Preprints and publications

The study of affine Deligne-Lusztig varieties originally arose from arithmetic geometry, but many problems on affine Deligne-Lusztig varieties are purely Lie-theoretic in nature. These geometric structures can be defined in the context of p-adic groups using parahoric subgroups of arbitrary level; however their study can be especially difficult at the Iwahori level due to the greater combinatorial complexity of affine Weyl groups. As a recurring theme in my work, I reduce certain questions on these infinite Coxeter groups to problems on their finite counterpart using the technical framework of quantum Bruhat graph and thus solve those problems.


  1. Pattern avoiding involutions and quantum Bruhat graph (2022); draft available on request.

  2. On the dimension formula of union of some affine Deligne-Lusztig varieties (2022); available at https://arxiv.org/abs/2212.06670.

  3. Affine Deligne-Lusztig variety and quantum Bruhat graph, (2021) published in Mathematische Zeitschrift, 303, 21 (2023).

  4. Tableau correspondences and representation theory, (2019) joint with Digjoy Paul and Amritanshu Prasad, published in Contemporary Mathematics, Vol. 738, pages 109-124.


Master's Thesis: General Linear Group and Symmetric Group - Commuting Actions and Combinatorics, (2017) completed at the Institute of Mathematical Sciences, Chennai, India.

"Langlands’s program is now the Indian parable of the blind men and the elephant. One man feels the trunk, a second a tusk, the others a piece of leg, ear, skin, or tail. Each has his own idea about what this object is—a snake, a tree, a wall, a piece of rope? Langlands imagined an elephant more than fifty years ago and mathematicians, even physicists, have been trying to combine the pieces and expand his picture of it ever since." - A Mathematical Rosetta Stone, Robbert Dijkgraff