Research

My research broadly lies in the fields of analytic number theory and automorphic forms. In particular, I am interested in problems regarding subconvexity estimates of L-functions, spectral theory of automorphic forms, and quantum unique ergodicity. I am also interested in the analysis of arithmetic manifolds, homogeneous dynamics, and representation theory. 

Publications and preprints

• Local representation theory and related

1. Analytic newvectors for GL(n,R), joint with Paul D. Nelson: submitted, arXiv.

2. Applications of analytic newvectors for GL(n): Math. Ann. 380 (3), 915-952, (2021), arXiv.

3. On the spectral aspect density hypothesis and application, joint with Edgar Assing: submitted, arXiv.

• Estimates of central L-values

1. The second moment of GL(n) x GL(n) Rankin--Selberg L-functions: Forum Math. Sigma, vol.10, e47, (2022), arXiv.

2. The Weyl bound for triple product L-functions, joint with Valentin Blomer and Paul D. Nelson: Duke Math J. 172 (6), 1173-1234, (2023), arXiv.

3. Spectral reciprocity for GL(n) and simultaneous non-vanishing of central L-values, joint with Ramon Nunes: to appear in Amer. J. Math., arXiv.

4. Moments of L-functions via the relative trace formula, joint with Ramon Nunes: submitted, arXiv.

5. Local integral transforms and global spectral decomposition, joint with Valentin Blomer and Paul D. Nelson: to appear in Geom. Funct. Anal., arXiv.

• Bounds of automorphic forms

1. Supnorm of an eigenfunction of finitely many Hecke operators: Ramanujan J. 48 (3), 623-638, (2019), arXiv.

2. On the local L2-Bound of the Eisenstein series, joint with Amitay Kamber: Forum Math. Sigma, vol.12, e76, (2024), arXiv.

• Equidistribution and Diophantine approximation

1. Joint equidistribution on the product of the circle and the unit cotangent bundle of the modular surface: J. Number Theory 226C, 271-283, (2021), arXiv.

2. Optimal Diophantine exponents for SL(n), joint with Amitay Kamber: Adv. Math. 443 (2024), Paper No. 109613, arXiv.

3. On Fourier asymptotics and effective equidistribution, joint with Shreyasi Datta: submitted, arXiv.

Theses

• Analytic newvectors for GL(n,R) and applications: Ph.D. thesis at ETH, advisor: Paul D. Nelson.

• Supnorm problem of certain eigenfunctions on arithmetic hyperbolic manifolds: M.Sc. thesis at UBC, advisor: Lior Silberman.

• Another reformulation of the Riemann hypothesis via a Hilbert space: B.Math. project at ISI, advisor: Bhaskar Bagchi.

Notes

1. Proof of positive entropy using one Hecke operator à la Brooks--Lindenstrauss: pdf.

2. A less technical proof of the existence of analytic newvectors for GL(3,R): pdf.

Seminars/Conferences organised

1. Queen Mary Algebra Number Theory seminar

2. Paul Nelson's birthday seminar series

3. Automorphic Forms and L-functions of higher rank

4. Aarhus Automorphic Forms Conference

Refereed for Journals

1. Forum of Mathematics, Pi

2. Journal of the European Mathematical Society

3. American Journal of Mathematics

4. Crelle's Journal

5. Compositio Mathematica

6. Advances in Mathematics

7. Mathematische Annalen (3)

8. Forum of Mathematics, Sigma (2)

9. Algebra Number Theory (2)

10. Transactions of the American Mathematical Society

11. Revista Matemática Iberoamericana

12. Journal of the Institute of Mathematics of Jussieu

13. Journal of the London Mathematical Society

14. Mathematische Nachrichten

15. Annales de l'Institut Fourier

16. L'Enseignement Mathématique

17. Acta Mathematica Hungarica

18. Electronic Research Archive