गणित में अनुसंधान

हमारे बारे में

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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.

बीजगणित और बीजगणितीय ज्यामिति:

समूह सिद्धांत (मनोज कुमार यादव)

Abstract Group Theory: Automorphisms, Conjugacy Classes, Commutator Word Map, and Low Dimensional Cohomology; Braces and Skew Braces; Yang-baxter Equation.

प्रतिनिधित्व सिद्धांत (पुनीता बत्रा)

Representations of Lie Algebras: Semisimple, Toroidal Lie Algebras.

बीजगणितीय ज्यामिति (उमेश दुबे, बी.एस.एस. श्रीधर)

Derived Categories of Coherent Sheaves, Matrix Factorization Categories, Tensor Triangulated Categories and T-structures, Algebraic Stacks, Algebraic K-theory, and Chow Groups.

विश्लेषण

आंशिक विभेदक समीकरण (तुहिन घोष, अमृता घोष)

Analysis of Partial Differential Equations, Inverse Problems, Homogenization, Mathematical Fluid Dynamics

हार्मोनिक विश्लेषण (पी के रत्नकुमार)

Harmonic Analysis of Hermite, Special Hermite, and Laguerre Differential Operators

ज्यामिति और टोपोलॉजी

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.

विभेदक ज्यामिति (हेमांगी एम. शाह)

Riemannian Geometry, Finsler Geometry.

संख्या सिद्धांत

The Research Interests in Number Theory at HRI Range Over Algebraic, Analytic and Combinatorial Number Theory, and Automorphic Forms.

बीजगणितीय और विश्लेषणात्मक संख्या सिद्धांत (डी सूर्या रमण, ज्ञान प्रकाश, आर थंगादुरई, अप्रमियो पाल, जिष्णु रे)

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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