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INTERESTS: Analytic Number Theory; Harmonic Analysis; Automorphic Forms, Representations, and L-functions; Hyperbolic Geometry and Spectral Theory; Group Actions and Ergodic Theory; Sieve and Circle Methods


PAPERS: (which may vary slightly/severely from the published version)

PhD Students and Theses

Alex Karlovitz (Rutgers PhD, ongoing).

Brooke Logan (Rutgers PhD, ongoing).

Edna Jones (Rutgers PhD, ongoing).

Katie McKeon (Rutgers PhD, 2018). "Low-Lying Geodesics in an Arithmetic Hyperbolic Three-Manifold." IDA-CCR.

Arseniy Sheydvasser (Yale PhD, 2018). Postdoc at CUNY Grad Center. "A Corrigendum to Unreasonable Slightness", Math Monthly 2016;
"Orders of Quaternion Algebras with Involution";
"Quaternion Orders and Superpackings", JNT 2019.

Liyang Zhang (Yale PhD, 2017). Postdoc at Rutgers/Boston College "Quantum unique ergodicity of degenerate Eisenstein series on GL(n)", Comm Math Phys, 2018.

Max Ehrman (Yale PhD, 2017). Washington Nationals (MLB) "Almost Primes in Thin Orbits of Pythagorean Triangles", IMRN 2017.

Shinnyih Huang (Yale PhD, 2015), Deutsche Bank. "An Improvement On Zaremba's Conjecture", GAFA 2015.

Xin Zhang (Stony Brook PhD 2014), postdoc at Tel Aviv/UIUC/IHES, tenure-track Asst Prof at Hong Kong University.
"On the Local-Global Principle for Integral Apollonian-3 Circle Packings", Crelle 2015.

Ilya Vinogradov (Princeton PhD 2012), postdoc at Bristol/Princeton. Now: Two Sigma.
"Effective bisector estimate with application to Apollonian circle packings", IMRN 2013.

REU Projects

  • 2018 Rutgers REU: Taxonomy of Crystallographic Sphere Packings Paper is available here.

  • Devora Chait (Queens College) Goldwater Scholarship winner

    Alisa Cui (Yale)

    Gabriel Eiseman (Rutgers)

    Zack Stier (Princeton)

  • 2015 Rutgers REU:

  • Peter Cohen (Bowdoin): Goldwater Scholarship honorable mention, now: Operations Research PhD student at MIT.
    "An Analytic Heuristic for Multiplicity Computation for Zaremba's Conjecture", Journal of Number Theory Volume 184, March 2018, Pages 179--191.

    Jenny Crawford (Rowan)

    Lolly Kenigsberg (Stony Brook). Goldwater Scholarship winner, now: math PhD student at Columbia.

    Matt Kownacki (Rutgers): math PhD student at Boston College
    "On the Distribution of Witnesses in the Miller-Rabin Test"


    I co-organize the Number Theory Seminar at Rutgers.

    I am a co-organizer on the ICERM workshop Illustrating Number Theory and Algebra, Oct 21 - 25, 2019.

    I am a co-organizer on the AIM workshop Arithmetic reflection groups and crystallographic packings, Mar 16 - 20, 2020.

    I am a co-organizer on the ICERM workshop Lattice Point Distribution and Homogeneous Dynamics, Jun 22 - 26, 2020.

    As part of our NSF FRG, Darren Long, Alex Lubotzky, Alan Reid, and I organized a research conference at Rice, on Thin groups in Number Theory, Geometry and Topology, May 14 - 18, 2018. It is supported in part by the NSF, BSF, and Rice.

    As part of our NSF FRG, Darren Long, Alex Lubotzky, Alan Reid, and I organized an educational workshop at IAS (Princeton), on Thin Groups and Super Approximation in Geometry and Arithmetic, March 28 - April 1st, 2016. It is supported in part by the NSF, BSF, IAS, and Rutgers.

    Dubi Kelmer and I organized an AMS Eastern Sectional Meeting (Nov 14-15, 2015, Rutgers) Special Session on Number theory, spectral theory, and homogeneous dynamics.

    Jeff Lagarias, Will Abram, and I organized an AMS-MAA Invited Paper Session at the MAA Centennial (Aug 6, 2015, DC) on the Arithmetic of Spheres.

    Uri Shapira, Tammy Ziegler, and I organized an Special Session on Dynamics and Number Theory for the Joint International Meeting of the AMS and IMU (Israel Math Union), June 16-19, 2014.

    Dubi Kelmer and I organized an AMS Eastern Sectional Meeting (Apr 6-7th, 2013, Boston College) Special Session on Counting and Equidistribution on Symmetric Spaces.

    EXPOSITORY: Informal lecture notes; use at own risk.