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.
Abstract Group Theory: Automorphisms, Conjugacy Classes, Commutator Word Map, and Low Dimensional Cohomology; Braces and Skew Braces; Yang-baxter Equation.
Representations of Lie Algebras: Semisimple, Toroidal Lie Algebras.
Derived Categories of Coherent Sheaves, Matrix Factorization Categories, Tensor Triangulated Categories and T-structures, Algebraic Stacks, Algebraic K-theory, and Chow Groups.
Analysis of Partial Differential Equations, Inverse Problems, Homogenization, Mathematical Fluid Dynamics
Harmonic Analysis of Hermite, Special Hermite, and Laguerre Differential Operators
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.
Riemannian Geometry, Finsler Geometry.
The Research Interests in Number Theory at HRI Range Over Algebraic, Analytic and Combinatorial Number Theory, and Automorphic Forms.
Ramsey Theory and Additive Representation Problems in Analytic Number Theory, Additive Combinatorics, Transcendental Number Theory.
Iwasawa Theory, Special Values of L-functions, Automorphic Representations and P-adic Families, Galois Representations, P-adic Hodge Theory and Langlands Program, Mod-p Modular Arithmetic, Drinfeld Modules.
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