Mathematics IISER BHOPAL

The Indian Institute of Science Education and Research (IISER) Bhopal was established in the year 2008 by the Government of India to promote research and education in basic sciences. The Department of Mathematics at IISER Bhopal has gradually grown to become one of the leading centres in the country for mathematical research and education. It is our constant endeavour to conduct quality research in mathematics, and to train students by providing them a broad and solid foundation in pure and applied mathematics and thereby prepare them for pursuing an academic career in mathematics and a non-academic employment in private and government sectors. The Department offers three degree programs: BS-MS (dual degree), Integrated Ph.D., and Ph.D. These programs attract highly motivated students from all over the country. Our students have secured admissions into the Ph.D. programs at reputed universities and institutes in the country and abroad, and have been recruited by various non-academic organisations.

The Department has nineteen faculty members. They represent a wide spectrum of research areas in mathematics. In particular, the Department has strong research groups in the areas of algebra, analysis, geometry, and topology. The Department Dr. Saurabh Shrivastava, aims to strengthen these areas further and expand to diversify into newer areas such as Applied Mathematics, Probability and Statistics in the near future. This will Head of the Department of Mathematics, promote the multidisciplinary research within the department.

We have taken up several initiatives in the past to promote and enhance the research IISER Bhopal. and teaching environment in the department. For example, our post-doctoral program and the visitors’ program are the key initiatives in this direction. We are in the process of setting up student exchange and joint degree programs with some of the leading universities in the world. The Department hosts several workshops, schools and conferences aimed at promoting mathematics education and collaborative research. Also, we are proud to have a well-established outreach program through which we reach out to the school children and motivate them by providing exposure to the subject and making them aware of various opportunities in the field.

In my opinion it is a significant achievement for a new department to sustain a Prologue balanced growth. I feel the department is progressing well and is set to become a prominent place for mathematical research and teaching. We, of course, need to maintain and improve the research quality. With the current strength and the initiatives that we have taken, we are confident to become a place known for doing great mathematics.

Faculty

At present, we have nineteen experienced faculty, trained in world class institutes or universities, working in various areas of mathematics including algebra and number theory, topology and geometry, analysis. You may find more information about them on the webpage of the department. Nikita Agarwal

Nikita’s broad research interests lie in ergodic theory and pure and applied dynamical systems. The topics include studying the statistical properties of dynamical systems, network theory — dynamics of complex systems as networks of coupled dynamical systems.

She is currently interested in the following topics:

• Piecewise smooth dynamical systems, known as Open dynamical systems; such systems can be explained using the dynamical billiards model. In particular, she focuses on understanding the ergodic properties of maps with holes using the tools from ergodic theory, symbolic dynamics, and combinatorics.

• Network dynamics — interacting discrete/continuous dynamical systems, deterministic as well as networks whose topology varies with time. Her work focuses on obtaining sufficient stability conditions of a continuous-time switched system with some or all unstable subsystems.

Selected Publications

Nikita obtained her Ph.D. degree from • Nikita Agarwal, Inflation of strongly connected networks, Math. Proc. Cambridge Philos. Soc. 150 (2011), no. 2, The University of Houston, Texas, USA, 367–384. in the year 2011. She joined the Department of Mathematics at IISER • Nikita Agarwal, Alexandre Rodrigues, and Michael Field, Dynamics near the product of planar heteroclinic Bhopal in July 2011 as an Assistant attractors, Dyn. Syst. 26 (2011), no. 4, 447–481. Professor. • Nikita Agarwal, A simple loop dwell time approach for stability of switched systems, SIAM J. Appl. Dyn. Syst. 17 (2018), no. 2, 1377–1394.

• Haritha C, and Nikita Agarwal, Product of expansive Markov maps with hole, Discrete Contin. Dyn. Syst. 39 (2019), no. 10, 5743–5774. Kumar Balasubramanian

Kumar joined IISER Bhopal as an assistant professor following the completion of his Ph.D. His primary research interest is in the representation theory of p-adic groups. He is currently interested in studying the sign associated to self-dual representations of p-adic groups.

When G is a finite group and π is an irreducible self-dual representation of G, a well known classical result of Frobenius and Schur says that the sign of the representation can be computed using its character. The sign of an irreducible self-dual representation also makes sense when G is a p-adic group. He is interested in exploring related problems in this context. Recently, he is also interested in studying the sign problem in the context of coverings of p-adic groups.

Selected Publications

• Kumar Balasubramanian, Self-dual representations of SL(n, F), Proc. Amer. Math. Soc. 144 (2016), no. 1, 435–444.

Kumar obtained his Ph.D. degree • Kumar Balasubramanian, M. Ram Murty, and Karam Deo Shankhadhar, Finite order elements in the integral from the University of Oklahoma, symplectic group, J. Ramanujan Math. Soc. 33 (2018), no. 4, 427—433. USA. He worked on some problems in the Representation theory of p-adic • Kumar Balasubramanian, K. S. Senthilraani, and Brahadeesh Sankarnarayanan, Self-dual representations of groups in his thesis. SL(2, F): an approach using the Iwahori-Hecke algebra, Comm. Algebra 47 (2019), no. 10, 4210—4215.

• Kumar Balasubramanian, A note on self-dual representations of Sp(4, F), J. Number Theory 199 (2019), 110 —125. Ajit Bhand

The study of reduced equations of motion under symmetries is an important theme in dynamical systems and geometric mechanics which goes back to Euler, Lagrange, Poisson, Liouville, Jacobi, Hamilton, Routh, Noether and Poincaré, among others. The modern reduction theory of mechanical systems was pioneered by Arnold (1966), Smale (1970), Meyer (1973) and Marsden and Weinstein (1974). Much of the work done by these authors was in the context of symplectic, Lagrangian and Hamiltonian frameworks. In his Ph.D. thesis, Ajit worked on an affine connection formulation of reduction theory.

He is interested in problems in differential geometry. Specifically, he is interested in studying reduction for nonholonomic systems in which the dynamics are constrained on an invariant, nonintegrable distribution.

More recently, he has also gotten interested in analytic number theory, integer-weight modular forms and quasimodular forms. One of the emerging themes in mathematical physics is the interplay of geometry, number theory and string theory. Ajit is interested in questions related to black holes in string theory which may possibly be answered using number theory.

Selected Publications Ajit obtained his Ph.D. from Queen's University, Kingston, Canada. As a • Ajit Bhand, Geodesic reduction via frame bundle geometry, SIGMA Symmetry Integrability Geom. Methods postdoctoral researcher, he was at the Appl. 6 (2010), Paper 020, 17 pp. University of Oklahoma, Norman, USA.

• Ajit Bhand, and Karam Deo Shankhadhar, On Dirichlet series attached to quasimodular forms, J. Number Theory 202 (2019), 91–106.

• Ajit Bhand, and M. Ram Murty, Class numbers of quadratic fields, Hardy-Ramanujan J. (accepted). Angshuman Bhattacharya

Anghshuman’s Ph.D. thesis was on aspects of the Weak Expectation Property for C*-algebras and operator systems. His research interest lies in C*-algebraic tensor products and related order theoretic properties. He is also interested in operator algebraic properties of (compact) quantum groups.

The Weak Expectation Property was introduced by E. C. Lance in 1973 to characterize maximum tensor product inclusions of C*-algebras and thereby showing the equivalence of amenability and nuclearity of discrete group C*-algebras. This property was put into further relevance in 1993 when E. Kirchberg showed the equivalence of the validity of the Connes Embedding conjecture and the question of the full group C*-algebra of the free group of two generators has the Weak Expectation Property or not. It is therefore of much interest to find out more about the C*-algebras with this property.

Operator algebraic properties of quantum groups have been a very active area of research in the recent years. Many properties of discrete group C*-algebras has been successfully studied in the discrete quantum group context using the duality of compact and discrete quantum groups. There are many interesting questions that arise in the noncommutative setting which do not have classical counterparts. Among others, there are questions relating to the non tracial nature of the Haar functional of quantum groups in general, connected to properties like amenability, factorization and other finite dimensional Angshuman obtained his Ph.D. approximation properties which are of particular interest. degree from the University of Regina, Canada. Following his Selected Publications Ph.D., he had a postdoctoral position at the University of • Angshuman Bhattacharya, Relative weak injectivity of operator system pairs, J. Math. Anal. Appl. 420 (2014), no. 1, 257–267. Georgia, Athens, USA from August

2014-May 2017. • Angshuman Bhattacharya, and Shuzhou Wang, Kirchberg's factorization property for discrete quantum groups, Bull. Lond. Math. Soc. 48 (2016), no. 5, 866–876.

• Angshuman Bhattacharya, Michael Brannan, Alexandru Chirvasitu, and Shuzhou Wang, Property (T), property (F) and residual finiteness for discrete quantum groups, J. Noncommut. Geom. (accepted). Atreyee Bhattacharya

Atreyee’s research interest lies in Riemannian Geometry, in particular, Geometric Analysis. More precisely, she works on problems related to Ricci flow and Riemannian functionals. Recently she has also been interested in exploring new applications of classical Riemannian geometric results in topics such as Contact Topology, Mapping class groups, Representation theory, etc.

Ricci flow is a geometric PDE that refers to the evolution of a Riemannian manifold by continuously deforming the metric of the manifold in a way that is analogous to the diffusion of heat. Roughly speaking, in analogy with the heat flow that aims to attain uniform temperature, Ricci flow tends to make the shape of a manifold more and more round, ultimately aiming to obtain a metric of uniform curvature properties.

The Ricci flow was first introduced by Richard S. Hamilton in 1982 in one of his seminal works. It is the key tool used in Grigori Perelman's remarkable proof of the Geometrization conjecture, also proving the famous Poincaré conjecture as a particular case. More recently, various techniques involving Ricci flow were used in the proof of the differentiable sphere theorem by Simon Brendle and Richard Schoen. Atreyee obtained her Ph.D. from Indian Institute of Science, Bengaluru, India. In her A classical problem in Geometric Analysis is to understand the rigidity/stability of the "standard doctoral thesis, she worked on certain geometries" by realizing them as critical points of certain functionals (generally known as Riemannian problems associated to Ricci flow, a fast functionals, obtained mostly, as exponents of integral norms of various curvature entities) and then growing topic in Differential Geometry. She appealing to techniques of Calculus of variations. Although, "standard geometries" such as compact joined RamaKrishna Mission Vivekananda irreducible symmetric spaces are known to be critical points for Riemannian functionals, a complete University, India, first as a postdoctoral classification of stable critical points is a hard open problem. fellow and later as an INSPIRE faculty. Selected Publications

n • Atreyee Bhattacharya, and Soma Maity, Some unstable critical metrics for the L 2 -norm of the curvature tensor, Math. Res. Lett. 21 (2014), no. 2, 235–240.

• Atreyee Bhattacharya, On the Curvature ODE associated to the Ricci Flow, Geom. Dedicata 175 (2015), 189–209.

• Atreyee Bhattacharya, and Harish Seshadri, A gap theorem for Ricci-flat 4-manifolds, Differential Geom. Appl. 40 (2015), 269–277. Rahul Garg

In his Ph.D. thesis, Rahul studied the role of the Bargmann transform in uncertainty principles. He is interested in Harmonic Analysis. In particular, he has been working on problems concerning Fourier multipliers.

Bochner-Riesz means are studied in order to understand the convergence of Fourier series and integral. In late 80’s, Carbery et al. showed pointwise convergence results by establishing certain weighted bound estimates. Later, Müller et al. extended some of these results to a class of connected Lie groups. There are many interesting open questions in this direction.

Bonami-Poornima studied Fourier multiplier spaces on Euclidean Sobolev spaces, establishing some of the very fundamental properties, specifically for functions/distributions whose derivatives are integrable. There is very little literature for analogous problems in the context of the Heisenberg group, and many interesting questions need to be answered.

Starting from Stein’s fundamental work, one studies mapping properties of Riesz potentials (fractional integral operators) which are also Fourier multipliers and have wide applications, such as in partial differential equations. It is a classical topic with continuous studies in the context of Euclidean space as well as Lie groups. Rahul obtained his Ph.D. degree from Indian Institute of Science, Selected Publications Bengaluru, India. As a postdoctoral researcher, he was at the Technion, • Rahul Garg, Amos Nevo, and Krystal Taylor, The lattice point counting problem on the Heisenberg groups, Israel Institute of Technology, Israel. Ann. Inst. Fourier (Grenoble) 65 (2015), no. 5, 2199—2233.

• Rahul Garg, and Daniel Spector, On the role of Riesz potentials in Poisson's equation and Sobolev embeddings, Indiana Univ. Math. J. 64 (2015), no. 6, 1697—1719.

• Rahul Garg, Luz Roncal, and Saurabh Shrivastava, Quantitative weighted estimates for Rubio de Francia's Littlewood-Paley square function, J. Geom. Anal. (accepted). Anjan Gupta

Anjan is interested in commutative algebra and homological algebra. His recent research concerns primarily the study of infinite free resolutions.

A core area in commutative algebra is devoted to constructing minimal free resolutions and describing their properties. The first step to construct the minimal free resolution of a module M is to understand R R the sequence of Betti numbers {βn (M )}. One collects the numbers βn (M ) into a more palatable form by considering their generating function R ∞ R i , called the Poincaré series of M. PM(t) = ∑i=0 βn (M )t ∈ ℤ [|t|]

R In 1950s, Kaplansky and Serre asked if the Poincaré series Pk (t) for a local ring (R, �, k) is always a R rational function, i.e., if there exist polynomials f (t), g(t) ∈ ℤ[t] such that Pk (t) = f (t)/g(t). An example due to Anick shows that the question has a negative answer in general. Nonetheless, there is an abundance of local rings (R, �, k), viz. local complete intersections, local rings of small embedding R codimension or small linkage number for which Pk (t) is rational. In fact more is true. All finitely generated modules over such rings have rational Poincaré series. McCullough and Peeva observed that a good understanding of how likely it is that rings with rational or irrational Poincaré series occur, is not yet available. Anjan's current research sheds light on the understanding of rationality of Poincaré series.

Anjan completed his Ph.D. from Tata Selected Publications Institute of Fundamental Research, Mumbai, India. In his doctoral • Dipankar Ghosh, Anjan Gupta, and Tony J. Puthenpurakal, Characterizations of regular local rings via dissertation, he worked on problems in syzygy modules of the residue field, J. Commut. Algebra 10 (2018), no. 3, 327–337. classical algebraic K-theory. Prior to joining IISER Bhopal, he was a • Anjan Gupta, A criterion for modules over Gorenstein local rings to have rational Poincaré series, Pacific J. postdoctoral researcher at IIT Bombay, Math. (accepted). India and Università degli studi di Genova, Italia. • Amanda Croll, Roger Dellaca, Anjan Gupta, Justin Hoffmeier, Vivek Mukundan, Denise Rangel Tracy, Liana M. Şega, Gabriel Sosa, and Peder Thompson, Detecting Koszulness and related homological properties from the algebra structure of Koszul homology, Nagoya Math. J. (accepted). Rohit Dilip Holkar

The broad area of Rohit’s works is known as Functional Analysis. In particular, he works in a specialised branch of Functional Analysis called Operator Algebras. His main interest is the interplay between topology and operator algebras, particularly, C*-algebras.

Topology or geometry can be studied in various ways; a modern popular subject, due to Alain Connes and called as Noncommutative Geometry, studies the geometrical aspects of physical phenomena using Operator Algebras. Motivated by this school of thoughts, Rohit uses topological groupoids and C*- algebras to study the interplay between topology and analysis.

At present, he and his collaborators, R. Meyer and A. Buss, are investigating if a C*-algebra of a, possibly unsaturated, Fell bundle over a groupoid fulfils some universal property. Usually, it is hard to assign category-theoretic universal properties to objects in Analysis. Nonetheless, having such a properties is practically useful. Fell bundles over groupoids represent not only various types of topological dynamical systems but also C*-algebraic dynamical systems. Thus, results proven for Fell bundles hold valid for several types of dynamical systems; this makes Fell bundles over groupoids a very useful generalised object. It is expected that above-mentioned universal property for Fell bundle C*-algebras shall offer cleaner proofs for various constructions such as stabilisation of twisted actions on C*-algebras or Rohit received his doctoral degree from construction of a C*-correspondence from a topological correspondence of Fell bundles. the University of Göttingen, Germany in 2014. Before joining IISER Bhopal in Selected Publications 2018, he worked as a postdoc in the Federal University of Santa Caterina, • Rohit Dilip Holkar, and Jean Renault, Hypergroupoids and C*-algebras, C. R. Math. Acad. Sci. Paris 351 Florianópolis, Brazil during 2014–2016 (2013), no. 23–24, 911—914. and as a SERB NPDF in IISER Pune during 2016–2018. • Rohit Dilip Holkar, Topological construction of C*-correspondences for groupoid C*-algebras, J. Operator Theory 77 (2017), no. 1, 217—241.

• Alcides Buss, Rohit Dilip Holkar, and Ralf Meyer, A universal property for groupoid C*-algebras.I, Proc. Lond. Math. Soc. (3) 117 (2018), no. 2, 345—375. Manas Kar

The main area of Manas’ research is related to inverse problems for partial differential equations. More precisely, he is interested in solving inverse parameter identification problems for various linear and nonlinear partial differential equations. In particular, he worked on problems related to Maxwell system, Helmholtz equation, Elasticity equation and the nonlinear p-Laplace model.

In 1980's Calderón published a seminal paper on inverse boundary value problems for conductivity equation. The problem asks to determine the conductivity of an object from the boundary voltage and current measurement. In 1987, motivated by Calderón's paper, Sylvester-Uhlmann proved the uniqueness theorem for identifying C2-conductivity for the conductivity equation from the Dirichlet to Neumann map as measurement data. Since then these problems received enormous attention towards understanding the stability, numerical reconstruction, proving the uniqueness for the low regular conductivity case and problems in manifold settings.

In 2012, Salo-Zhong considered inverse problems for nonlinear p-Laplace equation where they recovered the conductivity on the boundary of the domain. Guo, Kar and Salo proved that under a monotonicity assumption on the conductivity, the nonlinear Dirichlet to Neumann map is injective for Lipschitz Manas obtained his Ph.D. degree conductivities when n = 2 for 1 < p < ∞, and when n ≥ 3, one of the conductivities is closed to constant. from Johann Radon Institute for Solving inverse problems for p-Laplace equation is very challenging, since the equation is nonlinear and Computational and Applied the unique continuation principle for solutions of p-Laplace in three and higher dimensional domain is an Mathematics (RICAM), Linz, unknown open problem. So, it is interesting to find some new nonlinear techniques to solve inverse Austria. He was a postdoctoral problems for p-Laplace equation. fellow at University of Jyväskylä, Finland and NCTS-National Taiwan University, Taiwan. Selected Publications

• Manas Kar and Mourad Sini, Reconstruction of interfaces from the elastic farfield measurements using CGO solutions, SIAM J. Math. Anal. 46 (2014), no. 4, 2650—2691.

• Manas Kar, and Mourad Sini, An Hs,p(curl; Ω) estimate for the Maxwell system, Math. Ann. 364 (2016), no. 1-2, 559–587.

• Chang-Yu Guo, Manas Kar, and Mikko Salo, Inverse problems for p-Laplace type equations under monotonicity assumptions, Rend. Istit. Mat. Univ. Trieste 48 (2016), 79–99. Dheeraj Kulkarni

Dheeraj worked on relative symplectic capping results and its application to fibered knots. He is interested in problems in Geometry and Topology, in particular Contact and Symplectic Geometry.

Contact and Symplectic Geometry is an emerging area of research in Mathematics. The geometry of contact and symplectic structures was used in many context such as classical mechanics, wave propagation of light and Thermodynamics. However, in recent times work of many leading geometers and topologists have shown significance of these structures in various fields of mathematics. The work done in past six decades have laid the foundation for the field of Contact and Symplectic Geometry and Topology.

The area of Contact and Symplectic Geometry has several aspects to it. Symplectic and contact structures exhibit rigidity (like geometry) as well as flexibility (like topology). The study of two aspects have been pioneered and established by M. Gromov and Y. Eliashberg in their works. The fine line between the two features of these structures is elusive. Thus, no wonder it is an active area of research.

Dheeraj is currently working on problems related to fillability of contact structures and open book Dheeraj obtained his Ph.D. from Indian decompositions. Further, Legendrian knot theory is also his interest. He has been investigating Rack Institute of Science, Bengaluru, India. As invariants for Legendrian knots. a postdoctoral researcher, he was at the Georgia Institute of Technology (Atlanta, USA), Vivekananda University (Howrah, Selected Publications West Bengal) and Indian Statistical Institute (Kolkata, India). • James Conway, Amey Kaloti, and Dheeraj Kulkarni, Planar contact manifolds with vanishing Heegaard Floer Contact Invariants, Topology Appl. 56 (2013), 197–210.

• Siddhartha Gadgil and Dheeraj Kulkarni, Relative symplectic caps, 4-genus and fibered knots, Proc. Indian Acad. Sci. Math. Sci. 126 (2016), no. 2, 261–275. Anandteertha Mangasuli

He is interested in the spectral analysis of the Laplacian on a Riemannian manifold. More specifically, he focuses on eigenvalue problems, a brief description of which is given below.

It is a classical problem to understand the spectrum on a complete Riemannian manifold vis-à-vis the geometry of the manifold. Under suitable curvature conditions some very nice results are obtained which highlight the role played by the curvature in certain results that hold in Euclidean spaces seemingly not dependent on the zero curvature of these spaces. An illuminating illustration of this fact is the Liouville Theorem for harmonic functions on a complete Riemannian manifold with non-negative Ricci curvature proved by S. T. Yau in the early seventies. In general, on a complete Riemannian manifold with Ricci curvature bounded below the spectrum has a discrete as well as a continuous part. The point spectrum is a major focus of research.

The study of the point spectrum is qualitatively different in the compact case. One has the Sturm- Liouville decomposition theorem for the Laplacian in this case which allows one to orthogonally decompose the space of square integrable functions into finite dimensional eigenspaces of the Anandateertha obtained his Ph.D. Laplacian. Here the estimation of the eigenvalues in terms of geometric quantities, and the interplay degree from Purdue University, USA. As between the spectrum and the geometry of the manifold are major areas of interest. Especially, the first a postdoctoral researcher he was at ISI eigenvalue stores a considerable amount of geometric information as illustrated by Obata's theorem for Delhi, India and Bhaskaracharya compact manifolds with Ricci curvature bounded below by a positive constant. Pratisthana, Pune, India. Selected Publications

• Anandateertha Mangasuli, On the eigenvalues of the Laplacian for left-invariant Riemannian metrics on S3, Internat. J. Math. 18 (2007), no. 8, 895–901.

• Anandateertha Mangasuli, On the eigenvalues of the Laplacian for certain perturbations of the standard Euclidean metric on S2, Asian J. Math. 13 (2009), no. 2, 271–282. Kashyap Rajeevsarathy

In his thesis, Kashyap worked on a topological classification of the roots of certain generators of the mapping class groups known as Dehn twists. He is primarily interested in problems in Mapping class groups of surfaces. He also has a secondary interest in Algebraic graph theory.

Mapping class groups: He is interested in the following types of problems:

• The explicit realizations of finite subgroups of the mapping class group as isometry groups of hyperbolic structures on the surface.

• The classification of contact structures that arise on the mapping tori of “almost periodic” mapping classes such as the roots of Dehn twists and the finite-order mapping classes.

• Expressing certain mapping classes algebraically as words in their standard generators (i.e. Dehn twists), using their geometric or topological descriptions.

• Determining the liftable and symmetric (fiber-preserving) subgroups of mapping classes of finite- sheeted branched covers.

Algebraic graph theory: In this direction, he is interested in understanding certain spectral, algebraic and topological properties of the Cayley graphs of finite groups. He is also interested in exploring Kashyap obtained his Ph.D. degree from the University of Oklahoma, USA. possibilities of applying machine learning to better understand and predict the properties of graphs such as connectivity, diameter etc.

Selected Publications

• Kashyap Rajeevsarathy, and Prahlad Vaidyanathan, Roots of Dehn twists about multicurves, Glasg. Math. J. 60 (2018), no. 3, 555–583.

• Shiv Parsad, Kashyap Rajeevsarathy, and Bidyut Sanki, The geometric realizations of cyclic actions on surfaces, J. Topol. Anal. (accepted).

• Kashyap Rajeevsarathy, and Siddhartha Sarkar, Bound on the diameter of metacyclic groups, J. Algebra Appl. (accepted). Vivek Sadhu

Vivek worked on relative Cartier divisors in his thesis. He is interested in problems in Algebraic Geometry

and in K-theory. More precisely, he is interested in relative theory, i.e., when K-theoretical functors like K*,

Pic and NK* etc. are defined on a map of schemes f: X → S. One of the motivation to study these relative K-theoretic functors is to understand the nature of morphism.

In 1960, Grothendieck introduced the group K0 of a ring A as a group completion of the abelian monoid (P(A), ⊕), where P(A) is the isomorphism classes of finitely generated projective A-modules. In 1965, Bass

defined the negative part of K-groups, i.e., Kn for n < 0. Around 1970, Quillen defines the higher K-group of rings as a homotopy group of certain topological space. K-theory has a nice connection with other subjects like Topology, Algebraic Geometry and Number theory. In the last 50 years, several authors have studied the K-groups in various contexts to understand the underlying space. On the other hand, very few things are known about the relative K-theory. Therefore, it is interesting to study the relative K- groups to understand the morphism between the spaces.

Selected Publications

• Vivek Sadhu, and Balwant Singh, Subintegrality, invertible modules and polynomial extensions, J. Algebra 393 (2013), 16—23. Vivek obtained his Ph.D. degree from IIT Bombay. As a postdoctoral researcher, he • Vivek Sadhu, and Charles Weibel, Relative Cartier divisors and Laurent polynomial extensions, Math. Z. 285 was at IMSC Chennai, TIFR Mumbai and (2017), no. 1–2, 353–366. CMI Chennai, India. • Vivek Sadhu, On the vanishing of relative negative K-theory, J. Algebra Appl. (accepted) Jyoti Prakash Saha

Jyoti worked on algebraic p-adic L-functions in his thesis. He is interested in problems in Number Theory and in Expander families.

In 1980s, Hida constructed p-adic families of ordinary cusp forms. An important goal in Arithmetic Geometry was to extend this theory to non-ordinary forms, and also to automorphic representations. The subsequent works by Coleman and Mazur, Chenevier, Emerton, Buzzard, Urban (among others) constructed eigenvarieties, which interpolate p-adic automorphic forms. This provides a scope to study the variation of arithmetic data in such families.

In 2011, Nathanson asked several questions about the complements and asymptotic complements of subsets in groups. Since then, some of those questions have been answered in certain cases. However, even in the case of the free abelian group of rank two, it is not clear whether any infinite symmetric subset admits a minimal complement or not. It is important to investigate the analogous question in free abelian groups of higher rank.

The expander families are sequences of finite graphs which are sparse and highly connected. Constructing examples of expander families, and studying the properties of their spectrum is quite Jyoti obtained his Ph.D. degree from the exciting and challenging. In recent times, there has been significant progress in proving uniform Université Paris-Sud, France. As a expansion properties for certain type of random Cayley graphs. It would be interesting to construct postdoctoral researcher, he was at the graphs having similar properties. Université Paris-Sud, France, the Mathematisches Forschungsinstitut Selected Publications Oberwolfach, Germany, the Max Plank Institute for Mathematics, Germany and the Ben-Gurion University of the Negev, Israel. • Jyoti Prakash Saha, Purity for families of Galois representations, Ann. Inst. Fourier (Grenoble) 67 (2017), no. 2, 879–910.

• Jyoti Prakash Saha, Conductors in p-adic families, Ramanujan J. 44 (2017), no. 2, 359—366.

• Manish K. Pandey, Sudhir Pujahari, and Jyoti Prakash Saha, Distinguishing pure representations by normalized traces, J. Number Theory 195 (2019), 217—225. Siddhartha Sarkar

Siddhartha is interested in Hurwitz problem on symmetries of surfaces, Finite group theory and Ramanujan Graphs. Let G be a finite group. A spectrum sp(G) of G is a collection of non-negative integers g such that there is a Riemann Surface X of genus g on which G acts via orientation preserving diffeomorphisms. The main aim is to give a description of the contravariant functor G ↦sp(G). This problem is named as Hurwitz Problem by D. McCullough and A. Miller (1992). After the work of R. Kulkarni, C. Maclachlan, Y. Talu, it was conjectured that abelian finite p-groups are uniquely determined by their genus spectrum. Recently the work of S. Sarkar and J. Müller (2018) has showed that this conjecture is false. Currently over finite p-groups it is yet to determine properties of groups that will determine the spectrum uniquely.

Cayley graphs of finite groups are active areas of research as the connectivity of these graphs is applicable to various areas of computer science and telecommunication networks. Determining the spectral properties of these graphs is directly linked to the determination of the diameter of these groups. It was well known that the family of metacyclic groups do not form an expander family. However, determination of their diameter is a difficult problem. The specific values of the split metacylic groups which fail to be Ramanujan are obtained by P. Aurora, S. Lakshmivarahan, K. Rajeevsarathy, S. Sarkar and in another direction their effective diameter bounds are obtained by two of these authors. Siddhartha obtained his Ph.D. degree from the Harish-Chandra Research Institute, Allahabad, India. He worked on Finite p- Selected Publications group actions on Surfaces in his thesis. As a postdoctoral researcher, he was at the • Siddhartha Sarkar, On the genus spectrum for p-groups of exponent p and p-groups of maximal class, J. Institute of Mathematical Sciences, Chennai, Group Theory 12 (2009), no. 1, 39—54. India and Hebrew University of Jerusalem, • Jürgen Müller, and Siddhartha Sarkar, A structured description of the genus spectrum of Abelian p-groups, Israel. Glasg. Math. J. 61 (2019), no. 2, 381—423.

• Kashyap Rajeevsarathy, and Siddhartha Sarkar, Bound on the diameter of metacyclic groups, J. Algebra Appl. (accepted). Karam Deo Shankhadhar

Karam Deo works in Number Theory. More specifically, he is interested in the analytic aspects of automorphic forms: elliptic modular forms, Jacobi and Siegel modular forms, and analytic theory of L- functions.

The theory of modular forms and L-functions is of intense interest in number theory, which is also well connected to the subjects like representation theory, arithmetic and algebraic geometry, and mathematical physics etc. A systematic theory of modular forms is developed from the works of eminent mathematicians like Ramanujan, Hecke, Petersson, Siegel, Maaß and many more. Elliptic modular forms are certain functions on the complex upper half-plane and Siegel modular forms generalise the theory of modular forms to several complex variables. Jacobi forms are a cross between elliptic functions and modular forms and there are various well-known connections between elliptic and Siegel modular forms through Jacobi forms. An L-function is attached to a modular form encoding a good amount of information. In his Ph.D. thesis, Karam Deo worked on certain correspondences between Jacobi forms and modular forms, and non-vanishing of half-integral weight L-functions.

Any modular form admits a unique Fourier series expansion, and the associated Fourier coefficients and L-functions are very important and mysterious objects. There are several interesting research problems Karam Deo obtained his Ph.D. degree involving these objects which are needed to be explored. from Harish-Chandra Research Institute, Prayagraj (Allahabad), India. As a Selected Publications postdoctoral researcher, he was at the Institute of Mathematical Sciences, Chennai, India and Universidad de Chile, • Jaban Meher, Sudhir Pujahari, and Karam Deo Shankhadhar, Zeros of L-functions attached to cusp forms of Santiago, Chile. half-integral weight, Proc. Amer. Math. Soc. 147 (2019), no. 1, 131–143.

• Winfried Kohnen, Yves Martin, and Karam Deo Shankhadhar, A converse theorem for Jacobi cusp forms of degree two, Acta Arith. 189 (2019), no. 3, 223–262.

• Ajit Bhand, and Karam Deo Shankhadhar, On Dirichlet series attached to quasimodular forms, J. Number Theory 202 (2019), 91–106. Saurabh Shrivastava

Saurabh is an Euclidean Harmonic Analyst. His current research interests lie in the area bilinear Fourier multiplier operators, Littlewood-Paley theory, and weighted inequalities for operators in harmonic analysis.

The theory of bilinear multiplier operators is among the most active areas of research in harmonic analysis. The pioneering work of Michael Lacey and Christoph Thiele in late 1990’s on the bilinear Hilbert transforms lead the modern developments in the theory. There have been many important developments in the area since then. An important question in the theory of bilinear multipliers is to investigate the boundedness of bilinear multiplier operators associated with singular multiplier symbols. The bilinear Hilbert transform, bilinear Calderón-Zygmund operators are particular examples of such multiplier operators. There are many interesting open problems in the area to explore. The problems concerning weighted boundedness of bilinear operators and Littlewood-Paley type operators are of particular interest.

In 2013, Andrei Lerner et al. characterized multilinear weights for the multilinear Hardy-Littlewood maximal function and proved weighted estimates for multilinear Calderón-Zygmund operators. This work lead the researchers to investigate weighted boundedness of other bilinear (in general multilinear) Saurabh obtained his Ph.D. degree from the Indian Institute of Technology Kanpur, operators. Several important questions in this area remain unresolved till date. India in the year 2011. He was at the Harish-Chandra Research Institute, Selected Publications Allahabad, India for the post-doctoral studies. He joined the Department of • Loukas Grafakos, Parasar Mohanty, and Saurabh Shrivastava, Multilinear square functions and multiple Mathematics at IISER Bhopal in July 2012 weights, Math. Scand. 124 (2019), no. 1, 149–160. as an Assistant Professor. • Saurabh Shrivastava, and Kalachand Shuin, On composition of maximal function and Bochner-Riesz operator at the critical index, Proc. Amer. Math. Soc. (accepted).

• Rahul Garg, Luz Roncal, and Saurabh Shrivastava, Quantitative weighted estimates for Rubio de Francia's Littlewood-Paley square function, J. Geom. Anal. (accepted). Sanjay Kumar Singh

Sanjay Kumar Singh is interested in Algebraic Geometry. In his Ph.D. thesis, he has studied higher rank Brill-Noether theory over a smooth projective nodal curve. He has studied the stability of kernels of evaluation maps of globally generated torsion-free sheaves on a nodal and cuspidal curve in some important cases, and used them to study Brill-Noether loci for torsion-free sheaves with slope µ less than two.

Hitchin pairs on smooth varieties have been studied extensively by algebraic geometers, as well as, differential geometers in the last few decades. In his thesis, he has also worked on some aspects of the theory of Hitchin pairs on an integral projective curve.

He has been working on problems in algebraic geometry and algebraic coding theory. More specifically, his research interests include

• Vector bundles, Higgs Bundles, Moduli problems;

• The Diagonal and the Point property;

• Application of algebraic geometry in algebraic coding theory.

Sanjay obtained his Ph.D. from the Tata Institute of Fundamental Selected Publications Research, Mumbai, India. He worked as a postdoc at Institute of • Usha N. Bhosle, and Sanjay Kumar Singh, Weak point property and sections of Picard bundles on a Mathematics, Polish Academy of compactified Jacobian over a nodal curve, Proc. Indian Acad. Sci. Math. Sci. 126 (2016), no. 3, 329–339. Sciences, Warsaw, Poland.

• Nupur Patanker, and Sanjay Kumar Singh, Weight distribution of a subclass of ℤ2-double cyclic codes, Finite Fields Appl. 57 (2019), 287–308.

• Usha N. Bhosle, and Sanjay Kumar Singh, Fourier-Mukai Transform on a compactified Jacobian, Int. Math. Res. Not. IMRN (accepted). Prahlad Vaidyanathan

A C*-algebra is abstractly defined as a complete normed algebra satisfying certain axioms, and it occurs in the wild as a norm closed subalgebra of the space of bounded operators on a Hilbert space. They were introduced in the 1940s, but the subject received renewed interest in the 1970s, when George Elliott transplanted Atiyah-Hirzebruch's topological K-theory to the setting of C*-algebras. His work, together with that of Brown-Douglas-Fillmore and Kasparov, provided a wonderful pathway connecting problems in C*-algebras to problems in topology (and vice-versa), giving rise to the subject of noncommutative topology. It is this subject that Prahlad is most interested in. He began his mathematical career in the Classification Program, which aims to classify C*-algebras using their K-theory, and related invariants. Many of the important theorems in the program apply primarily to simple C*-algebras, i.e., ones with no two-sided closed ideals. His initial work revolved around trying to extend those theorems to non-simple C*-algebras, by viewing a non-simple C*-algebra as a continuous field of simple C*-algebras.

Since then, he has become more interested in nonstable K-theory, which is the study of the higher homotopy groups of the unitary group of a C*-algebra. The investigation began by understanding homotopical stable ranks, which help us determine when these homotopy groups are naturally Prahlad obtained his Ph.D. degree from isomorphic to the K-theory of the algebra. Now, he is trying to understand these groups from the point Purdue University, USA in 2012. He of view of rational homotopy theory. joined IISER Bhopal in July 2012. Recently, he has also developed a growing interest in Arveson's dilation theory, and its applications to a noncommutative analogue of Choquet's theorem.

Selected Publications

• Marius Dadarlat, and Prahlad Vaidyanathan, E-theory for C[0,1]-algebras with finitely many singular points, J. K-theory 13 (2014), no. 2, 249–274.

• Kashyap Rajeevsarathy, and Prahlad Vaidyanathan, Roots of Dehn twists about multicurves, Glasg. Math. J. 60 (2018), no. 3, 555–583.

• Prahlad Vaidyanathan, Homotopical Stable Ranks for certain C*-algebras, Studia Math. 247 (2019), no. 3, 299– 328. Adjunct/ Visiting Faculty

Prof. Dipendra Prasad (Adjunct) Automorphic forms and Representation theory

Prof. Akhil Ranjan (Visiting) Differential Geometry, Harmonic Manifolds

Prof. M. Ram Murty (Adjunct) Number theory

Postdocs Sayan Chakraborty

Sayan finished his Ph.D. from the University of Münster, Germany in 2018. Before joining IISER Bhopal in 2019, he worked in ISI Calcutta, Kolkata. He works in Operator Algebras and Noncommutative Geometry. Specifically, he is interested in K-theory of operators algebras and its applications in classical geometry, dynamical systems, and in classification of C*-algebra theory.

Kuldeep Saha

Kuldeep did his Ph.D. work from the Chennai Mathematical Institute. He has been visiting IISER Bhopal since March, 2019. Kuldeep is interested in geometric topology. He has studied embedding problems of smooth and contact manifolds in simple spaces (eg. Euclidean space). Currently he is working on a project that studies relation between mapping class group and fillability of contact 3-manifolds.

Soumya Dey Soumya completed his Ph.D. from IISER Mohali in 2018. He joined our department as a Post Doctoral Fellow in September 2018. In his Ph.D. thesis he concentrated on combinatorial aspects of commutator subgroups of some of the generalized braid groups. Currently, Soumya is working on geometry of surfaces. In particular, he is interested in combinatorial, topological and geometric aspects of mapping class groups of surfaces.

Partha Sarathi Patra

Partha obtained his Ph.D. from IIT Hyderabad, India in 2018. He joined our department as a postdoctoral fellow in the same year. His thesis work in Ph.D. includes characterization of images of some subspace of L2(ℝn+1) under Grushin semigroup as a weighted Bergman space and a variant of Hardy's theorem corresponding to Dunkl operator. At present he is working on boundedness of pseudo differential operator on modulation space associated with harmonic oscillators.

Makoto Sakagaito

Makoto received his Ph.D. from Tohoku University in 2012. Then, before joining IISER Bhopal, he was a postdoctoral fellow in Harish-Chandra Research Institute during 2013-2016 and in IISER Mohali during 2017-2019. He works in Number theory. His interest is the local-global principle and its application. He uses algebraic geometry for this study. Presently, he is investigating a generalized Brauer group. Manish Kumar Pandey

Manish obtained his Ph.D. from the Harish-Chandra Research Institute, Allahabad. He joined IISER Bhopal in August 2019. He works mainly in the theory of modular forms of half-integral weight. More specifically, he studies the complex analytic theory of associated L-functions. He is also interested in the p-adic properties of the associated L-functions. To study the analytic and arithmetic behaviour of the L-functions, he exploits the lifting maps between different spaces of automorphic forms.

Shailesh Tiwari

Shailesh worked in the Indian Institute of Technology Delhi during 2011-2016 to receive his Ph.D. He worked as a Visiting Assistant Professor in the Ambedkar University Delhi, India. Before joining IISER Bhopal, during 2017-18, he was a postdoctoral fellow in the Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, Brazil. Shailesh works in associative rings and algebras. Shailesh's interest is to study a differential polynomial identities on prime or semi-prime rings.

Indira Mishra Indira worked in the IIT Kanpur during 2008–2013 to receive her Ph.D. Then, before joining IISER Bhopal, during 2013-14, she was a postdoctoral fellow in the IMSc Chennai, worked as a visiting researcher in the Universidad de Chile, Santiago during 2014-15, then as a postdoctoral fellow at IISER Bhopal during 2015-17. Indira works in Partial Differential Equations in particular homogenization theory. She uses tools from Functional Analysis for this study. Presently she is investigating some optimal control problems in connection with Homogenization.

Makarand Sarnobat

Makarand worked in Indian Institute of Science Education and Research, Pune during 2012-2019 to receive his Ph.D. During his

Ph.D., Makarand worked on non-vanishing of (�, K )-cohomology of representations of GLn(ℝ), by using the Local Langlands correspondence for real groups. Currently, he is interested central simple algebras and its connections to number theory. He is also interested representation theory of GL2(ℝ) as well as p-adic groups.

Doctoral Students

The Department offers a PhD and an Integrated PhD programme. There are seventeen doctoral students in the prior programme and twenty-one in the IPhD programme. Students for these programmes are selected through national level entrance examinations such as NBHM, NET, GATE, JAM followed by an interview. Students from all regions of India apply for these programmes. PhD students

Sannidhi Alape Surjeet Singh Choudhary

Sannidhi is a Ph.D. student working under the guidance of Dr. Dheeraj Kulkarni and Dr. Atreyee Bhattacharya Surjeet joined the institute in Aug 2019. He obtained the since 2019. He did his master's from Chennai master’s degree from Indian Institute of Technology, Mathematical Institute (2014-2016) and bachelor's from Gandhinagar (2017-2019), and bachelor’s degree from Indian Statistical Institute, Bengaluru (2011-2014). His Central University of Rajasthan, Ajmer (2014-2017). area of research is Topology and Geometry. Currently, he is focusing on Symplectic and Contact Geometry.

Arusha C Prerak Deep

Arusha is pursuing her Ph.D. under the guidance of Dr. Sanjay Kumar Singh since 2015. She received her Master’s and Bachelor’s degree from M.S University of Baroda Prerak is a Ph.D. student working under the guidance of (2013-2015) and Krishnammal College, Coimbatore Dr. Dheeraj Kulkarni. He started his doctoral studies in (2010-2013), respectively. Her broad area of research is 2019. He did BS-MS from IISER Bhopal (2014—2019). He Algebraic Geometry, currently, focusing on diagonal and is interested in Geometric Topology. point properties of moduli spaces and certain stability problems.

Haritha C Neeraj Kumar Dhanwani

Haritha is a doctoral student working under the guidance Neeraj has been working under the guidance of Dr. of Dr. Nikita Agarwal since 2017. She did BS-MS from Kashyap Rajeevsarathy since August 2015. He did IISER Bhopal and decided to continue working on the master’s from Devi Ahilya Vishwavidyalaya, Indore (2013– same problem as her final year thesis project. She is 2015) and bachelor’s from Shia college Lucknow (2009— working on ergodic theory and dynamical systems, 2012). His area of interest is low dimensional Topology especially, various ergodic properties of open dynamical and Geometric group theory, in particular, the Mapping systems (or dynamical systems with a hole). Class Group. Diksha Garg Lokenath Kundu

Lokenath Kundu did his bachelor’s from the University of Diksha is pursuing her coursework, currently. She did her Burdwan, (2007–2010) and master’s from Visva Bharati, master’s from Panjab University, Chandigarh (2016— Santiniketan (2011–2013). He joined IISER Bhopal in 2018), and bachelor’s from Post Graduate Government 2016. He is interested in Algebra and Topology. Presently, College, Chandigarh (2013—2016). She is exploring he is working to classify the characters of a finite group G Algebraic Topology, Commutative Algebra and Measure that does not come from the action of G on a compact Theory which she wishes to use in her future research Riemann surface of genus g ≥ 2 under the guidance of work. Dr. Siddhartha Sarkar.

Md Amir Hossain Monika

Amir is doing his doctoral work with Rohit Dilip Holkar Monika is a Ph.D. student working under the guidance of since 2018. He got his master’s degree from West Bengal Dr. Dheeraj Kulkarni since 2019. She did her master's State University, Barasat (2016) and bachelor’s degree from Indian Institute of Technology, Kanpur (2015—2017), from Barasat Govt. College, Barasat (2013). At present, he and bachelor's from Sri Venkateswara College, University is investigating if the KMS-states on the full C*-algebra of of Delhi (2012—2015). Her area of research is Topology a Fell bundle over an étale groupoid can be and Geometry. Currently she is focusing on Symplectic characterised. and Contact Geometry.

Chaitanya Kulkarni Krishna

Chaitanya joined Dr. Angshuman Bhattacharya in 2018 for his doctoral studies. He did master’s from Savitribai Krishna Yamanappa Poojara is in his first year of Ph.D. He Phule Pune University (2015—2017), and bachelor’s from did his master’s from Pondicherry University, Puducherry Fergusson College, Pune (2012—2015). He is interested in (2017–2019) and bachelors from Poornaprajna College, applications of the disintegration theory to certain Udupi, Karnataka (2014–2017). completely positive maps on the C*-algebras called the weak expectation. Apeksha Sanghi Kalachand Shuin

Apeksha Sanghi has done her bachelor’s and master’s Kalachand has done his bachelors from Midnapore from the University of Delhi during 2010—2013 and 2013 college, West-Bengal during 2011—2013 and Masters —2015, respectively. She joined IISER Bhopal in 2016 for from IIT Kanpur during 2013–2015. His area of interest is her doctoral studies. Her area of interest is Algebra and Euclidean Harmonic analysis. He is working under the Topology. She is working under the guidance of Dr. guidance of Dr. Saurabh Shrivastava. Kashyap Rajeevsarathy.

Apurva Seth Shrinit

Apurva is a Ph.D. student working under the guidance of Shrinit is a Ph.D. student working under the guidance of Dr. Prahlad Vaidyanathan since 2017. She did her Dr. Anjan Gupta since 2019. He did BS-MS (2012–2017) Master's from Indian Institute of Technology, Kanpur and from IISER Mohali. He works in Algebra. Bachelor's from Allahabad University. She is currently working on Non-Stable K-theory for Operator algebras.

Shrikant Shekhar

Shrikant is 1st year Ph.D student at IISER Bhopal. He did masters from Indian Institute of Technology, Gandhinagar (2017—2019), and bachelors from Motilal Nehru College, (University of Delhi) (2014—2017). He was a member of Summer Research Fellowship Program (2018), Harish Chandra Research Institute Allahabad. I-PhD students

Anshu Krishan Chakraborty

Anshu joined IISER Bhopal in 2014. She has received her Krishan has done his bachelors from Institute of bachelor's degree from the University of Delhi. Her area Mathematics and Applications, Bhuwaneshwar during of interest includes Operator algebras and K-theory of 2016—2019. He joined IISER Bhopal in 2019. His area of C*-algebras. She has been working under the guidance interest is Algebra. of Dr. Prahlad Vaidyanathan.

Sourayan Banerjee Rajesh Dey

He has done his bachelors from Institute of Mathematics Rajesh has done his bachelor’s from Ramakrishna and Applications, Bhubaneswar during 2013—2016. He Mission Vidyamandira, Belur, West Bengal during joined IISER Bhopal in 2016. His area of interest is 2014–2017. He joined IISER Bhopal in 2017. His area of Algebraic Geometry and Algebraic K-Theory. He is interest is Geometry, Topology and Functional Analysis. working under the guidance of Dr. Vivek Sadhu. He is working under the guidance of Dr. Kashyap Rajeevsarathy.

Riju Basak Shubham Ramkisan Jathar

Shubham joined IISER Bhopal Integrated PhD program in Riju has done his bachelors from University of Gour Mathematics during August 2018 after graduating from Banga during 2012—2015. He joined IISER Bhopal in the New Art’s, Commerce and Science College, 2015. His area of interest is Harmonic Analysis. He is Ahmednagar under SP Pune University. He is presently working under the guidance of Dr. Rahul Garg and Dr. going through the coursework for Integrated PhD Saurabh Shrivastava. program. He is interested in Analysis, in general. Pooja Joshi Pankaj Kapari

Pooja Joshi has done her bachelor’s from University of Pankaj has done his bachelors from St.Stephens College, Delhi during 2016—2019. She joined IISER Bhopal in University of Delhi during 2014–2017. He joined IISER 2019. Her area of interest is Algebra. Bhopal in 2018.

Himanshi Khurana Naveen Kumar

Himanshi has done her bachelors from Kirori Mal Naveen did his bachelors from Keshav Mahavidyalaya, College, University of Delhi during 2015–2018. She has University of Delhi during 2012—2015. He joined IISER joined IISER Bhopal in 2018 for Integrated PhD. Her areas Bhopal in 2016. His area of interest is Algebraic Number of interest are Representation Theory and Algebraic Theory and Analytic Number Theory. He is working under the Topology. guidance of Dr. Ajit Bhand and Dr. Siddhartha Sarkar.

Pranav Kumar Amandeep Khera

Amandeep has done his bachelors from Institute of Pranav has done his bachelors from Patna Science College Mathematics & Applications, Bhubaneswar during 2014– during 2016—2019. He joined IISER Bhopal in 2019. His 2017. He joined IISER Bhopal in 2017. His area of interest is area of interest is Analysis. Differential Geometry. He is working under the guidance of Dr. Anandateertha Mangasuli.

Nupur Patanker Sagar Naganath Shinde

Sagar did his bachelors from Fergusson College, Pune Nupur has done her bachelors from Institute for Excellence during 2013—2016. He joined IISER Bhopal in 2016 for in Higher Education, Bhopal during 2011–2014. She joined Integrated PhD. He is working with Dr. Angshuman IISER Bhopal in 2014. Her area of interest is Algebraic Bhattacharya in some problems in Operator Algebra and Coding Theory. She is working under the guidance of Dr. Compact Quantum Groups. Sanjay Kumar Singh. Shashank Pathak Aniruddha Sudarshan

Shashank has done his bachelors from Sri Venkateswara Aniruddha joined IISER Bhopal in 2018. He did his College, University of Delhi during 2015—2018. He joined Bachelor's from the School of Sciences, Jain University, IISER Bhopal in 2018 for the Integrated PhD course. He is Bengaluru. He is interested in Number Theory. interested in Mathematical Logic.

Prachi Sahjwani Aditya Tiwari

Prachi has done her bachelors from Indraprastha College Aditya has done his bachelors from Deshbandhu College, for Women, University of Delhi during 2015—2018. She University of Delhi during 2013—2016. He joined IISER joined IISER Bhopal in 2018 for Integrated PhD. Her area Bhopal in 2016. His area of interest is Geometric Analysis. of interest is Topology and Geometry. He is working under the guidance of Dr. A. Mangasuli.

Prashant Tiwari Renu

Renu has done her bachelor’s from Shyama Prasad Prashant has done his bachelors from Delhi University Mukherji College, University of Delhi during 2012—2015. during 2012—2015. He joined IISER Bhopal in 2015. His area She joined IISER Bhopal in 2016. Her area of interest is of interest is Number Theory. He is working under the Finite p-Groups. She is working under the guidance of Dr. guidance of Dr. Karam Deo Shankhadhar. Siddhartha Sarkar.

Swapnil Tripathi

Swapnil joined as an Integrated Ph.D. student in 2015 at IISER Bhopal. He has been working under the guidance of Dr. Nikita Agarwal since 2018. He did his Bachelor's from Sri Venkateswara College, University of Delhi. He is currently working on switching of systems and non-linear dynamics.

BS-MS Students

The BS-MS programme is a five year dual-degree programme. The students are admitted into this programme through three different channels — State and Central Boards, JEE Advanced and KVPY. During the first two years of the programme, the students get training in all basic science subjects. In the third year, they choose a major subject, pursue their studies to the dual degree. In the final year of the programme, each student undertakes a project in an advanced topic. Aditesh joined IISER Bhopal in 2015. He is working in Differential Equation under the guidance of Dr. Anandateertha Mangasuli. His thesis is titled “Sturm Liouville theory of differential equations”. His area of interest is Differential equations.

Aditesh Kumar Anand

Sarfaraj joined IISER Bhopal in 2015. He is working in Harmonic Analysis under the guidance of Dr. Saurabh Shrivastava. His thesis is titled “Best constants in maximal functions inequalities”.

Sarfaraj Biswas

Amritendu Das joined IISER Bhopal in 2015. His area of interest is Harmonic Analysis. He is working under the guidance of Dr. Rahul Garg.

Amritendu Das

Vishal joined IISER Bhopal in 2015. He is working in Algebraic Graph Theory under the guidance of Dr. Kashyap Rajeevsarathy. His area of interest is Algebra, in particular Group Theory.

Vishal Gupta

Muttareddygari Sreechakra joined IISER Bhopal in 2015. His area of interest is Elliptic-curve Cryptography.

Muttareddygari Sreechakra Shreyas joined IISER Bhopal in 2015. He is working in Applied Topology under Dr. Dheeraj Kulkarni. His MS thesis is titled Topological Data Analysis.

Shreyas Samaga

Ranveer joined IISER Bhopal in 2015. He is working in Number Theory under the guidance of Dr. Ajit Bhand. His area of interest is Mathematical Physics, and his thesis is titled “Mock modular forms and Black hole physics”.

Ranveer Kumar Singh

Ekta joined IISER Bhopal in 2015. She is working in Representation Theory under the guidance of Dr. Kumar Balasubramanian. Her thesis is titled Representation Theory of GL(n) over p-adic fields.

Ekta Tiwari

Sreshta joined IISER Bhopal in 2015. She is working in Nonlinear Functional Analysis under the guidance of Dr. Prahlad Vaidyanathan. Her thesis is titled Topological Degree and Fixed Point Theorems.

Sreshta Venkatakrishnan Nonacademic staff

Kishore is a BBA graduate in Reena did her Master’s from Finance from Career College, CSJM University, Kanpur Bhopal (2010). He has done (2005). She is associated PGDM in Finance from with IISER Bhopal since IPER Bhopal (2013), and has August 2012, and currently been with our Department working at the Department since 2014. of Mathematics.

Kishore Yeolekar Reena Bhattacharya Arvind Patel (Project Office Assistant) (Project Office Assistant) (Project Office Assistant)

Activities

The Department organises and hosts various conferences and meetings for experts from all around the world; workshops and training programmes for graduate and undergraduate students in India; and multiple gathering for the members of Institute. These programmes are supported by multiple bodies such as NBMH, NCM, DST and the Institute itself.

On the right is a snap from the Math Day celebration organised by students in the Department. The Math Day “MTH eiπ + 1”

The first edition of math day celebration was conducted in order to engage students beyond the traditional setting of classroom lectures and seminars, to attract first-year and second-year BS- MS students to Mathematics by showing them a glimpse of its beauty, profundity and ubiquity. The event was named as MTH eiπ + 1and was held on 8th and 9th of March, 2019.

Various activities like competitions, talks and games were organized by students with the support of faculties which include Integration bee, Explain to your junior, Math quiz and Mathathon (a mathematical treasure hunt). Dr. Rohit Dilip Holkar, and Dr. Kashyap Rajeevsarathy were invited to give talks during the event. The students also arranged an exhibition of still models, posters and photographs which explain some elementary or complex mathematical concepts. The event was indeed a good platform to promote the spirit of mathematical learning and enhanced creative thinking and team work among students. The Mathematics Exhibition Winners of the Mathematics Photography Competition

Caption: The intermediate Caption: Not a manifold, value theorem, Winner: Vishal Gupta. Winner: Shubham Subhash Patil. Second prize. Third prize.

Caption: Convergence, Winner: Apurva Seth. First prize. Gallery of the Math Day Celebbration

Mathematics to play with!

Programming Mathematics Various Problem Solving Talks by faculty Competitions In-House Symposium 2018 & 2019

The In-House Symposium of the Department of Mathematics was conceived as a platform for post- doctoral researchers and PhD students to present their research, and to engender fruitful discussion amongst them and faculty members with disparate research interests.

The first In-House Symposium of the Department of Mathematics was conceived as a platform for post- doctoral researchers and PhD students to present their research, and to engender fruitful discussion amongst them and faculty members with disparate research interests. The Symposium was held on February 03, 2018, and Prof. V. Srinivas (TIFR Mumbai) was present as an external guest. In addition to his plenary talk, there were six other talks; three by post-docs and three by PhD students. The Symposium ended with a poster presentation by some PhD students, along with lively discussions.

The second symposium was held on 8th and 9th of The mug design for the In-House Symposium 2019 February, 2019. Dr. Manjunath Krishnapur from IISc Bangalore was invited as the special guest. In addition to his excellent plenary talk, there were eleven other talks — five by postdocs, six by PhD students, and several lively discussions over coffee. The Symposium also included a poster presentation by some PhD students.

The culture of free exchange of ideas that has been a core value of the department was there for all to see, and it is hoped that future iterations continue building on this. Group photo with Prof. Manjunath Krishnapur (IISc) during the In-House Symposium 2019. (Prof. Krishanpur is marked by the yellow dot) NCMW - Operator Algebras, Quantum Groups and Noncommutative Geometry, July 1-13, 2019

In this workshop, we studied three fundamental areas of Operator Algebras, each of which is an important and involved field in its own right: (i) Noncommutative Geometry [taught by Dr. Sayan Chakraborty (IISER, Bhopal) and Prof. Arup K. Pal (ISI, Delhi)], (ii) K-theory [taught by Dr. Rohit Holkar (IISER Bhopal), and Dr. Prahlad Vaidyanathan (IISER Bhopal)], and (iii) Quantum Groups [taught by Dr. Sutanu Roy (NISER, Bhubaneshwar)]. Each course consisted of some introductory lectures in the first week, while the second week consisted of more advanced material, reflecting modern research trends within the subject. The students attending the workshop were either in an advanced stage of their PhD program, or post- docs working in related fields. The feedback from the students and the faculty was overwhelmingly positive, and the workshop was a great success.

Group photo during the NCM workshop in 2019. The National Conference on Commutative Algebra and Algebraic Geometry (CAAG), July 2- 6, 2019

The National Conference on Commutative Algebra and Algebraic Geometry (CAAG) was held at IISER Bhopal during July 2-6, 2019. This is a part of biennial national / international conference on Commutative Algebra and Algebraic Geometry being held over the last two decades. Around sixty people participated in the conference. The conference brought together senior and young researchers for exchange of ideas. It also provided a platform for the young researchers to be updated on the latest developments in the subject.

Group photo during CAAG, 2019. Simon Marais Mathematics Competition (SMMC) 2018

The SMMC is an international mathematics competition involving participation from students from various institutions from the Asia Pacific region.

NCM workshop on Contact and Symplectic Geometry, December 3-14, 2018

In the last two decades, the area of Contact and Symplectic Geometry has been growing very rapidly. The geometry and topology of Contact and Symplectic structures is intimately tied with the properties of the manifolds on which these structures rest. This area has interesting and intriguing connections with many fields in mathematics and physics.

In this workshop, we wish to give the audience a fairly good knowledge about the two dominant features of Contact and Symplectic structures, namely "Flexibility" and “Rigidity" as envisaged by Gromov and propagated further by Eliashberg and others. The flexibility refers to a feature of these structures where "h-principle” type results can be proved while the rigidity refers to an aspect that relies on the use of “J-holomorphic curves”. The fine line that differentiates the flexibility and the rigidity has been elusive, and is a matter of great mathematical interest.

The first week of the workshop will recall briefly the basics of Contact and Symplectic Geometry. The connections with other fields of mathematics and physics will be discussed. Eliashberg's classification of overtwisted contact structures in dimension three will also be discussed. There will be talks on the introduction to J-holomorphic curves.

The second week will consist of lectures on advanced topics that reflect the current research trends in Contact and Symplectic Geometry. The students in the advanced stages of PhD program, postdocs and young faculty members working in this or related fields will greatly benefit from this workshop.

AFS - I (2018) IISER Bhopal | NCM, December 3-29, 2018

Basic knowledge in algebra, analysis and topology forms the core of all Advanced Instructional Schools organized by NCM. The main objectives of AFS are to bring up students with diverse background to a common level and help them acquire basic knowledge in these subjects required in Advanced Instructional Schools. AFS programs are targeted at fresh Ph. D. students in research institutions and universities in the country. Science Academies’ Lecture Workshop on “Geometry and Topology”, January 20-21, 2018

The purpose of this two-day workshop is to provide an opportunity to young teachers, researchers and students of Mathematics to learn about important topics in Geometry, Topology and their applications from active researchers and experts.

About the Workshop

A workshop on “Geometry and Topology” was held on 20th & 21st January 2018 at IISER Bhopal. The workshop was organized by the Department of Mathematics, in association with the Indian National Science Academy, New Delhi, The National Academy of Sciences, Allahabad and Indian Academy of Sciences, Bangalore.

Prof. A. J. Parameswaran, TIFR, Mumbai was the Convener and Dr. Sanjay Kumar Singh, from IISER Bhopal was the Coordinator. Fellows from Science Academies and eminent academicians from reputed institutions were invited in the workshop to disseminate the proposed concepts to the participants.

The lectures in this workshop have covered specific topics which were relevant to the teachers' classroom instructions. An important component of this program was the discussion session during which the participants interacted with each other, cleared their doubts and worked-out routine into advanced exercises. In this workshop, participants learnt the basics of Mathematics and used them to study some specific topics in Geometry and Topology. The speakers discussed questions of current interest to give a flavor of ongoing research in these areas.

The aim of this workshop was to promote Mathematics and improve the quality of teaching which is essential for motivating students for pursuing research in Mathematics. We hope that after attending this school, our participants were motivated to study Mathematics at a higher level.

Resource Persons

• Prof. Satya Deo Tripathi, HRI, Allahabad

• Prof. A J Parameswaran, TIFR, Mumbai

• Prof. Mukut Mani Tripathi, BHU, Varanasi

• Dr. Sanjay Kumar Singh, IISER Bhopal

Publications

1. Nikita Agarwal, A simple loop dwell time approach for stability of switched systems, SIAM J. Appl. Dyn. Syst. 17 (2018), no. 2, 1377–1394. 2. Nikita Agarwal, Stabilizing Graph-dependent Linear Switched Systems with Unstable Subsystems, Eur. J. Control (accepted).

3. Nikita Agarwal, Riddhi Shah, and Geetha Venkataraman, Maryam Mirzakhani: The Master Artist of Curved Surfaces Resonance – Journal of Science Education 23 (2018), no. 3, 253–262.

4. Mohammad Ashraf, Vincenzo De Filippis, Sajad Ahmad Pary, and Shailesh Kumar Tiwari, Derivations vanishing on commutator identity involving generalized derivation on multilinear polynomials in prime rings, Comm. Algebra 47 (2019), no. 2, 800–813. 5. Kumar Balasubramanian, M. Ram Murty, and Karam Deo Shankhadhar, Finite order elements in the integral symplectic group, J. Ramanujan Math. Soc. 33 (2018), no. 4, 427—433. 6. Kumar Balasubramanian, K. S. Senthilraani, and Brahadeesh Sankarnarayanan, Self-dual representations of SL(2, F): an approach using the Iwahori-Hecke algebra, Comm. Algebra 47 (2019), no. 10, 4210—4215. 7. Kumar Balasubramanian, A note on self-dual representations of Sp(4, F), J. Number Theory 199 (2019), 110—125. 8. Ajit Bhand, and M. Ram Murty, Class numbers of quadratic fields, Hardy-Ramanujan J. (accepted).

9. Ajit Bhand, and Karam Deo Shankhadhar, On Dirichlet series attached to quasimodular forms, J. Number Theory 202 (2019), 91–106. 10. Angshuman Bhattacharya, Michael Brannan, Alexandru Chirvasitu, and Shuzhou Wang, Property (T), property (F) and residual finiteness for discrete quantum groups, J. Noncommut. Geom. (accepted). 11. Usha N. Bhosle, and Sanjay Kumar Singh, Fourier-Mukai Transform on a compactified Jacobian, Int. Math. Res. Not. IMRN (accepted). 12. Christian Bönicke, Sayan Chakraborty, Zhuofeng He, and Hung-Chang Liao, Isomorphism and Morita equivalence classes for crossed products of irrational

rotation algebras by cyclic subgroups of SL2(ℤ), J. Funct. Anal. 275 (2018), no. 11, 3208–3243. 13. Tommi Brander, Joonas Ilmavirta, and Manas Kar, Superconductive and insulating inclusions for linear and non-linear conductivity equations, Inverse Probl. Imaging 12 (2018), no. 1, 91–123.

14. Tommi Brander, Bastian Harrach, Manas Kar, and Mikko Salo, Monotonicity and enclosure methods for the p-Laplace equation, SIAM J. Appl. Math. 78 (2018), no. 2, 742–758. 15. Alcides Buss, Rohit Dilip Holkar, and Ralf Meyer, A universal property for groupoid C*-algebras.I, Proc. Lond. Math. Soc. (3) 117 (2018), no. 2, 345–375.

16. Haritha C, and Nikita Agarwal, Product of expansive Markov maps with hole, Discrete Contin. Dyn. Syst. 39 (2019), no. 10, 5743–5774. 17. Sayan Chakraborty, and Franz Luef, Metaplectic transformations and finite group actions on noncommutative tori, J. Operator Theory 82 (2019), no. 1, 147– 172. 18. Sayan Chakraborty, and Makoto Yamashita, Tracing cyclic homology pairings under twisting of graded algebras, Lett. Math. Phys. 109 (2019), no. 7, 1625– 1664. Publications

19. Amanda Croll, Roger Dellaca, Anjan Gupta, Justin Hoffmeier, Vivek Mukundan, Denise Rangel Tracy, Liana M. Şega, Gabriel Sosa, and Peder Thompson, Detecting Koszulness and related homological properties from the algebra structure of Koszul homology, Nagoya Math. J. (accepted). 20. Soumya Dey, and Krishnendu Gongopadhyay, Commutator subgroups of twin groups and Grothendieck’s cartographical groups, J. Algebra 530 (2019), 215– 234. 21. Soumya Dey, and Krishnendu Gongopadhyay, Commutator subgroups of welded braid groups, Topology Appl. 237 (2018), 7–20. 22. Basudeb Dhara, Krishna Gopal Pradhan, and Shailesh Kumar Tiwari, Engel type identities with generalized derivations in prime rings, Asian-Eur. J. Math. 11 (2018), no. 4, 1850055, 11 pp. 23. Rahul Garg, Luz Roncal, and Saurabh Shrivastava, Quantitative weighted estimates for Rubio de Francia's Littlewood-Paley square function, J. Geom. Anal. (accepted). 24. Dipankar Ghosh, Anjan Gupta, and Tony J. Puthenpurakal, Characterizations of regular local rings via syzygy modules of the residue field, J. Commut. Algebra 10 (2018), no. 3, 327–337.

25. Abhishek Ghosh, Saurabh Shrivastava, and Kalachand Shuin, Weighted boundedness of multilinear maximal function using Dirac deltas, Rend. Circ. Mat. Palermo (2) (accepted).

26. Abhishek Ghosh, and Kalachand Shuin, Local one-sided maximal function on fractional Sobolev spaces, Math. Inequal. Appl. 22 (2019), no. 2, 519–530. 27. Loukas Grafakos, Parasar Mohanty, and Saurabh Shrivastava, Multilinear square functions and multiple weights, Math. Scand. 124 (2019), no. 1, 149–160. 28. Anjan Gupta, A criterion for modules over Gorenstein local rings to have rational Poincaré series, Pacific J. Math. (accepted).

29. Abhash Kumar Jha, Abhishek Juyal, and Manish Kumar Pandey, On simultaneous non-vanishing of twisted L-functions associated to newforms on Γ0(N ), J. Ramanujan Math. Soc. 34 (2019), no. 2, 245–252. 30. Winfried Kohnen, Yves Martin, and Karam Deo Shankhadhar, A converse theorem for Jacobi cusp forms of degree two, Acta Arith. 189 (2019), no. 3, 223–262.

31. M. Manickam, and Karam Deo Shankhadhar, An Eichler-Zagier map for Jacobi cusp forms on ℋ × ℂ(g,1), J. Number Theory 194 (2019), 319–334. 32. Jaban Meher, Sudhir Pujahari, and Karam Deo Shankhadhar, Zeros of L-functions attached to cusp forms of half-integral weight, Proc. Amer. Math. Soc. 147 (2019), no. 1, 131–143.

33. Jaban Meher, Karam Deo Shankhadhar, and G. Viswanadham, On the coefficients of symmetric power L-functions, Int. J. Number Theory 14 (2018), no. 3, 813– 824. 34. Indira Mishra, and Madhukant Sharma, Approximate controllability of a non-autonomous differential equation, Proc. Indian Acad. Sci. Math. Sci. 128 (2018), no. 3, Art. 34, 13 pp. 35. Jürgen Müller, and Siddhartha Sarkar, A structured description of the genus spectrum of Abelian p-groups, Glasg. Math. J. 61 (2019), no. 2, 381—423.

36. Nupur Patanker, and Sanjay Kumar Singh, Weight distribution of a subclass of ℤ2-double cyclic codes, Finite Fields Appl. 57 (2019), 287–308. Publications

37. Partha Sarathi Patra, and D. Venku Naidu, Images of some subspaces of L2(ℝm) under Grushin and Hermite semigroup, J. Pseudo-Differ. Oper. Appl. 9 (2018), no. 2, 247–264.

38. Partha Sarathi Patra, C. Sivaramakrishnan, and D. Venku Naidu, Benedicks' theorem for the Weyl transform associated with the Heisenberg group, Integral Transforms Spec. Funct. 29 (2018), no. 6, 442–449.

39. Shiv Parsad, Kashyap Rajeevsarathy, and Bidyut Sanki, The geometric realizations of cyclic actions on surfaces, J. Topol. Anal. (accepted).

40. Manish K. Pandey, Sudhir Pujahari, and Jyoti Prakash Saha, Distinguishing pure representations by normalized traces, J. Number Theory 195 (2019), 217—225.

41. Kashyap Rajeevsarathy, and Siddhartha Sarkar, Bound on the diameter of metacyclic groups, J. Algebra Appl. (accepted).

42. Kashyap Rajeevsarathy, and Prahlad Vaidyanathan, Roots of Dehn twists about multicurves, Glasg. Math. J. 60 (2018), no. 3, 555–583.

43. A. Raghuram, and Makarand Sarnobat, Cohomological representations and functorial transfer from classical groups, Cohomology of arithmetic groups, 157– 176, Springer Proc. Math. Stat., 245, Springer, Cham, 2018.

44. Vivek Sadhu, On the vanishing of relative negative K-theory, J. Algebra Appl. (accepted)

45. Vivek Sadhu, and Charles Weibel, Relative Cartier divisors and K-theory, K-Theory—Proceedings of the International Colloquium, Mumbai, 2016, 1–19, Hindustan Book Agency, New Delhi, 2018.

46. Saurabh Shrivastava, and Kalachand Shuin, On composition of maximal function and Bochner-Riesz operator at the critical index, Proc. Amer. Math. Soc. (accepted).

47. S. K. Tiwari, Identities with Generalized Derivations and Multilinear Polynomials, Bull. Iranian Math. Soc. (accepted).

48. S. K. Tiwari, Generalized derivations with multilinear polynomials in prime rings, Comm. Algebra 46 (2018), no. 12, 5356–5372.

49. S. K. Tiwari, R. K. Sharma, and B. Dhara, Some theorems of commutativity on semiprime rings with mappings, Southeast Asian Bull. Math. 42 (2018), no. 2, 279– 292.

50. S. K. Tiwari, and R. K. Sharma, On Lie ideals with generalized (α, α)-derivations in prime rings, Rend. Circ. Mat. Palermo (2) 67 (2018), no. 3, 493–499.

51. S. K. Tiwari, and B. Prajapati, Generalized derivations act as a Jordan homomorphism on multilinear polynomials, Comm. Algebra 47 (2019), no. 7, 2777–2797.

52. Prahlad Vaidyanathan, Homotopical Stable Ranks for certain C*-algebras, Studia Math. 247 (2019), no. 3, 299–328. Visitors

Sharp Inequalities, their extremals and related problems, October 18, On nodal sets of eigenfunctions of the Laplacian, with randomness, 2019, Speaker: Prof. K Sandeep February 9, 2019 Affiliation: TIFR Centre for Applicable Mathematics, Bangalore Speaker: Dr. Manjunath Krishnapur Affiliation: IISc Bangalore

Group action on non-commutative spaces, September 19, 2019 Graph-theoretic operator theory, March 4, 2019 Speaker: Dr. Safdar Quddus Speaker: Prof. Sameer Chavan Affiliation: IISc Bangalore Affiliation: IIT Kanpur

Circle method and sub-convexity problems: Some history and recent Computational Mathematics in Biomedical Sciences, February 7, developments, August 23, 2019 2019 Speaker: Dr. Saurabh Kumar Singh Speaker: Dr. Aarti Jajoo Affiliation: ISI Kolkata Affiliation: Baylor College of Medicine, Houston, Texas

Symmetrically-Normed Ideals and Characterizations of Absolutely Surfaces and three-folds, January 29-31, 2019 Norming Operators, June 26, 2019 Speaker: Prof. Parameswaran Sankaran Speaker: Dr. Satish Kumar Pandey Affiliation: IMSc, Chennai Affiliation: Technion - Israel Institute of Technology Haifa, Israel

Experiments in Teacher Capacity Building, April 3, 2019 Convexity of level lines of Martin functions, January 24, 2019 Speaker: Ms. Sneha Bhansali Speaker: Dr. Koushik Ramachandran Affiliation: University of Iowa, USA Affiliation: TIFR-CAM, Bangalore

On the maximal function associated to the Lacunary spherical means An introduction to Mathematical Logic, January 21-24, 2019 on the Heisenberg group, March 20, 2019 Speaker: Dr. Sujata Ghosh Speaker: Dr. Sayan Bagchi Affiliation: ISI, Chennai Affiliation: IISER Kolkata Visitors

Negative curvature and a new proof of a classical result in complex Topology of Manifolds, December 26, 2018 analysis, October 23, 2018 Speaker: Prof. A J Parameswaran Speaker: Prof. Gautam Bharali Affiliation: Tata Institute of Fundamental Research, Mumbai Affiliation: IISc, Bangalore

A proof of the Fundamental Theorem of Algebra using `only' Variants of Equidistribution In Arithmetic Progressions, October 9, 2018 elementary linear algebra, December 21, 2018 Speaker: Dr. Akshaa Vatwani Speaker: Prof. Anant R. Shastri Affiliation: IIT, Gandhinagar Affiliation: IIT Bombay

Nature of sums associated to zeros of Riemann zeta function, Noncommutative geometry, December 11, 2018 September 25, 2018 Speaker: Prof. Jean Renault Speaker: Dr. Purusottam Rath Affiliation: Université d'Orléans Affiliation: Chennai Mathematical Institute

KMS states and groupoid C*-algebras, December 7, 2018 Ramanujan function, September 24, 2018 Speaker: Prof. Jean Renault Speaker: Dr. Sanoli Gun Affiliation: Université d’Orléans Affiliation: IMSc, Chennai

A multivariable calculus proof of Brouwer’s fixed point theorem, Fundamental group of moduli of principal bundles over a curve, November 26, 2018 September 18, 2018 Speaker: Dr. Akhil Ranjan Speaker: Dr. Arjun Paul Affiliation: IIT, Bombay Affiliation: IMSc, Chennai

A weak notion of negative curvature for the Kobayashi metric and On Fourier multipliers on the Heisenberg groups and Hermite psudo- analytical approaches to Kobayashi geometry, October 26 & 26, 2018 multipliers, May 04, 2018 Speaker: Prof. Gautam Bharali Speaker: Dr. Sayan Bagchi Affiliation: IISc, Bangalore Affiliation: IISc Bangalore Visitors

On Holomorphic Sectional Curvature of Hermitian Manifolds, March Diophantine Equations, February 3, 2018 27, 2018 Speaker: Prof. Vasudevan Srinivas Speaker: Dr. Ananya Chaturvedi Affiliation: TIFR Mumbai Affiliation: TIFR-CAM, Bangalore

Analysis on Semihypergroups: An Overview, February 7, 2018 Speaker: Dr. Choiti Bandyopadhyay Affiliation: University of Alberta, Edmonton

Alumni Network

Former Postdoctoral Fellows BS-MS 2008 Batch Dr. Umamaheshwaran A., PDF, Harish-Chandra Research Institute, Chiraag Lala, M.S., University of Edinburgh, Scotland Allahabad Mahesh Sunkula, Ph.D. Student, University of Oklahoma Dr. Senthil Raani Nimalan, Assistant Professor, IISER Berhampur Abhay Singh Chandel, Indian Armed Forces Dr. Divakaran Divakaran, Assistant Professor, Azim Premji University Dr. Jotsaroop Kaur, Assistant Professor, IISER Mohali Dr. Shiv Parsad Bansal, Assistant Professor, IIT Goa BS-MS 2009 Batch Dr. A. Antony Selvan, Assistant Professor, IIT (ISM) Dhanbad Saurabh Gosavi, Ph.D. Student, The University of Georgia Dr. Partha Sarathi Patra, Assistant Professor, SRM University, Aranya Lahiri, Ph.D. Student, Indiana University Bloomington Amaravati Dr. Bijan Kumar Patel, Assistant Professor, KIIT University, Bhubaneswar Alumni Network

BS-MS 2010 Batch BS-MS 2013 Batch Sudhanshu Srivastava, Ph.D. student, University of Rochester, USA Georgy C. Luke, Ph.D. student, IISER Tirupati Sourabh Kumar Goyal, PGDM, Finance, IMT Ghaziabad Saoji Shravan Bhushan, Ph.D. student, University of Oklahoma Sweta Pandey, Ph.D. student, University of Connecticut, USA M V Ajay Kumar Nair, Ph.D. student, IISc Bangalore Saparya Suresh, Ph.D. student, IIM Bangalore Maya Verma, Ph.D. student, University of Oklahoma

BS-MS 2011 Batch BS-MS 2014 Batch Sanjana Agarwal, Ph.D. student, Indiana University Bloomington Deo Ashish Samanta, Post graduate diploma in business analytics Vishnu P Iyer, Ph.D. student, The University of Kansas at ISI Kolkata, IIM Kolkata and IIT Kharagpur Mitesh Modasiya, Ph.D. student, IISER Pune Kucheriya Gaurav Sunil, MS in Applied Mathematics, Russia Mayank Jain, MBA, IIM Kashipur (Uttarakhand) Prerak Deep, Ph.D. student, IISER Bhopal BS-MS 2012 Batch Suman Dutta, Ph.D. student, ISI Kolkata Brahadeesh Sankarnarayanan, Ph.D. student, IIT Bombay Palkar Grishma Gurudas, Ph.D. student, University of Pittsburgh Aneesh Ramdas Palsule, Nishikawa Communications India Pvt. Ltd., Pune Shubham Namdeo, Ph.D. student, IIT Indore Merin Abraham, Assistant Professor, TKM College of Engineering, Kollam Haritha C, Ph.D. student, IISER Bhopal Gallery

Prof. Jean Rénault, a celebrated Operator Algebraist, from Prof. Mahuya Datta, from ISI Kolkata, delivering an the University of Orléans, France, during his seminar talk. invited lecture. Gallery

Inter IISER-NISER Meet, 2018 Gallery

Teachers’ Day Celebration, 2018 Gallery

A gathering of the Department at Jehan Numa, Bhopal, January 13, 2018 Department of Mathematics Indian Institute of Science Education and Research Bhopal

Bhopal Bypass Road, Bhauri Bhopal, 462066, Madhya Pradesh, India. Website: https://maths.iiserb.ac.in. Emails: [email protected], offi[email protected]. Phone : +91 755 269 2577, Fax : +91 755 269 2392.