Research

Publications

12. (with A. Ghosh and D. Kelmer) Effective density for inhomogeneous quadratic forms II: fixed forms and generic shifts (pdf), Int. Math. Res. Not. IMRN 2023, no.22, 19507-19545.

11.(with D. Kelmer) Second moment of the light-cone Siegel transform and applications (pdf), Adv. Math. 432 (2023), Paper No. 109270, 70pp.

10. (with D. Kelmer) Fourier expansion of light-cone Eisenstein series (pdf), J. Lond. Math. Soc (2) 108 (2023), no. 6, 2175-2247.

9.(with D. Kleinbock and A. Strömbergsson) A measure estimate in geometry of numbers and improvements to Dirichlet's theorem (pdf), Proc. Lond. Math. Soc. (3) 125 (2022), no. 5, 778-824.

8. (with A. Ghosh and D. Kelmer) Effective density for inhomogeneous quadratic forms I: generic forms and fixed shifts (pdf), Int. Math. Res. Not. IMRN 2022, no. 6, 4682-4719.

7. (with C. Burrin and U. Shapira) Translates of rational points along expanding closed horocycles on the modular surface (pdf), Math. Ann. 382 (2022), no. 1-2, 655–717.

6. (with M. Alam and A. Ghosh) Quantitative Diophantine approximation with congruence conditions (pdf), J. Théor. Nombres Bordeaux 33 (2021) no. 1, pp. 261-271.

5. (with D. Kelmer) The second moment of the Siegel transform in the space of symplectic lattices (pdf),  Int. Math. Res. Not. IMRN 2021, no. 8, 5825-5859.

4. (with D. Kelmer) Values of random polynomials in shrinking targets (pdf), Trans. Amer. Math. Soc. 373 (2020), 8677-8695.

3. (with D. Kleinbock) A dynamical Borel-Cantelli lemma via improvements to Dirichlet's theorem (pdf), Mosc. J. Comb. Number Theory, 9 (2020), 101–122.

2. (with D. Kelmer) Shrinking targets problems for flows on homogeneous spaces (pdf), Trans. Amer. Math. Soc. 372 (2019), no.9, 6283-6314.

1. Logarithm laws for unipotent flows on hyperbolic manifolds (pdf), J. Mod. Dyn., 11 (2017) 447-476.

My papers are also available on the arXiv, but some of the versions there might be slightly outdated.

Other writings

2. A refinement of Khintchine's theorem via unipotent flows (pdf).

1. The second moment of the Siegel transform on the space of rank two unimodular lattices (pdf).