Research

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. 

Convolution sums and applications: We compute convolution sums of divisor function using the theory of modular forms and quasi modular forms and apply those to find number of representations of an integer by certain quadratic forms. 

SpecialisationTheoretical 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

Partial Differential Equations; Generalized functions of Colombeau;  Delta-waves; Measure Theory.

I work in Commutative Algebra. The prime focus of my research has been in Projective modules and Complete Intersections.

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. 

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.

 

 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.

Contact us

School of Mathematical Sciences

NISERPO- Bhimpur-PadanpurVia- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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