Mathematics & Statistics

• Fall 2022, MAT 259 is on Brightspace.
• Fall 2022, MAT 426 is on Brightspace.
• Fall 2022, MAT 259 was on Brightspace.
• Fall 2022, MAT 425 was on Brightspace.
• Spring 2022, MAT 228 was on Brightspace.
• Spring 2022, MAT 500 was on Brightspace.
• Fall 2021, MAT 126 was on Brightspace.
• Spring 2021, MAT 465 was on Brightspace.
• Spring 2021, MAT 524 was on Brightspace.
• Fall 2020, MAT 228 was on Brightspace.
• Fall 2020, MAT 523 was on Brightspace.
• Spring 2020, MAT 228 was on Blackboard.
• Spring 2020, MAT 452 was on Blackboard.
• Fall 2019, MAT 463 has its own webpage.
• Fall 2019, MAT 228 was on Blackboard.
• Spring 2019, MAT 465 had its own webpage.
• Fall 2018, MAT 126 was on Blackboard.

My current research is on the use of techniques from classical analytic number theory in the study of higher-rank 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 L-functions.
Research statement. 

NSF Grant DMS-1601919

Publications:

• Bessel functions on GL(n), I, on the arXiv, submitted.
• On sums of hyper-Kloosterman sums, on the arXiv, submitted.
• The arithmetic Kuznetsov formula on GL(3), II: The general case, in Algebra & Number Theory (arXiv).
• Subconvexity for L-functions of non-spherical cusp forms on GL(3), with V. Blomer, in Acta Arithmetica (arXiv).
• The arithmetic Kuznetsov formula on GL(3), I: The Whittaker case, in Revista Matemática Iberoamericana (arXiv).
• Kuznetsov, Petersson and Weyl on GL(3), II: The generalized principal series forms, in the Mathematische Annalen (arXiv).
• Kuznetsov, Petersson and Weyl on GL(3), I: The principal series forms, in the American Journal of Mathematics (arXiv).
• Weights, raising and lowering operators, and K-types for automorphic forms on SL(3,ℝ), (book chapter) with S. D. Miller (arXiv).
• Higher weight on GL(3), II: The cusp forms, in Algebra & Number Theory (arXiv).
• Plancherel distribution of Satake parameters of Maass cusp forms on GL₃, 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 L-functions on GL(3), with V. Blomer, in the Annales scientifiques de l’École normale supérieure (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 L-functions, 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).
• L⁴ norms of Hecke newforms of large level, with R. Khan, in the Mathematische Annalen (arXiv).
• A Sato-Tate 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 Waring-Goldbach 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.