My research interest is Arithmetic Geometry and Representation Theory.
My Ph.D thesis work focuses on the various Isospectrality notions of Locally Symmetric Spaces from Representation Theoretic point of view. My thesis can be found here (preliminary version), which is currently under review. The following are the publications/preprint for the content of my thesis.
A Finite Linear Dependence of Discrete Series Multiplicities (with Gunja Sachdeva); to appear in Nagoya Mathematical Journal.
On Infinitesimal 𝝉-Isospectrality of Locally Symmetric Spaces (with Chandrasheel Bhagwat and Gunja Sachdeva); Canadian Mathematical Bulletin,Volume 68, Issue 1, March 2025, pp. 246-261.
On Representation Equivalence and Multiplicity Measure for Lattices in Lie Groups (with Chandrasheel Bhagwat); Preprint.
In the recent past I have been working on Integral p-adic Hodge theory and p-adic Galois representations (in families). I am mostly interested in using (analytic, completed etc.) variants of Prismatic F-crystals to understand certain phenomenon in Relative p-adic Hodge theory. Here is my recent preprint in this direction.
Talks and Presentations :
Student Seminar at the Department of Mathematics at IISER Pune (28th May, 2026); "An Introduction to Spectral Spaces" (The transcript of the board talk will be uploaded soon).
Research Talk at Harish Chandra Research Institute, Prayagraj on 10th April, 2026; hosted by Muskan Bansal; "A Finite Linear Depedence of Discrete Series Multiplicities" (It is the transcript of the board talk).
Short Talk in GANIT Symposia 2026, at Indian Institute of Technology, Gandhinagar on 17-19th Jan, 2026; "Representation Equivalence and Isospectrality " (It is the pdf of the Keynote Presentation slides).
Two talks in Student Seminar at the Department of Mathematics at IISER Pune (14th August and 21st August, 2025); "An Introduction to Adic Spaces I & II" (The transcript of the board talk will be uploaded soon).
Research Talk at Indian Institute of Technology, Bombay on 16th June, 2025, hosted by Dipendra Prasad; "A Finite Linear Depedence of Discrete Series Multiplicities" (It is the transcript of the board talk).
Research Talk at BITS Pilani, Goa Campus on 24th April, 2025, hosted by Gunja Sachdeva; "Representation Equivalence and Isospectrality of Locally Symmetric Spaces" (It is the transcript of the board talk).
International Conference on Algebra, Analysis, Dynamics and its Application, 22nd - 26th Jan, 2025 on the occasion of 100 year celebration of Math Department at at Midnapore College (Autonomous) "On the Coarse Expansion of Arthur's Trace Formula " (It is the pdf of the Keynote Presentation slides).
Mathematics Departmental Symposium at IISER Pune (10-11 Jan, 2025) "On Infinitesimal 𝝉-Isospectrality of Locally Symmetric Spaces"(It is the transcript of the board talk).
Departmental Seminar at IISER Pune on 10/07/24 "Representation Equivalence and Isospectrality" (It is the pdf of the Keynote Presentation slides).