The Department of Mathematical Sciences, IISER BERHAMPUR promotes various areas of research in the discipline of pure and applied mathematics.

The following are the mass areas of research done:

**Analytic & Algebraic Number Theory***(Dr. Kasi V*,*Dr. Prem Prakash Pandey)***Representation Theory and Automorphic Forms***(Dr. Amiya Kumar Mondal)*

The members in the department at present are working in analytic properties of multiple zeta functions and their weighted variants, properties of Fourier coefficients of modular forms and their variants, discrepancy estimates and Exponential sums over primes, together with some topics in Algebraic number theory including the study of class groups, Units, Annihilators of class groups and Diophantine Equations.

The members in this area study the complex representations of p-adic groups and their contribution to Langlands' program. They use representation theory knowledge to understand the L-functions associated with the automorphic representations. Such understanding about L-functions is expected to have applications in number theory as well.

**Algebraic Geometry**(*Dr. Pabitra B*,*Dr. Seshadri Chintapalli*)

The group members work on problems related to linear series, specifically k-jet ampleness and syzygies of an ample line bundle on a smooth projective varieties, Higgs bundles, moduli problems of bundles.

**Harmonic Analysis**(*Dr. Senthil Raani*)**Analysis of Partial Differential Equations**(*Dr. Prashanta Garain*)**Operator Theory**(*Dr. Ritabrata Sengupta*)

The group members are interested in Euclidean Harmonic Analysis, in particular, $L^p-L^q$ multipliers of Fourier transforms, Fourier analysis on fractals.

Our research group focuses on the mathematical analysis of partial differential equations (PDEs). More precisely, we are interested in the theory of regularity, existence and uniqueness of elliptic and parabolic PDEs. The study involves investigation of variants of p-Laplace equations, for example, weighted p-Laplace equations, fractional p-Laplace equations, mixed local and nonlocal problems, anisotropic problems etc.

The Operator Theory Group's research topics currently encompasses various themes motivated by quantum theory questions. The group understands operator theory in a broad sense, including both the finite dimensional version i.e. matrix analysis as well as the infinite dimensional operator algebra settings. It also follows the mathematical developments inspired by physics ideas. Recent works include, for instance, the study of entanglement theory for C* algebra, Szegő limit theorem, structure of completely positive maps in Fock spaces, and resource theory in quantum information.