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Research

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


LETTERS:


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


Papers by PhD Students

Katie McKeon (Rutgers PhD, 2018). 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" .

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

Max Ehrman (Yale PhD, 2017). Washington Nationals "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. "On the Local-Global Principle for Integral Apollonian-3 Circle Packings", Crelle 2015.

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


REU Projects

  • 2018 Rutgers REU: Taxonomy of Crystallographic Sphere Packings
  • Devora Chait (Queens College)
    Alisa Cui (Yale)
    Gabriel Eiseman (Rutgers)
    Zack Stier (Princeton)

  • 2015 Rutgers REU:
  • Peter Cohen (Bowdoin): "An Analytic Heuristic for Multiplicity Computation for Zaremba's Conjecture", published in Journal of Number Theory, 2017.
    Jenny Crawford (Rowan)
    Lolly Kenigsberg (Stony Brook)
    Matt Kownacki (Rutgers): "On the Distribution of Witnesses in the Miller-Rabin Test"

    Organization

    I co-organize the following seminars at Rutgers:

    Number Theory Seminar


    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.