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*)**Operator Theory**(*Dr. Ritabrata Sengupta*)**Complex Analysis**(*Dr. Ratna Pal*)

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

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.

The group member in this research area is primarily interested in Holomorphic Dynamics which is the study of iterations of holomorphic functions in complex manifolds. Currently the member is exploring the following research areas in holomorphic dynamics: (1) Dynamics of Henon maps (2) Non-autonomous basins of attraction of automorphisms in higher dimensions (3) Dynamics of multi-resonant maps in higher dimensions. Apart from holomorphic dynamics, the member is also interested in Potential theory and in Function Theory in Several Complex Variables, in particular in the following two research topics: Bergman spaces of unbounded pseudo-convex domains in higher dimensions and the squeezing functions of some special domains in higher dimensions.