Rutgers University - Hill Center

110 Frelinghuysen Rd.

Piscataway, NJ 08854, USA

Since January 2015 I'm a Hill Assistant Professor at Rutgers University. In Fall 2014 I was at the Centre de Recherches Mathematiques in Montreal, for the thematic semester in analytic number theory. Previously I spent a year at the Institute for Advanced Study, and before that I was a PhD student at Stanford working with Prof. Soundararajan.

I am interested in analytic number theory, probability theory, and harmonic analysis. The published version of the papers below is always the more definitive one.

1. Quantum Unique Ergodicity for half-integral weight forms (with Steve Lester)

2. Small gaps in the spectrum of the rectangular billiard (with Valentin Blomer, Jean Bourgain and Zeev Rudnick)

3. Selberg's central limit theorem for $\log \zeta(1/2 + it)$ (with Kannan Soundararajan)

4. Sign patterns of the Liouville and the Mobius function (with Kaisa Matomäki and Terence Tao)

5. A note on Helson's conjecture on moments of random multiplicative functions (with Adam Harper and Ashkan Nikeghbali) In C. Pomerance, M. Th. Rassias, * "Analytic Number Theory" in honor of Helmut Maier's 60th birthday*, Springer

6. An averaged form of Chowla's conjecture
(with Kaisa Matomäki and Terence Tao), * Algebra & Number theory*, to appear

7. Multiplicative functions in short intervals (with Kaisa Matomäki), * Ann. of Math*, to appear

+ Exposition: A short note on the Liouville function in short intervals (with Kaisa Matomäki)

8. Zeros of modular forms in thin sets and effective quantum unique ergodicity (with Stephen Lester and Kaisa Matomäki)

9. The mean square of the product of the Riemann zeta-function with Dirichlet polynomials (with Sandro Bettin and Vorrapan Chandee), * J. Reine Angew. Math.*, to appear

10. On the typical size and cancelations among the coefficients of some modular forms (with Florian Luca and Igor Shparlinsky)

11. Refinements of Gal's theorem and applications (with Mark Lewko)

12. Counting arithmetic formulas (with Edinah Gnang and Carlo Sanna), *European J. Combin.* **47** (2015), pp. 40-53

13. Sign changes of Hecke eigenvalues (with Kaisa Matomäki), * Geom. Funct. Anal.* **25** (2015), no. 6, pp. 1937-1955

14. Moments and distribution of central L-values of quadratic twists of elliptic curves (with Kannan Soundararajan), * Invent. Math. * **202** (2015), no. 3, pp. 1029-1068

15. Discrepancy bounds for the distribution of the Riemann zeta-function and applications (with Youness Lamzouri and Stephen Lester)

16. Gaps between zeros of $\zeta(s)$ and the distribution of zeros of $\zeta'(s)$, * Adv. Math. * **257** (2014), pp. 6-24

17. Simple zeros of primitive Dirichlet L-functions and the asymptotic large sieve (with Vorrapan Chandee, Yoonbok Lee and Sheng-Chi Liu), *Q. J. Math* **65** (2014), no. 1, pp. 63-87

18. The Riemann zeta-function on vertical arithmetic progressions (with Xiannan Li), *Int. Math. Res. Notices* **2** (2015), pp. 325-354

19. Limitations to mollifying $\zeta(s)$

20. Continuous lower bounds for moments of zeta and L-functions (with Kannan Soundararajan), *Mathematika* **59** (2013), no. 1, pp. 119-128

21. The 4.36-th moment of the Riemann zeta function, *Int. Math. Res. Notices* **18** (2012), pp. 4245-4259

22. Large deviations in Selberg's central limit theorem

23. A converse to Halasz's theorem

24. A structure theorem in probabilistic number theory

**B. Sc Thesis**

On large deviations of additive functions

Here is my public key (and two mirrors)