
Research
My current research is on the use of techniques from classical analytic number theory in the study of higherrank automorphic forms.
I hope to apply these methods to classical equidistribution problems and problems related to polynomials and primes.
My interests and methods are in analytic number theory, harmonic analysis on symmetric spaces, complex analysis, the spectral theory of autormorphic forms, trace formulas, exponential sums, and Lfunctions.
Research statement.
NSF Grant DMS1601919
Publications:
 Subconvexity for Lfunctions of nonspherical cusp forms on GL(3), with V. Blomer, on the arXiv.
 The arithmetic Kuznetsov formula on GL(3), I: The Whittaker case, on the arXiv.
 Kuznetsov, Petersson and Weyl on GL(3), II: The generalized principal series forms, on the arXiv.
 Kuznetsov, Petersson and Weyl on GL(3), I: The principal series forms, on the arXiv.
 Weights, raising and lowering operators, and Ktypes for automorphic forms on SL(3,ℝ), with S. D. Miller, on the arXiv.
 Higher weight on GL(3), II: The cusp forms, on the arXiv.
 Plancherel distribution of Satake parameters of Maass cusp forms on GL_{3}, with F. Zhou, in International Mathematics Research Notices (arXiv).
 On the fourth moment of Hecke Maass forms and the Random Wave Conjecture, with R. Khan, in Compositio Mathematica (arXiv).
 Higher weight on GL(3), I: The Eisenstein series, in Forum Mathematicum (arXiv).
 Global decomposition of GL(3) Kloosterman sums and the spectral large sieve, with V. Blomer, in Crelle's Journal (arXiv).
 On the subconvexity problem for Lfunctions on GL(3), with V. Blomer, on the arXiv.
 The spectral Kuznetsov formula on SL(3), in the Transactions of the American Mathematical Society (arXiv).
 A mean value of a triple product of Lfunctions, with R. Khan, in Mathematische Zeitschrift (arXiv).
 Applications of the Kuznetsov formula on GL(3), II: the level aspect, with V. Blomer and P. Maga, in the Mathematische Annalen (arXiv).
 L^{4} norms of Hecke newforms of large level, with R. Khan, in the Mathematische Annalen (arXiv).
 A SatoTate law for GL(3), with V. Blomer and N. Raulf, in Commentarii Mathematici Helvetici.
 On Sums of SL(3,ℤ) Kloosterman Sums. In the Ramanujan Journal (arXiv).
 UCLA Doctoral Thesis  On Sums of SL(3,ℤ) Kloosterman Sums.
 A note on the WaringGoldbach problem. In the Journal of Number Theory.
 A translation of Hadamard's Sur la distribution des zéros de la function ζ(s) et ses conséquences arithmétiques.

