Currently, with my advisor, I am working on representations of Lie algebras, specifically certain cyclic modules of symmetrisable Kac-Moody Lie algebras known as Kostant-Kumar Modules. We are also exploring applications of this to questions like Schur-positivity.
Talk at CONTACT-V Conference on Generators & Relations, Multiplicity of Irreducibles for Kostant-Kumar Modules and Applications to Schur-Positivity Type Problems: Slides
Other Projects and Workshops
2019- Independent Study, Read a classical paper by Rimhak Ree “A family of simple groups associated with simple Lie algebra of type (F4)” and read about the Classification Theorem for Finite Simple Groups. Unsupervised
2021- Reading Project on Galois Theory and Inverse Galois Problem- As part of Visiting Students’ Research Program (VSRP), organised by Tata Institute of Fundamental Research, Under the supervision of Prof. Vijayalaxmi Trivedi, TIFR, Mumbai
2021-2022- Master’s Thesis on Lindstrom-Gessel-Viennot Lemma Proofs of Determinantal Schur Polynomial Identities, Under the supervision of Prof. Amritanshu Prasad, Institute of Mathematical Sciences, Chennai
2022- Participated in Advanced Instructional School on Representation Theory at Chennai Mathematical Institute, organised by ATM Schools, NCM
2022- Participated in Program on Combinatorial Algebraic Geometry, at ICTS, TIFR
2022- Participated in Advanced Instructional Course on Compact Lie Groups and their Representations, organised by ATM Schools, NCM
2023- Reading Project on Projectivity of Compact Riemann Surfaces, Under the supervision of Prof. Jaya Iyer, Institute of Mathematical Sciences, Chennai
2023- Participated in Advanced Instructional School on Lie Groups and Lie Algebras at Indian Institute of Science, organised by ATM Schools, NCM
2024- Participated in Program on Combinatorial Methods in Enumerative Algebra, at ICTS, TIFR
2025- Participated in Program on Combinatorics, Geometry and Representation Theory, at ICTS, TIFR, 2025