Algebra and Algebraic Geometry

Group Theory (Manoj Kumar Yadav)

Abstract group theory: Automorphisms, conjugacy classes, commutator word map, and low dimensional cohomology; Braces and skew braces; Yang-Baxter equation.

Representation Theory (Punita Batra)

Representations of Lie algebras: semisimple, toroidal Lie algebras.

Algebraic Geometry (Umesh Dubey, B.S.S. Sreedhar)

Derived categories of coherent sheaves, matrix factorization categories, Tensor triangulated categories and t-structures, Algebraic stacks, Algebraic K-theory, and Chow groups.

°Some familiar topics in Algebra & Algebraic Geometry to carry out `Research Projects' , see here.

Number theory

Analytic Number Theory (D Surya Ramana, Gyan Prakash, R Thangadurai)

Ramsey theory and additive representation problems in analytic number theory, additive combinatorics, transcendental number theory.

Arithmetic Geometry (Aprameyo Pal, Jishnu Ray)

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.

°Some familiar topics in Number Theory to carry out `Research Projects' , see here.

Analysis

Partial Differential Equations (Tuhin Ghosh, Amrita Ghosh)

Analysis of partial differential equations, Inverse Problems, Homogenization, Mathematical Fluid Dynamics.

Harmonic Analysis (P K Ratnakumar)

Harmonic analysis of Hermite, Special Hermite, and Laguerre differential operators.

°Some familiar topics in Analysis to carry out `Research Projects' , see here.

Geometry

Differential Geometry (Hemangi M. Shah)

Riemannian geometry, Finsler geometry.

°Some familiar topics in Geometry to carry out `Research Projects' , see here.

 

 

 

 

 

---