xu, Y. (2009). A test for University of Pune with visiting constant fatality rate of an emerging epidemic, with applications to the SARS syndrome in Hong positions at the Michigan State Kong and Beijing. Biometrics 64(3):869-876. University, the University of Edinburgh and University of Abegaz, F. and Naik-Nimbalkar, U.V (2008). Modeling statistical dependence of markov chains via Waterloo. copula models. Journal of Statistical Planning and Inference 138(4):1131-1146.

Algebraic Geometry

My research can be divided into three categories: intersection theory, derived categories, and T-varieties.

Intersection theory In intersection theory, one defines invariants of algebraically defined geometric spaces in terms of how the spaces lying on the given space intersect each other. One can study those invariants to determine deep geometric properties of the space.

Derived category Vivek Mohan Given a variety (a type of algebraically define geometric space), one can define Mallick another algebraic object called derived category. It is known that a lot of the geometric properties of the space translate to algebraic properties of the derived Assistant Professor category. [email protected] T-variety

While studying an object one many times first determine its group of symmetries. After completing BStat (1999) and MStat (2001) from Indian Statistical The same holds for varieties. When the group of symmetries contain a torus, one Institute, Vivek Mallick got his PhD can, with some additional hypothesis describe a variety purely in terms of some from Tata Institute of Fundamental combinatorial data. Currently I am working on such varieties. Research (TIFR) Mumbai, India in 2008. He has joined IISER Pune in 2012 after completing his postdoctoral research at the Selected Publications Institute of Mathematical Sciences Dubey, U.V. and Mallick, V.M. (2012). Reconstruction of a superscheme from its derived category. in Chennai and Centre de Recerca Journal of the Ramanujan Mathematical Society 27(4). Matematica in Barcelona, Spain. Dubey, U.V., Mallick, V.M. (2012). Spectrum of some triangulated categories. Journal of Algebra 364:90-118. Mallick, V.M. (2009). Roitman's theorem for singular projective varieties in arbitrary characteristic. Journal of K-Theory 3:501-531.

Adjunct Faculty Members

SA Katre

Professor & Head Department of Mathematics University of Pune, Pune E-mail: [email protected] [email protected]

SA Katre received Masters degree in Mathematics from University of Pune and PhD from Panjab University, Chandigarh, India. He began his academic career from SP College of Pune and moved to University of Pune in 1988 as a faculty member and has been there since. Prof Katre’s work is in the area of Algebra and Number Theory, in particular, cyclotomy, number of points on curves over finite fields, Waring's problem for matrices, coding theory, and group theory. His pedagogical interests include contributing to mathematics olympiads, open source mathematical software, and e-learning in mathematics. Prof Katre had served as the editor of pedagological journal Bona Mathematica and has organized the NBHM sponsored ATM Schools in Mathematics during 2004-2012.

Sujatha Ramdorai

Canada Research Chair, Department of Mathematics University of British Columbia, Canada

Sujatha Ramdorai obtained her PhD in TIFR/Bombay University in 1992 and was with TIFR till January 2012. She currently holds a Canada Research Chair at the Department of Mathematics, University of British Columbia. Her research interests include Iwasawa theory and the theory of motives. Prof Ramdorai is a recipient of the Shanti Swarup Bhatnagar Award and the ICTP Ramanujan Award. She was a Member of the National Knowledge Commission and is a Member of the Scientific Advisory Council to the Prime Minister, and also the National Innovation Council. She is also interested in broader educational issues and in policy matters related to Higher Education and Research.

Postdoctoral Fellows

Amlan Barua Postdoctoral Research Associate (till January 2015)

Amlan’s research work focuses primarily on the numerical solution of partial differential equations that are encountered in different fields of applications. Earlier, he had worked on problems of Materials Science where his task was to find effective solvers for boundary integral equations. More lately, he has developed an interest in the field Bio-Mathematics. With Dr Pranay Goel at IISER Pune, Amlan was working on several research projects ranging from clinical biology to numerical simulation of partial differential equations that emerge from the modeling of Islets of Langerhans. Apart from applied mathematics, he is also interested in functional analysis and theoretical partial differential equations. Amlan is presently working as a Development Engineer with Comsol Multiphysics in Bangalore.

Barua, A., Li, S., Feng, H. and Li, X. (2013). An efficient rescaling algorithm for simulating the evolution of multiple elastic precipitates. Communications in Computational Physics 14(4):940-959. Feng, H., Barua, A., Li, S. and Li, X. (2013). A parallel adaptive treecode algorithm for evolution of elastically stressed solids. Communications in Computational Physics 15(2):365-387.

Bhakti Bhushan Manna Postdoctoral Research Associate

Bhakti did his PhD from TIFR-CAM Bangalore. His area of research is partial differential equation. He has completed the degree on December 2014 under the guidance of Prof PN Srikanth. He has joined IISER Pune as a Post doctoral Research Associate (PRA) on March 1, 2015. His thesis work involved mainly two classes of problems: First one concerning concentrating solutions and the other on the so-called problem of resonance. Singularly perturbed elliptic equations have been a great interest in PDE for last two decades. And his focus has been on finding solutions with higher dimensional concentrations. He is also interested in finding the existence results for the classical resonance problem which has been partly answered in one of their recent works.

Manna, B.B. and Srikanth, P.N. (2015). On a problem of resonance with exponential nonlinearity. Journal of Mathematical Analysis and Applications 421(2):1603-1615. Manna, B.B. and Srikanth, P.N. (2014). On the solutions of a singular elliptic equation concentrating on a circle. Advances in Nonlinear Analysis 3(3):141-155. Manna, B.B. and Srikanth, P.N. (2014). On the solutions of a singular elliptic equation concentrating on two orthogonal spheres. Nonlinear Differential Equations Applications NoDEA 21(6):915-927. Manna, B.B. and Santra, S. On a superlinear Ambrosetti Prodi problem: Interior concentration on geodesics (preprint).

Chitrabhanu Chaudhuri Postdoctoral Research Associate

Chitrabhanu did his PhD in Mathematics from Northwestern University 2007-2013 and was a postdoctoral fellow at Max Plank Institute for Mathematics (2013-2014) before joining IISER Pune. His research revolves around the topology and geometry of the Moduli of Curves over Complex numbers. The Moduli Space of Curves parameterize algebraic curves or Riemann surfaces, up to isomorphisms. It has been a central topic in mathematical research for several decades and brings various fields of mathematics together, for example Algebraic Geometry, Geometric Group theory and Teichmüller theory. It has important connections with physics as well. There are mainly two directions of research that Chitrabhanu has pursued: one roughly concerns finding some bounds on the topological complexity of certain partial compactifications on the Moduli of genus g curves. This involves computing certain cohomology groups; and the other line of research is about certain geometrically relevant subrings of the cohomology ring of the Moduli space known as the Tautological ring.

The Cohomological Excess of Certain Moduli Spaces of Curves of Genus g. International Mathematical Research Notices IMRN (2013). Topological Bounds on Certain open Subvarieties of the Compactified Moduli space of Curves; PhD thesis, Northwestern University 2013. Equivariant Polynomial of certain Moduli of Weighted Pointed Rational Curves (In preparation)

Postdoctoral Fellows

Dipramit Majumdar Postdoctoral Research Associate

Dipramit Majumdar obtained his PhD from Brandeis University, USA in 2013. He was a visiting scientist in ISI Bangalore from 2013-2014 before joining IISER Pune in 2014. Dipramit's research interest lies in number theory. Even though he is sometimes intrigued by elementary number theoretic problems such as Class Groups and Diophantine equations, his main research interest lies in p-adic families of modular forms. Modular forms are certain functions on the complex upper half planes with a lot of symmetries. To a modular form one can associate certain object called the L-function. One of the most promising ways to understand classical modular forms and their associated L-function is via study of their p-adic analogue. Study of p-adic modular forms was initiated by Serre, later Hida and then Coleman-Mazur constructed p-adic familes of 'nice' modular forms, called Hida family and eigencurve respectively. These objects plays crucial role in understanding and solving many problems in number theory, for example, key step in Mazur-Wiles proof of Iwasawa main conjecture for rational numbers is understanding geometry of the eigencurve at certain points.

Majumdar, D. Geometry of the eigencurve at critical Eisenstein series of weight 2. To appear in Journal de Théorie des Nombres de Bordeaux. Majumdar, D. Endoscopic transfer between eigenvarieties of definite unitary groups (Submitted) Kulkarni, M., Majumdar, D. and Balasubramanian, S. l-Class groups of cyclic extensions of prime degree l (Submitted)

Graduate Students, BS MS Project Students & Teaching Assistants

Advait Phanse Girish Kulkarni Graduate Student Graduate Student

Advait has completed MSc from Sir Girish completed MSc Mathematics Parshurambhau College in July from IIT Madras in 2010 and MSc 2014 and joined IISER Pune in from University of Western Ontario, August 2014. Presently he is doing Canada in 2012. Girish joined IISER PhD program related course work. Pune in 2013. In December 2014 he attended Advanced Instructional School on Schemes and Cohomology and has done minor thesis under the guidance of Prof Tejas Kalelkar. He is working toward PhD with the guidance of Dr Amit Hogadi. Girish’s expository article has appeared recently (Representation Theory and Particle Physics, Forays-14 Souvenir 55-56).

Ayesha Fatima Gunja Sachdeva Graduate Student Graduate Student

Ayesha completed her BS-MS from Gunja completed MPhil in IISER Pune in 2012 before joining Mathematics from Dayalbagh the PhD program in August 2013. Educational Institute, Deemed She has since completed her University, Agra in December 2011 course work and is and joined IISER Pune in August currently reading about Lie 2012. She is currently working Algebras with Dr Bhagwat. Her toward PhD under the guidance of interest lies in Number Theory and Prof A Raghuram in the area of Representation Theory. Number Theory.

Chaitanya Ambi Hitesh Raundal Graduate Student Graduate Student

Chaitanya completed his MSc from Hitesh obtained MSc in Applied IIT Kharagpur in 2009. He joined Mathematics from the University of IISER Pune in August 2013 as a Hyderabad and joined IISER Pune Project Fellow. He is a PhD student in January 2011. He is a graduate now and is completing the course student with Dr Rama Mishra in the work. area of knot theory. He has been working on the minimal polynomial representations of knots and their super bridge indices, and trying to build relation between various numerical knot invariants particularly polynomial degree, edge number and super bridge index of knots.

Debangana Mukherjee Jyotirmoy Ganguly Graduate Student Graduate Student

Debangana has completed her MSc Jyotirmoy completed MSc in from Mount Carmel College (under Mathematics from University of Bangalore University) in 2013 and Hyderabad in 2013 and joined joined IISER Pune soon after as a IISER Pune soon after. He has graduate student and has completed completed a one year course work a one year coursework as a part of as a part of the Mathematics PhD the Mathematics PhD program. She is program at IISER Pune. His currently reading in the area of elliptic research interest is in partial differential equations under the guidance of Dr Mousomi Bhakta. Representation Theory of Lie groups.

Makarand Sarnobat Prabhat Kushwaha Graduate Student Graduate Student

Makarand completed MSc in Prabhat completed MSc from the Mathematics from Sir Department of Mathematics, Banaras Parshurambhau College, Pune in Hindu University, Varanasi and joined 2012 and joined IISER Pune IISER Pune in January 2012. He has immediately after that. He is successfully completed all the working with Prof Raghuram toward requirements by the Institute viz. course PhD in the area of algebraic work, comprehensive exams and minor- number theory and representations thesis. Prabhat is currently working with theory. Makarand has been a Dr Ayan Mahalanobis his broad area of teaching assistant for these research is public key cryptography. courses: Introduction to Proofs; Linear Algebra; Multivariable Calculus; and Complex Analysis. He has attended a conference on Lie Groups and Lie Algebras in IIT Bombay in July 2014.

Manidipa Pal Pralhad Shinde Graduate Student Graduate Student

Manidipa joined IISER Pune in Pralhad completed Masters in January 2012. She has completed Mathematics in 2011 from University of course work, comprehensive exams Pune, Pune and joined IISER Pune in and minor thesis, which are January 2012. He is working with Dr in partial fulfillment of PhD program. Ayan Mahalanobis and Dr Anupam Her minor thesis was carried out Singh in the areas of cryptography and with guidance from Chandrasheel computational group theory. Bhagwat. Manidipa’s is now working with Dr Baskar Balasubramanyam in the area of algebraic number theory.

Milan Kumar Das Rashmi Kulkarni Graduate Student Graduate Student

Milan completed MSc from Rashmi obtained MSc in Microbiology Vidyasagar University, West Bengal from MS University, Baroda and an in 2012. He joined IISER Pune in MTech from the Centre for Modeling August 2013. and Simulation, University of Pune, Pune. She joined IISER Pune in August 2010 and is working with Dr Pranay Goel toward her PhD. Her research involves quantitating oxidative stress in the development of insulin resistance.

Neha Prabhu Rohit Joshi Graduate Student Graduate Student

Neha completed her MSc in Rohit has a Masters degree from IIT Mathematics from IIT Bombay and Kanpur. He has completed course work joined IISER Pune in August 2012. and cleared comprehensive exams She is currently working toward toward IISER Pune’s PhD program in PhD under the guidance of Dr Mathematics and is currently working Kaneenika Sinha. Her interests lie with Dr Steven Spallone. He was the in number theory and winner of silver medal in International representation theory. Mathematics Olympiad in 2004 while in his 12th standard and was chosen as the IISER Pune Mathematics Student of the Year in 2013.

Sudhir Pujahari Akash Krishna Graduate Student BS MS Student

Sudhir obtained MSc in Akash is currently working on his BS Mathematics from Utkal University, MS thesis with Dr Anindya Goswami. Orissa. He joined IISER Kolkata in His thesis studies option pricing January 2011 as a CSIR JRF and problem in a market model where semi- shifted to IISER Pune in December Markov switching of the parameters is 2012. He is working with Dr considered in a Levy process dynamics. Kaneenika Sinha in the area of Analytic Number Theory. Some of his work has been accepted for publication (with Meher, J. and Shankhadhar, K.D.; Sign changes of coefficients of certain Dirichlet series Functiones Et Approximatio Commentarii Mathematici).

Sushil Bhunia K Hariram Graduate Student BS MS Student

Sushil completed MSc Hariram is doing his fifth year project (Mathematics) in 2010 from with Dr Ayan Mahalanobis. He is Jadavpur University, Kolkata, India. studying how to solve the discrete log He joined IISER Pune in January problem using Function field sieve for 2012 and completed course work index calculus-in particular, a new along with comprehensive method to improve the sieving step examinations that are part of the called pinpointing which reduces the graduate program. Sushil is computation time significantly. He is presently working with Dr Anupam also investigating whether this Singh on algebraic groups. improvement can be adopted for other similar problems like integer factorization.

Tathagata Mandal Nishad Mandlik Graduate Student BS MS Student

Tathagata completed his MSc in Nishad is working on his fifth year thesis Mathematics from Visva-Bharati project with Dr Rabeya Basu. The topic University, Santiniketan, India in of his project is 'K-Theory: Completion 2012. He joined IISER Pune in of Unimodular Rows.' He is using the August 2013. He is presently doing software 'Singular' to replicate a result coursework as a part of the on the completion of unimodular rows of Mathematics PhD program at length 3. Nishad is also interested in IISER Pune and is interested in math and science education. Number Theory and Algebraic Geometry.

Yasmeen Akhtar Preeti Graduate Student BS MS Student

Yasmeen completed MSc in Preeti is currently working on her BS Mathematics from University of MS fifth year project with Dr Ayan Pune and joined IISER Pune in Mahalanobis on Secret sharing January 2011. She is working schemes and its various applications. toward her PhD with Dr Soumen This topic uses Lagrange interpolation Maity in the area of combinatorics in finite fields and has many and graph theory. Recent Publications: applications in real life. Notable ones Akhtar, Y., Maity, S. and Chandrasekharan, are e-voting and secure multiparty R.C. Covering Arrays of Strength four with budget constraints. Mathematical and computations. Computational Sciences 106-114, Narosa Publishing; Akhtar, Y., Maity, S. and Chandrasekharan, R.C. Covering arrays of strength four and software testing. Springer Proceedings in Mathematics and Statistics (To appear).

Reshma Aman Jhinga Teaching Assistant Chandrasekharan BS MS Student Aman graduated with BSc (Hons)- Maths and Computing degree in June Reshma is working toward her BS 2010 and MSc (Mathematics) degree in MS fifth year project with Dr June 2012 from Panjab University, Soumen Maity on the topic Chandigarh. She has assisted Dr Amit "Construction of covering arrays". Hogadi in conducting Single Variable She likes programming and is Calculus course, Dr Steven Spallone for interested in developing tools for Introduction to Proofs and Dr Baskar solving mathematical problems. Balasubramanyam for Linear Algebra Publications: Chandrasekharan, R.C. and for fall semester 2014. Aman is Maity, S. Covering Arrays of Strength Two and Pair wise Software Testing, Mathematical and currently assisting Dr Soumen Maity in Computational Sciences, Narosa, 2015, 115- conducting Probability & Statistics 121; Akthar, Y., Maity, S. and course, Dr Debargha Banerjee for Chandrasekharan, R.C. Covering Arrays of Strength Four and Software Testing, Springer Multivariable Calculus and Dr Collins Proceedings in Mathematics and Statistics (To Assisi in conducting Introduction to appear). Computation course for Spring semester 2015. She is also doing a reading project with Dr Steven Spallone on p-adic numbers.

Sanket Nandan Jatin Majithia BS MS Student Teaching Assistant

Sanket is doing his project on Jatin has an MSc in Mathematics Statistical inference of semi- degree from University of Pune and is Markov process and application in presently assisting with teaching at finance with Dr Anindya Goswami. IISER Pune.

Shirish Kulhari Uday Jagadale BS MS Student Teaching Assistant

Shirish is working with Dr Anindya Uday has completed MSc from the Goswami toward his BS MS fifth Department of Mathematics, University year project. The title of his of Pune in 2014 and joined IISER Pune research project is “Implied as a Teaching Assistant. He has Volatility in a Regime Switching assisted Dr Amit Hogadi and Dr Steven Market: Theory and Computation”. Spallone for courses on Calculus of One Variable and Introduction to Proofs respectively. Currently he is a teaching assistant for these courses: Calculus of multivariable (taught by Dr Debargha Banerjee); and Probability and Statistics (taught by Dr Soumen Maity). Shiva Chidambaram BS MS Student

Shiva is currently working on his fifth year project with Prof A Raghuram on Cohomology of GL(2). The goal of this project is to understand, in the language of automorphic forms of GL(2,F) for a number field F, the sheaf cohomology of a sheaf of vector spaces defined on a locally symmetric space attached to GL(2,F) from a highest weight irreducible representation of it. A specific goal is to understand the inner cohomology. He is also a Teaching Assistant for the course Multivariable Calculus taught by Dr Debargha Banerjee and Dr Anup Biswas.

Support Staff

Kalpesh Pednekar Office Assistant

Kalpesh Pednekar completed his Bachelor Degree in Commerce from University of Mumbai. He joined IISER Pune in March 2013 and is presently assisting Mathematics group in various administrative responsibilities in addition to assisting the Physics Group at IISER Pune.

R Bhagyalaxmi Office Assistant

Bhagyalaxmi completed her BSc from Osmania University, Hyderabad. Microbiology, Chemistry and Computer Applications were the subjects of her study in BSc. She also completed her MSc in Computer Science from Annamalai University, Tamilnadu. She joined IISER Pune in December 2014 and is providing administrative support to the Mathematics group.

Suvarna Gharat Office Assistant

Suvarna completed her BSc in Physics from Fergusson College and her post-graduation from Modern College, Pune. She joined IISER Pune in July 2011 and is presently assisting the Mathematics group in various administrative responsibilities.

Publications

2015 Akhtar, Y., Chandrasekharan, R.C. and Maity, S.- Covering Arrays of Strength Four and Software Testing. Springer Proceedings in Mathematics & Statistics (Accepted) Akhtar, Y., Chandrasekharan, R.C. and Maity, S.- Covering Arrays of Strength four with budget constraints. Mathematical and Computational Sciences 106-114, Narosa Publishing House, 2015. Banerjee, D. and Raghuram, A. - p-adic L-functions for GL_n (Submitted) Banerjee, D. and Krishnamoorthy, S.- The Eisenstein elements inside the modular symbols for product of two distinct primes (Submitted) Barua, A.; Goel, P. - The lattice origin of small-world networks in pancreatic tissues. (Submitted) Bhakta, M. - Entire solutions for a class of elliptic equations involving p-biharmonic operator and Rellich potentials. Journal of Mathematical Analysis and Applications 423 (2015), no. 2, 1570-1579. Bhunia, S., Mahalanobis, A. and Singh, A.- Gaussian Elimination in Symplectic and Split Orthogonal groups (Submitted) Chandrasekharan, R.C. and Maity, S.- Covering Arrays of Strength Two and Pairwise Software Testing. Mathematical and Computational Sciences 115-121, Narosa Publishing House, 2015. Chaudhuri, C.- The Cohomological Excess of Certain Moduli Spaces of Curves of Genus g. International Mathematics Research Notices 4 (2015) 1056-1074. Goswami, A., Patel, J. and Sevgaonkar P.- The optimal hedging in a semi-Markov modulated market (Submitted) Kalelkar, T. Roberts, R.- Taut foliations in surface bundles with multiple boundary components. Pacific Journal of Mathematics Vol No. 273 (2015) 257-275. Mahalanobis, A., Singh, A.- The MOR cryptosystem and unitary group in odd characteristic. (Submitted) Kulkarni, M., Majumdar, D. and Sury, B.- l-class groups of cyclic extensions of prime degree l. The Journal of the Ramanujan Mathematical Society (Accepted) Mishra, R. and Raundel, H. - Spaces of polynomial knots in low degree (Submitted)

2014 Balasubramanyam, B. and Majumdar, D.- Ordinary families over definite unitary groups (Submitted) Balasubramanyam, B. and Raghuram, A.- Special values of adjoint L-functions and congruences for automorphic forms on GL(n) over a number field (Submitted) Banerjee, D.- A note on the Eisenstein elements for prime square level. Proceedings of the American Mathematical Society 142 (2014), 3675-3686. Banerjee, D. - Differential modular forms on the Shimura curves over totally real fields. Journal of Number Theory 135 (2014), 353-373.

Basu, R.- Local-global principle for quadratic and Hermitian groups and the nilpotence of KH1 (Submitted) Bhagwat, C.- On Deligne's periods for tensor product motives. Comptes rendus - Mathématique DOI: 10.1016/j.crma.2014.11.016. Bhakta, M.- Infinitely many sign changing solutions of an elliptic problem involving critical Sobolev and Hardy-Sobolev exponent (Submitted) Bhakta, M.- Caffarelli-Kohn-Nirenberg type equations of fourth order with the critical exponent and Rellich potential (Submitted) Bhakta, M.- Semilinear elliptic equation with biharmonic operator and multiple critical nonlinearities. Advanced Nonlinear Studies (Accepted) Bhakta, M. and Marcus, M. - Semilinear elliptic equations admitting similarity transformations. Journal of Functional Analysis Vol 267 (2014), no. 10, 3894-3930. Bhakta, M. and Marcus, M.- Reduced limit for semilinear boundary value problems with measure data. Journal of Differential Equations Vol 256 (2014), no. 8, 2691-2710. Arapostathis, A., Biswas, A. and Pang, Guodong - Ergodic control of multi-class M/M/N+M queues in the Halfin-Whitt regime . Annals of Applied Probability (Accepted) Atar, R., Biswas, A., Kaspi, H.- Fluid limits of G/G/1+G queues under non-preemptive Earliest-Deadline- First discipline . Mathematics of Operation Research (Accepted) Biswas, A.- Risk-sensitive control for the multiclass many-server queues in the moderate deviation regime. Mathematics of Operation Research 39 (2014), no. 3, 908-929. Atar, R. and Biswas, A.- Control of the multiclass G/G/1 queue in the moderate deviation regime. Annals of Applied Probability 24 (2014), no. 5, 2033-2069. Chorwadwala, A. and Mahadevan, R.- A shape optimization problem for the $p$-Laplacian. Proceedings of the Royal Society of Edinburgh (Accepted) Chorwadwala, A., Mahadevan, R. and Toledo, F. - On the Faber-Krahn Inequality for the Dirichlet $p$- Laplacian. ESAIM:Control, Optimization and Calculus of Variations; Cambridge Journal (2014) DOI:10.1051/cocv/2014017. Deshpande, J., Lam, K.F., Naik-Nimbalkar, U.V. and Xu, Y.- Tests for comparing the progression of an epidemic in two groups. Journal of Indian Statistical Association (Accepted) Dwivedi, A. (Sponsor: Goel, P.) - A Stochastic Version of the Pedersen-Sherman Insulin Secretion Model. SIAM Undergraduate Research Online (SIURO) Published electronically Vol. 7. (2014) http://dx.doi.org/10.1137/12S011994. Goswami, A. and Saini, R.K. - Volterra equation for pricing and hedging in a regime switching market. Cogent Economics and Finance 2(2014), no.1, 1-11. Atar, R., Shwartz, A. and Goswami, A.- On the risk-sensitive cost for a Markovian multiclass queue with priority. Electronic Communications in Probability 19 (2014), no. 11, 1-13. Kaipa, K.- An asymptotic formula in q for the number of [n,k] q-ary MDS codes. IEEE Transactions on Information Theory Vol PP, Issue 99 (early access). Kaipa, K.- An asymptotic formula in q for the number of [n,k] q-ary MDS codes. IEEE Transactions on Information Theory 60 (2014), no. 11, 7047-7057. Majumdar, D.- Endoscopic transfer between eigenvarieties for definite unitary groups (Submitted) Majumdar, D.- Geometry of the eigencurve at critical Eisenstein series of weight 2. Journal de Théorie des Nombres de Bordeaux (Accepted) Sebastian, R. - Examples of smash nilpotent cycles on rationally connected varieties (Submitted)

Colloquia & Seminars

Colloquia

Speaker Date Title of the Talk

Prof Nitin Nitsure Mar 13, 2015 Euclidean Geometry and Physics TIFR, Mumbai

Dr Abhishek Banerjee Feb 27, 2015 Hecke operators on Line bundles over Modular curves IISc Bangalore

Dr Chitrabhanu Chaudhary Jan 23, 2015 Operads and Moduli of Curves IISER Pune

Prof L Mahadevan

Jan 09, 2015 Of flags and fishes Harvard University Prof Michel Waldschmidt Institut de Mathématiques de Jussieu, Dec 18, 2014 Continued fractions : Introduction and applications Paris VI Dr Manoj Kumar Yadav Dec 05, 2014 Automorphisms of groups preserving conjugacy classes HRI, Allahabad

Prof Siegfried Boecherer Oct 31, 2014 Siegel modular forms mod p Universität Mannheim, Germany

Dr Anupam Kumar Singh Oct 17, 2014 Word problem in finite classical Chevalley groups IISER Pune

Dr Tejas Kalelkar

Sep 19, 2014 Incompressible surfaces and normality in 3-manifolds IISER Pune

Dr Joël Riou Aug 22, 2014 Purity and duality in étale cohomology (after O. Gabber) Université Paris-Sud, France

Dr Raghav Kulkarni Decision Trees, Evasiveness, Solvable Groups, and Aug 04, 2014 Centre for Quantum Technologies Music of Primes

Prof Jeffrey Adler Representation Theory and p-adic Numbers: What and Jul 24, 2014 American University Why

Dr Moira Chas Jul 11, 2014 The Goldman Bracket on Surfaces Stonybrook University

Prof Steven Weintraub Jul 07, 2014 The adjoint of differentiation Lehigh University Prof Mahan Maharaj RKM Vivekananda University, Belur Jun 06, 2014 3-manifolds and (quasi)projective varieties Math Dr Shanta Laishram May 02, 2014 Grimm's Conjecture and Smooth Numbers ISI Delhi

Prof Uttara Naik-Nimbalkar Statistical tests for comparing the fatality of an epidemic Apr 25, 2014 University of Pune in two groups

Prof CS Aravinda Apr 11, 2014 Dynamics of geodesic conjugacies TIFR-CAM, Bangalore Prof Parameswaran Sankaran Apr 04, 2014 Twisted conjugacy in R. Thompson's groups IMSC-Chennai

Prof Amitava Bhattacharya Mar 21, 2014 Existence problems in Set Systems TIFR, Mumbai

Dr Stefan Friedl Mar 14, 2014 The profinite completion of knot groups University of Regensburg

Prof MS Narasimhan Mathematical Research in India after Independence: Mar 08, 2014 IISc, Bangalore The early years

Prof Ravi Ramakrishna Mar 07, 2014 Galois Representations Cornell University

Algebraic Geometry Seminars

Speaker Date Title of the Talk

Prof Kapil Hari Paranjape Mar 04, 2015 The work of Grothendieck: Some aspects of his work IISER, Mohali

Prof Kapil Hari Paranjape Lindel's theorem: A Vector bundle on X x A^1 comes

Mar 03, 2015 IISER, Mohali from X

Analysis Seminars

Speaker Date Title of the Talk

Dr M Ashok Kumar Statistical inference based on a parametric family of Feb 25, 2015 Indian Institute of Science, Bangalore divergences

Dr Amogh Deshpande On the role of Follmer-Schweizer minimal martingale Jan 7, 2015 University of Liverpool,UK measure in risk sensitive control asset management

Dr Ronnie Sebastian Nov 07, 2014 Bounded Hermitian Operators and Schur's lemma IISER Pune

Dr Ronnie Sebastian Oct 31, 2014 Bounded Hermitian Operators and Schur's lemma IISER Pune

Dr Anisa Chorwadwala Oct 24, 2014 Geometric overview of Symmetric Spaces IISER Pune

Dr Anisa Chorwadwala Oct 17, 2014 Geometric overview of Symmetric Spaces IISER Pune

Dr Rahul Garg, Technion The lattice point counting problem on the Heisenberg Oct 14, 2014 Israel Institute of Technology groups

Dr Anisa Chorwadwala Oct 10, 2014 Geometric Overview of Symmetric Spaces IISER Pune

Dr Supriya Pisolkar Sept 26, 2014 Representation of SL2(R) IISER Pune Dr Debdip Ganguly Sept 25, 2014 Partial Differentiation Equation on Hyperbolic Space TIFR-CAM, Bangalore

Dr Supriya Pisolkar Sept 19, 2014 Representation of SL2(R) IISER Pune

Dr Chandrasheel Bhagwat Sept 12, 2014 Representation of SL2(R) IISER Pune

Dr Chandrasheel Bhagwat Aug 29, 2014 Representation of SL2(R) IISER Pune

Dr Ronnie Sebastian Representation theory of topological groups, Peter- Aug 20, 2014 IISER Pune Weyl Theorem for compact groups A Vorticity-Velocity Formulation for Incompressible 2-D Mr Souvik Roy Jun 05, 2014 Euler Flows using Discontinuous Finite Element TIFR-CAM, Bangalore Methods Dr Supriya Pisolkar Analysis Lecture Series on Representation Theory and Jun 04, 2014 IISER Pune Linear Lie Groups (Lecture XV)

Dr Supriya Pisolkar Analysis Lecture Series on Representation Theory and Jun 03, 2014 IISER Pune Linear Lie Groups (Lecture XIV)

Dr Supriya Pisolkar Analysis Lecture Series on Representation Theory and May 30, 2014 IISER Pune Linear Lie Groups (Lecture XIII)

Dr Chandrasheel Bhagwat Analysis Lecture Series on Representation Theory and May 22, 2014 IISER Pune Linear Lie Groups (Lecture XII)

Dr Anisa Chorwadwala Analysis Lecture Series on Representation Theory and May 20, 2014 IISER Pune Linear Lie Groups (Lecture XI)

Dr Chandrasheel Bhagwat Analysis Lecture Series on Representation Theory and May 15, 2014 IISER Pune Linear Lie Groups (Lecture X)

Ms Neha Prabhu Analysis Lecture Series on Representation Theory and May 13, 2014 IISER Pune Linear Lie Groups (Lecture IX)

Dr Chandrasheel Bhagwat Analysis Lecture Series on Representation Theory and May 06, 2014 IISER Pune Linear Lie Groups (Lecture VIII)

Dr Chandrasheel Bhagwat Analysis Lecture Series on Representation Theory and Apr 29, 2014 IISER Pune Linear Lie Groups (Lecture VII)

Prof Raju George Controllability of Systems Described by Differential Apr 21, 2014 IIST Thiruvantapuram Equations Using Tools of Functional Analysis

Dr Anisa Chorwadwala Analysis Lecture Series on Representation Theory and Apr 18, 2014 IISER Pune Linear Lie Groups (Lecture VI)

Dr Anisa Chorwadwala Analysis Lecture Series on Representation Theory and

Apr 16, 2014 IISER Pune Linear Lie Groups (Lecture V)

Dr Apala Majumdar Biaxial defect cores in nematic equilibria: an asymptotic

Apr 11, 2014 University of Bath result

Prof CS Aravinda

Apr 10, 2014 Homotopy type and volume of locally symmetric spaces TIFR-CAM, Bangalore

Dr Anisa Chorwadwala Analysis Lecture Series on Representation Theory and

Apr 09, 2014 IISER Pune Linear Lie Groups (Lecture IV)

Dr Supriya Pisolkar Analysis Lecture Series on Representation Theory and Apr 02, 2014 IISER Pune Linear Lie Groups (Lecture III) Dr Supriya Pisolkar Analysis Lecture Series on Representation Theory and

Mar 26, 2014 IISER Pune Linear Lie Groups (Lecture II)

Dr Praveen C Kinetic schemes for convection-diffusion and Navier-

Mar 25, 2014 TIFR-CAM, Bangalore Stokes equations

Dr Supriya Pisolkar Analysis Lecture Series on Representation Theory and

Mar 19, 2014 IISER Pune Linear Lie Groups (Lecture I)

Prof Gopal Basak

Mar 07, 2014 Diffusion Approximation to Adaptive MCMC ISI Kolkata

Number Theory Seminars

Speaker Date Title of the Talk

Dr Jonathan Huang Higher Fitting ideals and the structure of ideal class Mar 09, 2015 University of Maryland groups

Dr Debargha Banerjee Mar 02, 2015 Eisenstein ideals IISER Pune

Dr Steven Spallone Feb 20, 2015 Weyl's Law: Euclidean Case IISER Pune

Dr Debargha Banerjee Feb 16, 2015 Eisenstein ideals IISER Pune

Dr Steven Spallone Feb 13, 2015 Weyl's Law: Euclidean Case IISER Pune Dr Chandrasheel Trace formula and its applications in isospectrality Bhagwat Feb 06, 2015 problems IISER Pune Dr Supriya Pisolkar Jan 30, 2015 Trace Formula IISER Pune

Dr Steven Spallone Jan 19, 2015 Trace Formula IISER Pune

Dr Florian Sprung Rational points of modular abelian varieties in towers of Jan 15, 2015 Princeton Univerity number fields: How to bound the rank.

Dr Abhishek Saha Siegel modular forms of degree 2: Fourier coefficients,

Jan 12, 2015 University of Bristol L-functions, and functoriality

Dr Dipramit Majumdar

Jan 05, 2014 An introduction to Eigenvarieties IISER Pune

Prof Wintenberger Jean-Pierre University

Nov 06, 2014 Ramification and Iwasawa theory of Strasbourg, France

Dr Debargha Banerjee

Nov 03, 2014 Hecke Theory for GL2 and converse theorem IISER Pune

Dr Chandrasheel Bhagwat

Oct 27, 2014 Tate's thesis and Hecke Theory for GL2 IISER Pune

Dr Steven Spallone

Oct 13, 2014 (g,K)-module IISER Pune Dr Supriya Pisolkar

Oct 10, 2014 Jacquet Functors IISER Pune

Dr Baskar Balasubramanyam

Sep t 15, 2014 Principal series representations, parabolic induction IISER Pune

Dr Debargha Banerjee

Sep t 08, 2014 Whittaker Functionals IISER Pune

Dr Debargha Banerjee

Aug 25, 2014 Global representations of GL(2) IISER Pune

Dr Dipramit Majumdar

Aug 20, 2014 Representations of GL(2) over non-archimedean places IISER Pune

Dr Steven Spallone

Aug 11, 2014 Representations of GL(2) over archimedean places IISER Pune

Dr Ronnie Sebastian Aug 04, 2014 Automorphic forms as function of adele groups IISER Pune

Dr Supriya Pisolkar

May 21, 2014 Witt vectors and Hasselholt's Conjecture IISER Pune

Dr Dipramit Majumdar

Apr 30, 2014 Overconvergent modular symbols IISER Pune

Dr Baskar Balasubramanyam Apr 23, 2014 Exceptional zero conjecture IISER Pune

Dr Baskar Balasubramanyam Apr 16, 2014 Two variable p-adic L-functions IISER Pune

Dr Debargha Banerjee Explicit construction of the p-adic distribution attached Mar 26, 2014 IISER Pune ordinary elliptic Hecke eigenform

Dr Debargha Banerjee Mar 19, 2014 p-adic L-functions attached to modular forms IISER Pune

Dr Chandrasheel Bhagwat Mar 12, 2014 Siegel modular forms and automorphic representations IISER Pune

Visitors’ Seminars

Speaker Date Title of the Talk

Dr Xavier Viennot

Feb 17, 2015 Trees in various sciences Emeritus research director at CNRS

Dr Shilpa Gondhali

Feb 03, 2015 Higher Toda brackets and Massey products University of Haifa

Dr Umesh Dubey

Jan 30, 2015 Twisted sheaves and twisted integral transforms IISc, Bangalore

Dr Florian Sprung Rational points of modular abelian varieties in towers of

Jan 15, 2015 Princeton University number fields: How to bound the rank Dr Nikhil Savale

Lumpkins Visiting Assistant Professor, Jan 07, 2015 Asymptotics of the eta invariant University of Notre Dame Dr Swarnava Mukhopadhyay

Jan 06, 2015 Rank-Level duality and Conformal Blocks divisors University of Maryland Dr Shibasish Dasgupta A Bayesian Predictive Approach to Design Studies for

Department of Information Systems and Jan 02, 2015 Comparing Biomarkers Analytics - Miami University, Ohio Dr Pritam Rajan Sequential design schemes for efficient estimation of

Dec 23, 2014 Acadia University, Canada pre-specified process features in computer experiments Prof Siegfried Boecherer Congruence primes for Siegel modular forms via

Institut für Mathematik - Universität Oct 29, 2014 twisted L-functions. Mannheim, Germany Dr R Venkatesh Unique Factorization of Tensor Products for finite

Oct 24, 2014 TIFR, Mumbai dimensional simple Lie Algebras

Dr Arnab Mitra Norm correspondence for unipotent radicals in classical

Sep t 26, 2014 Ben-Gurion University of the Negev groups

Dr Anandam Bannerjee

Aug 28, 2014 Tensor Structure on Smooth Motives TIFR, Mumbai

Dr Anandam Bannerjee

Aug 26, 2014 Equivalence relations on algebraic cobordism TIFR, Mumbai

Dr Manoj Gopalkrishnan

Aug 12, 2014 The Geometry of Reaction Networks TIFR, Mumbai

Prof Jeffrey Adler

Jul 30, 2014 Lifting representations of finite reductive groups American University

Dr Asilata Bapat

Jul 23, 2014 Morse theory and intersection cohomology University of Chicago

Prof Steven Weintraub Jul 09, 2014 A generalization of continued fractions Lehigh University

Prof R Parthasarathy

May 22, 2014 On the modules $A_{(\mathfrak q, \lambda)}$ Bharathiar University, Coimbatore

Dr Krishna Kaipa

Apr 22, 2014 Linear Codes and Grassmannians IISER Bhopal

Dr Kashyap Rajeevsarathy

Apr 07, 2014 Multicurves and primitivity in Mod(Sg) IISER Bhopal

Mini-courses by Visitors

Speaker Date Title of the Talk

Prof Siddhartha Bhattacharya Nov 10-14, A brief introduction to ergodic theory (Mini course)

TIFR, Mumbai 2014

Prof Jose Ignacio Burgos Gil Nov 04-07, Arakelov geometry of toric varieties (series of 4

ICMAT, Madrid Spain 2014 lectures)

Prof Ramanan Mar 18 - Apr Mini-course on Algebraic Geometry

CMI, Chennai 01, 2014

Dr Stefan Friedl Mar 05 - 12, The geometrization theorem for 3-manifolds (series of 3

University of Regensburg 2014 lectures) Minor Thesis Seminars

Speaker Date Title of the Talk

Mr Hitesh Raundal Computing Hodge-Deligne Numbers of Hypersurfaces

Jul 11, 2014 on Toric Varieties

Mr Sudhir Pujahari Jul 2, 2014 Graph Homomorphisms

Mr Prabhat Kumar Kushwaha Apr 24, 2014 Ito Calculus Without Probabilities

Ms Manidipa Pal Apr 14, 2014 Can one hear the shape of a drum?

Extremal first Dirichlet Eigenvalue for the Laplacian and Mr Pralhad Shinde Mar 23, 2014 Dihedral Symmetry

Mr Makarand Sarnobat Mar 12, 2014 A topological Proof of Grushko's Theorem

Ms Gunja Sachdeva Mar 10, 2014 Membership Problem in the Bitprobe Model

Student Seminars

Speaker Date Title of the Talk

Mr Makarand Sarnobat Mar 12, 2015 The Local Langlands Correspondence

Quadratic Reciprocity: A proof using Algebraic Number Ms Neha Prabhu Mar 5, 2015 Theory-Part 2

Quadratic Reciprocity: A proof using Algebraic Number Ms Neha Prabhu Feb 26, 2015 Theory-Part 1

What is Public Key Cryptography and why do we need Mr Prabhat Kushwaha Feb 12, 2015 it?

Mr Sushil Bhunia Jan 29, 2015 Clifford Algebras and Spin Groups

Ms Manidipa Pal Nov 19, 2014 Siegel modular forms

Ms Manidipa Pal Nov 12, 2014 Siegel modular forms

Ms Neha Prabhu Nov 5, 2014 Introduction to Classical Modular Forms

Ms Neha Prabhu Oct 22, 2014 Introduction to Classical Modular Forms

Mr Makarand Sarnobat Oct 22, 2014 Representation Theory of Finite groups Mr Makarand Sarnobat Oct 8, 2014 Representation Theory of Finite groups

Ms Ayesha Fatima Sept 24, 2014 Representation Theory of Finite groups

Ms Ayesha Fatima Sept 17, 2014 Representation Theory of Finite groups

Symposia, Conferences & Events

Symposium on Math-Finance March 5, 2015

Organizer Anindya Goswami

This half-day in-house symposium on Math-Finance was organized to give the students an overall knowledge of research works in Math-finance being done in the department. This was open to all from IISER Pune and required no prior registration. There were three sessions with two short breaks. The sessions were chaired by Dr Anup Biswas, Prof Uttara Naik-Nimbalkar and Dr Anindya Goswami respectively. Four students (Sanket Nandan, Shirish Kulhari, Nimit Rana and Akash Krishna) presented their Master’s project work.

This was the first symposium organized by the department where students had an opportunity to present their ongoing research. The talks in the symposium were on advanced research topics; nevertheless, efforts were made to make basic ideas tangible. In particular, the mathematical formulation of a real world problem, the relevant mathematical and statistical techniques were clarified carefully. A good number of students from inside and outside IISER Pune attended the event. Home page: https://sites.google.com/site/anindyagoswami/home/symp2015

ICTS Program on Advances in Mathematical Biology December 7-16, 2014

Organizers LS Shashidhara, Pranay Goel and Sujatha Ramdorai In addition to ICTS and IISER Pune, this Program was also supported by the Pacific Institutes of Mathematical Sciences (PIMS), Canada. The Program brought together leading mathematical biology researchers from Canada together with Indian scientists to deliver a series of pedagogical lectures on contemporary topics of interest. The opening lectures by Pranay Goel on the first day were an introduction to some essential mathematical techniques that were useful to later topics. The rest of the time was divided between three themes: 1. Mark Lewis, Daniel Coombs and Pauline van den Driessche lectured on topics in Ecology, Epidemiology and Immunology. Milind Watve, Ram Rup Sarkar and Sutirth Dey participated in the Discussions sessions centred on these topics. 2. Subhash Lele, Anil Gore, Shailaja Deshmukh and Akanksha Kashikar delivered lectures on Statistical inference in biological systems. 3. Lectures on Collective behaviour in cellular and organismal biology were delivered by Sitabhra Sinha, Debashish Chowdhury, Somdatta Sinha and Madan Rao. Collins Assisi participated in the discussion session on the topic.

Over 65 participants attended the Program from both Pune and all over India. The participants were drawn from varied backgrounds, rooted in theoretical science in some form or another, be it physics or mathematical biology or bioinformatics and so on. The participants were mostly at the early PhD level although some faculty and younger students also attended. The atmosphere was vibrant with a very active participation from students, which was well appreciated by the speakers. The participants as well as speakers gave excellent feedback. All seemed to welcome the breadth of lectures, the high quality of the Program, the organization itself, and were generally pleased to have participated in the meeting. The Program’s success indicates just how attractive topics in mathematical biology are for students in the country at this time. It speaks to a burgeoning development of the field, and the awareness and maturity of the participants begs for an even greater investment in the conduction of such Programs that will disseminate high quality instruction to a very willing audience.

Mathematics Research Advisory Council July 26-28, 2014

The MRAC consists of the following five mathematicians of eminence: Professor Manindra Agarwal, Indian Institute of Technology, Kanpur Professor TR Ramadas, Chennai Mathematical Institute Professor Ram Murty, Queen's University, Kingston, Canada Professor Dinesh Thakur, University of Rochester, USA Professor SRS Varadhan, Courant Institute, New York, USA

The first four members visited IISER Pune campus from July 26-28, 2014. The campus visit started with the Coordinator of Mathematics giving a presentation on mathematics at IISER Pune. This was followed for the next three days with meetings with each individual faculty member lasting for about 30 minutes; a meeting with each of the two postdocs; a meeting with all the mathematics PhD students; and a meeting with BS-MS students including the 5th year project students. At the end of their campus visit, the MRAC met with all discipline Coordinators and the Director to give their feedback about the entire mathematics programme. Later, they sent in their feedback in writing with critical comments and recommendations.

"Overall, the mathematics department is doing very well and is on track for becoming a leading department in India in terms of both teaching and research. Its present research strengths include number theory, representation theory and algebraic geometry. These areas are not unrelated to some of the other research areas of the department such as coding theory, graph theory, algebra and analysis and so there is room for some collaborative seminars amongst some of the research groups. In addition, the fact that IISER Pune has been the venue for high level research conferences and workshops, is an indication that it is moving in the right direction. The idea for PhD students to do a minor thesis before they embark on their doctoral thesis enables students to have a broader view of mathematics. This is an excellent initiative that we have not seen at many other universities. Clearly, some new and strategic appointments are needed to buttress the existing strengths of the department. The mathematics department of IISER Pune has had substantial growth and now has an impressive group of young faculty. It is doing quite well under a very good leadership. It is already on the international map, at least in the area of number theory and representation theory, because of the well- chosen high level research conferences and workshops organized or hosted here, as well as the innovative outreach activities. It will be a leading mathematics department in India once the other mathematics areas are also strengthened." Young Women and Mathematics July 25-27, 2014

Scientific Committee & Organizers Anisa Chorwadwala (Convener); Anita Naolekar; Jaya Iyer (Chair); Mousumi Mandal; Pooja Singla Thakur

The Symposium Young Women and Mathematics (YWM-2014) was a follow-up of the Indian Women and Mathematics (IWM) symposia held twice in the past. The first one was IWM-2012 held at Institute of Mathematical Sciences, Chennai during January 8-10, 2012 and the next was IWM-2013 held at IISER Pune during July 26-28, 2013. The earlier IWMs were modeled to facilitate interaction between women mathematicians who are established researchers, and college teachers, and for undergraduate and graduate students. Keeping in mind the increasing number of young women researchers in India in the recent years, the current meet, the third in the series, was named as "Young Women and Mathematics (YWM) Symposium". With National Board for Higher Mathematics (NBHM) India offering support for this venture, over 70 young women mathematicians from all over the country participated in the symposium. There were a few participants who were of Indian origin, either working or pursuing their doctoral studies abroad. The plan of the symposium was to have (i) a few mini-courses, in order to introduce advanced areas of mathematics, (ii) some plenary talks by prominent researchers and (iii) some contributory talks by participants from varied fields of mathematics. There were two mini courses, one on “Knots, Graphs and Applications” and the second one was on "Lie Algebras and Representations". There were 9 plenary talks delivered by young women researchers from reputed Indian Institutes and Universities. The range of subjects varied from Number Theory to Commutative algebra, and from Homotopy Theory to Partial Differential Equations and Harmonic Analysis. All these focused and motivational talks were received with great enthusiasm from an informed audience. There were around 15 contributory talks by researchers and post doctoral students. These talks were held in three parallel sessions namely (1) Analysis, (2) Algebra and its Applications and (3) Miscellaneous. There was a talk on the impact of some results from algebraic geometry to arithmetic circuits. The contributory talk by Seemin Rubab, NIT Srinagar titled "STEM Career and Women: Situation in Kashmir Valley” was interesting. There was an invited talk by Dr Neena Gupta (INSA Young Scientist Award Recipient this year) from ISI Kolkata on her celebrated work "On Zariski's Cancellation Problem". We also heard about her inspiring journey (she being a young woman achiever). There was also a poster presentation session by participants, which showcased some interesting areas in mathematics. There was also a panel discussion on a career in Mathematics in India in the current scenario. The discussion focused on the funds and opportunities available to women, present research/job opportunities in India etc. The young audience comprising of graduate/ undergraduate students benefited highly from this discussion. The symposium concluded with a session on feedback from the participants. In this age of specialization, many voices aired requests for Group Discussions, to initiate collaboration among women working in related areas. There was a very good suggestion that under the IWM funding, a group of women mathematicians planning to have a collaborative research work should gather at some specific location for a reasonably sufficient period of time. They need not hold formal lectures during this meet. They should hold discussions leading to the proposed collaborative research work. Some participants also expressed that more women of Indian origin, pursuing a career abroad should be invited to share their expertise. The Mathematics discipline of IISER Pune, its Coordinator Professor Raghuram and Professor KN Ganesh, the Director of IISER Pune gave their whole-hearted support to host the event. Home page: https://sites.google.com/site/ywmiisc/home

Topology and Geometry of Surfaces Symposium at the 29th Annual Conference of Ramanujan Mathematical Society June 30-July 7, 2014

Symposium Organizers Ravi Kulkarni, Tejas Kalelkar

Local Organizers A Raghuram (Convener), Anisa Chorwadwala, Chandrasheel Bhagwat, Kaneenika Sinha and SA Katre (Co-convener)

Invited Speakers Moira Chas (Stonybrook University), Ara Basmajian (CUNY)

This symposium was part of the 29th Annual Conference of the Ramanujan Mathematical Society held in the week after the conclusion of the main events. It consisted of a mini-course on ”Computer driven theorems and questions in geometry” by Prof Moira Chas and a mini-course on ”Identities of Hyperbolic surfaces” by Prof Ara Basmajian. Apart from students of IISER Pune, we also had participants from IISER Mohali, Pune University, Fergusson College and from industry.

Homepage 29ac.ramanujanmathsociety.org

The 29th Annual Conference of Ramanujan Mathematical Society June 23-27, 2014

Local Organizers A Raghuram (Convener), Anisa Chorwadwala, Chandrasheel Bhagwat Kaneenika Sinha, and SA Katre (Co-convener)

Invited Speakers Hyman Bass, V Suresh, KB Athreya, S Weintraub, Dinesh Thakur, G Rangarajan, S Sane, K Shiohama, S Thangavelu and Amiya Mukherjee

The RMS meeting is an annual event organised by RMS to promote mathematical research in India. With an attendance of more than 300 people, including junior and senior researchers from a wide range of institutions and universities across India, this is possibly the biggest annual mathematical event in India. We were extremely delighted to host this important event at IISER Pune in 2014.

Apart from plenary talks by highly accomplished researchers and educators from across the world like Hyman Bass (University of Michigan, USA), Amiya Mukherjee (ISI Kolkata), KB Athreya (Iowa State University, USA), Dinesh Thakur (University of Rochester, USA) and K Shiohama (Fukuoka University, Japan), Weintraub (Lehigh University, USA), SS Sane (IIT Bombay), G Rangarajan (IISc, Bangalore) and S Thangavelu (IISc, Bangalore), there were parallel symposia in several exciting research areas like Number Theory, Partial Differential Equations, Harmonic Analysis, Riemannian and Finsler Geometry, Complex Function Theory, Finite Groups, Logic, Discrete Mathematics, Topology and Geometry of Surfaces.

An entire day was devoted to talks by experts on many recent advances in Mathematics which originate from Ramanujan's work. There were also several opportunities for graduate students to present their research work to a wide audience during contributed talk sessions.

This meeting is very special because we hosted it at our Lecture Hall Complex almost immediately after it was dedicated to the nation by the President of India. We were able to accommodate almost all the participants in our brand new hostel and guest house buildings. Organizing an event of this magnitude and hosting huge number of participants at a new institute like ours was a huge administrative challenge. This was accomplished seamlessly through coordination between the Mathematics group, technical team, finance section, hostel and guest house staff, canteen staff and transport managers. Participants from all over the world and RMS executive committee members were highly impressed with the academic facilities and technical equipment made available by the institute. In fact, thanks to the near perfect execution of this meeting, RMS formally requested IISER Pune to host a joint meeting of RMS and Indian Mathematical Society with the American Mathematical Society --an international event of far bigger proportions in 2016!

Homepage 29ac.ramanujanmathsociety.org

Number Theory Symposium at the 29th Annual Conference of Ramanujan Mathematical Society June 23-27, 2014

Symposium Organizer Debargha Banerjee

Local Organizers A Raghuram (Convener), Anisa Chorwadwala, Chandrasheel Bhagwat, Kaneenika Sinha and SA Katre (Co-convener)

Invited Speakers M Manickam (KSOM), VG Narasimha Kumar (IIT, H), Supriya Pisolkar (IISER Pune), Baskar Balasubramanyam (IISER Pune), B. Ramakrishnan (HRI), K Srinivas (IMSC), S Katre (UoP).

The number theory symposium started this year as part of the annual Ramanujan Mathematical Society meeting. This conference was supported by NBHM.

Homepage 29ac.ramanujanmathsociety.org

ICTS Program on p-adic Aspects of Modular Forms June 10-20, 2014

Organizers A Raghuram, Baskar Balasubramanyam, Haruzo Hida, Jacques Tilouine

Invited Speakers (a) For the workshop: R. Sujatha, Jacques Tilouine, Baskar Balasubramanyam, David Geraghty, Mladen Dimitrov, Haruzo Hida, A. Raghuram and Debargha Banerjee (b) For the advanced discussion meeting: Jeanine van Order, Haruzo Hida, Baskar Balasubramanyam, Olivier Fouquet, Chandrakant Sharma, Giovanni Rosso, Riccardo Brasca, Denis Benois, Mahesh Kakde, David Geraghty, Ming-Lun Hsieh, Devika Sharma, Fabian Januszewski, Eknath Ghate, Tadashi Ochiai, Mladen Dimitrov, Sudhanshu Shekhar, Ashay Burungale, Jacques Tilouine

The aim of this program was to focus on the p-adic aspects of modular forms and related topics. The program consisted of two components, an instructional workshop followed by a discussion meeting. There were seven mini-courses in the workshop that focused on two broad themes: on p-adic families of automorphic forms with some modularity lifting applications in mind and on the construction of p-adic L-functions in various situations and their applications.

The final part of the program was a three day discussion meeting in which the state of current research in these topics were discussed.

Homepage http://www.icts.res.in/program/PAMF2014

Pune-Mumbai Number Theory Seminar April 4-5, 2014

Organizers Debargha Banerjee, Eknath Ghate, Ravi Raghunathan,

Invited Speakers Jyoti Sengupta (TIFR), Amiya Kumar Mondal (IIT,B), Debargha Banerjee (IISER,P), Steven Spallone (IISER,P), Ravi Raghunathan (IIT,H), CS Rajan (TIFR)

The inaugural Pune-Mumbai number theory meeting was organized at the Department of Mathematics, IIT Bombay. The aim of this seminar was to increase collaboration and interaction among the number theorists at IISER Pune, IITB and TIFR. This event has provided an opportunity for young number theorists to interact and collaborate with established mathematicians and is planned to be organized regularly every year/semester.

Homepage https://sites.google.com/site/punebombaynumbertheoryseminar/

Mathematics Day 2014 March 08 The 2014 Math day had several following fun events along with a colloquium by Prof MS Narasimhan. • We tested our mental arithmetic with the Shakuntala Devi Competition! • Players squared off against an opponent in the Room of Games, in which you'll clash over NIM and Hackenbush, and learn the math to step up your game. • We returned to LHC 101 for three party-type math games in the "Math Carnival". • There were two activities in the Room of Symmetries: For one, we learned to make, decorate, and manipulate our own Hexaflexagons. We also learned the secrets of the timeless 15 Puzzle of sliding tiles, and its exotic variations! • At the "Bubbles as Minimal Surfaces" workshop, we formed manifold shape-optimizing surfaces with soap and wires. • The Prime Number Bee began at noon, which proceeded as follows: Students lined up as in a spelling bee, and successive students recited the prime numbers 2,3,5, ... Any student who gave a composite number, skipped a prime, or took too long had to sit, and the last two standing received a cash prize. Chandrasheel taught us some prime number trivia along the way. • Women in Math Poster Competition and Showcase was conducted by Anisa during which teams of students designed a poster and quick talks to compete for a cash prize. Afterwards we watched the beloved Math Day Skit, bringing Scotland Yard to Pune with the "Sherlock Holmes: Game of Chances"! • Then we had our eminent guest MS Narasimhan deliver his lecture "Mathematical Research in India after Independence: The Early Years", followed by the Award Ceremony where we celebrated our winners. • Hard-core mathletes returned at 11pm for the CRYPTEX finals: our "Mathematical Treasure Hunt". A Glimpse of Life in Math@IISER Pune

At work…

With Mathematics Research Advisory Council (MRAC) Members

Turning coffee into theorems…

At Amlan’s farewell party WAY The

Rationality is Overrated

Indian Institute of Science Education and Research (IISER) Pune Dr Homi J Bhabha Road, Pashan, Pune – 411 008, Maharashtra, India Phone: +91 20 2590 8001 Fax: +91 20 2586 5086 Website: www.iiserpune.ac.in