Research

Research Interests:

My research interests include Number Theory, Representation Theory of Lie Groups, Spectral Theory of Differential operators on locally symmetric spaces,  Special values of L-Functions associated with Motives etc. In the recent past, I have been also working on some problems in Galois theory and Spectral Graph theory.

Preprints:

• 1. Bhagwat C. and Raghuram A., Eisenstein cohomology for orthogonal groups and the special Values of L-functions for GL_1×O(2n)  (click here for the arXiv link.)

  2. Bhagwat C. and Sachdeva G.  Results on Strong multiplicity one theorem (click here for the arXiv link.)

  3.  Bhagwat C. and Mondal Kaustabh, On representation equivalence and multiplicity measure for lattices in Lie Groups (click here  for the arXiv link.)

  4. Bhagwat C. and Jaiswal, Shubham, Right Splitting, Galois Correspondence, Galois Representations and Inverse Galois Problem (click here  for the arXiv link.)

Publications:

1. Bhagwat C., and Rajan C. S., On a spectral analogue of the strong multiplicity one theorem, published online in Inter. Math. Res. Notices (IMRN), VOLUME 2011 NUMBER 18,  p. 4059-4073, 2011.

2. Bhagwat C., and Rajan C. S., On a multiplicity one property for the length spectra of even-dimensional compact hyperbolic spaces,  J. Number Theory,  131 (11), p. 2239-2244, 2011.

3. Bhagwat C., Pisolkar S., and Rajan C. S., Commensurability and representation equivalent arithmetic lattices, Inter. Math. Res. Notices (IMRN), Volume 2014, Issue 8, P. 2017–2036, 2014.

4. Bhagwat C., and Raghuram A., Ratios of periods for tensor product motives. Math. Res. Letters, 20 (2013) , No.4, 615-628.

5. Bhagwat C., On Deligne's periods for tensor product motives, Comptes Rendus Mathematique,  353 (3), p. 191-195, 2015.

6. Shekatkar S. M., Bhagwat C., Ambika G., Divisibility patterns of natural numbers as a complex network, Scientific Reports, 5:14280, 2015.

7. Bhagwat C., Pisolkar S., On uniform lattices in real semisimple groups, Proc. Amer. Math. Soc. 144(7) , p. 3151-3156, 2016.

8. Bhagwat C., Raghuram A., Endoscopy and the cohomology of GL(N), Bulletin of Iranian Math. Soc., Volume 43, Issue 4 (Special Issue), August 2017, Page 317-335, 2017.

9. Bhagwat C., Raghuram A., Special values of $L$-functions for orthogonal groups, Comptes Rendus Mathematique, 355 (3), p. 263-267,  2017.

10. Bhagwat C. and Ayesha Fatima, On The Length Spectra of Simple Regular Periodic Graphs, Volume 35, Issue 2, June 2020  pp. 139–147.

11. Bhagwat C. and Mondal S., On the growth of cuspidal cohomology of GL_4, Journal of Number Theory, Vol. 228, November 2021, Pages 162-173.

12. Bhagwat C. and Mondal S., Automorphic tensor products and cuspidal cohomology of the GL_4, Accepted for publication in International Journal of Number Theory (click here  for the arXiv link.)

Students (Present & Past):

• Phd Students:

1.  Ayesha Fatima:   Worked on some problems in Representation theory of Lie groups and discrete  subgroups of Lie  groups and Zeta functions on graphs  (graduated in May 2019.)

2.   Sudipa Mondal : Working on Cuspidal cohomology and automorphic forms (Expected to graduate by spring 2022.)

3.  Shubham Jaiswal : Working on some problems in Galois theory (Expected to graduate by summer 2024.)

4. Nasit Darshan (Expected to graduate by summer 2024.)

5. Kaustabh Mondal (Expected to graduate by summer 2026.)

•  Masters Thesis students

           1.  Ajith Nair:    Fifth year BS-MS student from IISER Pune,  

                graduated with BS-MS degree in May 2017.

                Topic: Harmonic analysis on locally symmetric spaces associated to a cocompact discrete                 subgroup of SL(2,R).

           2. Abhishek Inamdar:  Fourth year M.Sc. student from BITS Pilani, 

                graduated with MSc degree in May 2017.

            Topic: Representation Theory of finite groups

             3. Shashank Pratap Singh:  Fifth year BS-MS student from IISER Pune, 

                  graduated with BS-MS degree in May 2018.

            Topic: Class Field Theory

           4.  Rahul Mistry: Fifth year BS-MS student from IISER Pune, 

                   Graduated with BS-MS degree in May 2019.

            Topic:  Tate's thesis and L-functions

           5. Amol Hinge: Fifth year BS-MS student from IISER Pune, 

                Graduated with BS-MS degree in May 2019.

            Topic:  Spectral Graph Theory

           6. Garima Agarwal:  Integrated Ph.D. student from IISER Pune 

            Topic for Master's thesis: Topological groups and Representation theory of compact groups

            7. Ronit Debath:  Integrated Ph.D. student from IISER Pune (Expected to graduate in Summer 2023)

            Topic for Master's thesis: Fourier Analysis on number fields

          8.  Nazia V. : Fifth year BS-MS student from IISER Pune, Graduated with BS-MS degree in May 2020

             Topic: Local Langlands correspondence for GL(2)

          9. P. Narayanan:  Integrated Ph.D. student from IISER Pune, Masters thesis in 2019

              (Expected to graduate in Summer 2024)

            Topic for Master's thesis: Harmonic Analysis on topological groups and Tate’s thesis

        10. Kaustabh Mandal :  Integrated Ph.D. student from IISER Pune, Masters thesis in 2021

              (Expected to graduate in Summer 2026)

             Topic for Master's thesis:  Lie groups and Lie algebras

       11. Umesh Pandey:  Fifth year BS-MS student from IISER Tirupati, 

             Graduated with BS-MS degree in May 2023

             Topic: Compact Lie groups

        12. Priyanka Dey (MSc student from IISER Pune, Masters thesis in 2019

              (Expected to graduate in Summer 2024)

             Topic for Master's thesis: p-adic numbers and Tate's thesis