Publications
Preprints:
21. The Gauss circle problem for Penrose tilings w/ A. Haynes, (2025), [ArXiv], [pdf].
20. Sign changes along geodesics of modular forms w/ D. Kelmer, and A. Kontorovich, (2024), [ArXiv], [pdf].
19. Average variance bounds for integer points on the sphere, (2024), [ArXiv], [pdf].
18. Counting in lattice orbits , w/ A. Kontorovich, (2024), [ArXiv], [pdf].
Publications:
17. Diffusion of the random Lorentz process in a magnetic field, w/ B. Tóth, J. Math. Phys. 66(11), (Editor’s Pick) , (2025), [Link], [ArXiv], [pdf].
16. Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces, w/ T. Weich and L. Wolf, (Accepted: Duke Math. J.) (2024), [ArXiv], [pdf].
15. An abstract spectral approach to horospherical equidistribution Nonlinearity 38(10), 105014, (2025) [ArXiv], [pdf].
14. Hyperbolic lattice point counting in unbounded rank, w/ V. Blomer, J. Reine Angew. Math. 2024(812), 257-274) (2024), [Link], [ArXiv], [pdf].
13. Mean square bounds on Eisenstein series, w/ D. Kelmer, and A. Kontorovich, Int. J. of Number Theory 20 (08), 2083-2098 (2024) [ArXiv], [pdf].
12. These numbers look random but aren’t, mathematicians prove (2024) Scientific American [Link].
11. $m$-Point correlations of the fractional parts of $\alpha n^\theta$ w/ N. Technau, (2021) (Accepted: Amer. J. of Math.) [ArXiv], [pdf].
10. Full poissonian local statistics of slowly growing sequences w/ N. Technau Compos. Math. 161(1), 148-180, (2025), [Link], [ArXiv], [pdf].
9. Effective counting in sphere packings w/ A. Kontorovich, (2022) J. of the Assoc. Math. Res. 2, 15-52 , (2024) [Link], [ArXiv], [pdf].
8. Sarnak’s spectral gap question w/ D. Kelmer, and A. Kontorovich, J. Anal. Math. (Special edition dedicated to P. Sarnak) 151, 171-179 , (2023) [Link], [ArXiv], [pdf].
7. Pair correlation of the fractional parts of $\alpha n^\theta$ w/ A. Sourmelidis, and N. Technau J. of the Eur. Math. Soc. (JEMS) 27(10), 4069-4082 (2024), [Link], [ArXiv], [pdf].
6. Long-range correlations of sequences modulo 1 J. of Number Theory, 234, 333-348 , (2022) [Link], [ArXiv], [pdf].
5. Farey sequences for thin groups. Int. Math. Res. Not. (IMRN), 15, 11642-11689 , (2022) [Link], [ArXiv], [pdf].
4. Invariance principle for the random wind-tree process w/ B. Tóth, Ann. Henri Poincaré, 22(10), 3357-3389 (2021) [Link],[ArXiv], [pdf].
3. Invariance principle for the random Lorentz gas—beyond the Boltzmann-Grad limit w/ B. Tóth, Comm. in Math. Phys., 379 , 589–632 (2020) [Link], [ArXiv], [pdf].
2. Directions in orbits of geometrically finite hyperbolic subgroups. Math. Proc. of the Cambridge Phil. Soc. 171 (2), 277-316 (2020) [Link], [ArXiv], [pdf].
1. Microscopic approach to nonlinear reaction-diffusion: The case of morphogen gradient formation. w/ J. P. Boon, and J. F. Lutsko, Phys. Rev. E, 85 , 021126 (2012) [Link], [ArXiv], [pdf].
PhD Thesis:
Statistical properties of dynamical systems: from statistical mechanics to hyperbolic geometry University of Bristol , (2020), [Link], [pdf].
Conference Proceedings:
- Invariance principle for random Lorentz gas in the Boltzmann-Grad Limit, Oberwolfach Report 10/2019 p. 33-35 (2019).
- Invariance principle for random Lorentz gas — Beyond the Boltzmann-Grad Limit, Oberwolfach Report 42/2019 p. 12-15 (2019)