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

LETTERS / EXPOSITORY:

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

Alex Karlovitz (Rutgers PhD, ongoing).
Brooke Logan (Rutgers PhD, ongoing). Edna Jones (Rutgers PhD, ongoing). Katie McKeon (Rutgers PhD, 2018). "LowLying Geodesics in an Arithmetic Hyperbolic ThreeManifold." IDACCR. 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, tenuretrack Asst Prof at Hong Kong University. "On the LocalGlobal Principle for Integral Apollonian3 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. 
Devora Chait (Queens College) Goldwater Scholarship winner Alisa Cui (Yale) Gabriel Eiseman (Rutgers) Zack Stier (Princeton) 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 179191. 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 MillerRabin Test" 
I coorganize the Number Theory Seminar at Rutgers. I am a coorganizer on the ICERM workshop Illustrating Number Theory and Algebra, Oct 21  25, 2019. I am a coorganizer on the AIM workshop Arithmetic reflection groups and crystallographic packings, Mar 16  20, 2020. I am a coorganizer 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 1415, 2015, Rutgers) Special Session on Number theory, spectral theory, and homogeneous dynamics. Jeff Lagarias, Will Abram, and I organized an AMSMAA 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 1619, 2014. Dubi Kelmer and I organized an AMS Eastern Sectional Meeting (Apr 67th, 2013, Boston College) Special Session on Counting and Equidistribution on Symmetric Spaces. 
EXPOSITORY: Informal lecture notes; use at own risk.
