# Research in Mathematics

The mathematics group at Harish-Chandra Research Institute conducts research in algebra, analysis, geometry and topology, and number theory. The group consists of faculty members, visiting scientists, postdoctoral fellows, and graduate students. An accompanying document contains more information on the research interests of individual members of the group.

## Algebra

The areas of research in algebra at HRI are theory of finite groups, infinite-dimensional Lie algebras, and representation theory.

## Analysis

In analysis, the areas of research are harmonic analysis and PDEs, with an emphasis on inverse problems, homogenization, and mathematical theory of fluid mechanics.

## Geometry and topology

Geometry and topology at HRI includes work on algebraic topology, differential equations arising in mathematical physics, differential geometry, discontinuous groups, Riemann surfaces, algebraic surfaces over local fields, and moduli spaces of vector bundles.

## Number Theory

The research interests in number theory at HRI range over algebraic, analytic and combinatorial number theory, and automorphic forms.