+91-674-249-4082

Vector bundles over complex projective hypersurfaces.

Order structure in normed spaces and operator spaces (matricially normed spaces); Theory of operator ideals (Geometry of Banach Spaces).

Incidence Geometry, Groups, Algebraic Combinatorics

**Specialisation: Number Theory, Modular Forms **

**Present Research Interests:**

** Supercongruences: **The numbers which occur in Ap\'{e}ry's proof of the irrationality of zeta(2) and zeta(3) have many interesting congruence properties.Work started with F. Beukers and D. Zagier, then extended by G. Almkvist, W. Zudilin and S. Cooper recently has complemented the Ap\'{e}ry numbers with set of sequences know as Ap\'{e}ry-like numbers which share many of the remarkable properties of the Ap\'{e}ry numbers. We study supercongruences properties of Ap\'{e}ry-like numbers.

** Differential Operators: **There are many interesting connections between differential operates and modular forms. Using Rankin-Cohen type differential operators on Jacobi forms/ Siegel modular forms we study certain arithmetic of Fourier coefficients.

**Specialisation: **Theoretical Computer Sciences, Coding Theory, Cryptology, Discrete Mathematics.

**Present Research Interests: **Symmetric ciphers, Algebraic Attack, Boolean Functions, Combinatorics.

Cowen-Douglas Class of operators, Hilbert modules over function algebra and Dilation theory.

Modular forms, L-functions

Transcendental number theory, Modular forms and Multiple zeta values

Combinatorics, Algebraic Graph Theory

- Spectral Theory of Differential Operators

Partial Differential Equation; Generalized functions of Colombeau; Delta-waves, Measure Theory, Fractional differential equations.

Moduli of vector bundles, partial differential equations, mathematical physics, representation theory

Disordered systems pops up quite often in physics (spin glass), biology (artificial neural network), social sciences (matching) and many other places. To analyze, usually these systems are identified with the stochastic models. My main research interest is on the application of probabilistic tools to analyze these stochastic models.

My Primary research area is functional analysis. I work in operator algebra. I study one parameter family of endomorphisms on von Neumann agebras. I also study structure theory of von Neumann algebras, Connes's classifications theory of type III factors and various others property of type III factors. https://sites.google.com/a/niser.ac.in/panchugopal-bikram/system/app/pages/sitemap/hierarchy

Enumerative geometry of singular curves, using methods from Differential Topology.

I work in the field of noncommutative geometry specifically on the confluence of algebra, geometry and analysis.

I work on Harmonic Analysis on Euclidean Spaces and Heisenberg Groups.

At present my research interest is Spherical harmonics, Hermite and Laguere expansion and Dunkl Transform.

My primary area of research is nonlinear boundary value problems. Currently my work is focused on two topics in quasilinearelliptic partial differential equations:

- The structure of the second eigenfunctions of the p-Laplacian on a ball,
- Quasilinear elliptic problems in the exterior domain.

I am also interested in spatial ecology. I have worked on some reaction-diffusion models that have been used to analyze the existence of alternate stable states in ecosystems.

Statistical Inference, Sequential Analysis, Stochastic Processes. More specifically, I am interested in:

(1) Multiple hypothesis testing controlling various error rates for sequential data

(2) Multistage and sequential procedures for point and confidence interval estimation

Topological Quantum Groups, Operator Algebras, Noncommutative Geometry.

In general revolves around the study of Banach algebras and their multipliers associated to locally compact groups, hypergroups. In particular interested in the studies related to Fourier algebras.

**School of Mathematical Sciences**

NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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