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

FORMALIATIONS:

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

Andre HernandezEspiet (Rutgers PhD, ongoing).
Edna Jones (Rutgers PhD, 2022). Griffiths Postdoc at Duke U. "The Kloosterman Circle Method and Weighted Representation Numbers of Positive Definite Quadratic Forms." Alex Karlovitz (Rutgers PhD, 2022), Lockheed Martin. "An Extension of Hejhal's Algorithm to Infinite Volume Fundamental Domains." Brooke Ogrodnik (Rutgers PhD, 2021), Metron. "On the LocalGlobal Conjecture for Commutator Traces." J. Number Theory, 2022. Katie McKeon (Rutgers PhD, 2018). IDACCR. "LowLying Geodesics in an Arithmetic Hyperbolic ThreeManifold." Arseniy Sheydvasser (Yale PhD, 2018). Postdoc at CUNY Grad Center, The Technion. "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; tenuretrack Asst Prof at Fairfield University. "Quantum unique ergodicity of degenerate Eisenstein series on GL(n)", Comm Math Phys, 2018. Max Ehrman (Yale PhD, 2017). "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 Investments. "Effective bisector estimate with application to Apollonian circle packings", IMRN 2013. 
Enver Aman (Rutgers). Strong Approximation for the Markoff Surface Emma Hasson (Bard College at Simon's Rock). Analytic Number Theory in Lean Max Lind (Princeton). Maass Forms and Computations Archana Mohandas (MIT). Inversive Geometry in Lean Colin Fan (Rutgers), Weill Scholarship and Tilla Weinstein Award, now math PhD student at Northwestern. Brittany Gelb (Muhlenberg), now math PhD student and Presidential Fellow at Rutgers. Brandon Gomes (Rutgers), now software engineer. Saket Shah (Princeton), now math PhD student a U Michigan. Kai Shaikh (UC Berkeley), now math Masters student at Oxford, then math PhD student at U Toronto. Devora Chait (Queens College) Goldwater Scholarship winner 2019, now CS PhD student at NYU Alisa Cui (Yale) Gabriel Eiseman (Rutgers), now CS PhD student at Georgia Tech Zack Stier (Princeton), now NSF grad research fellow, math PhD student at UC Berkeley Peter Cohen (Bowdoin): Goldwater Scholarship honorable mention 2016, 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 2016, now: math PhD student at Columbia Matt Kownacki (Rutgers), now: math PhD student at Boston College "On the Distribution of Witnesses in the MillerRabin Test" 
I coorganize the Number Theory Seminar and the Colloquium at Rutgers. I coorganize (with Kolya Bogachev and Sasha Kolpakov) the Vinberg Distinguished Lecture Series. I coorganized (with Alla Detinko, Dane Flannery, Alexander Hulpke, and Misha Kapovich) the Collaborate@ICERM Group on Practical Computation with Infinite Linear Groups, Jun 6  10, 2022. I coorganized (with Alice Mark and Daniel Allcock) of the AIM workshop Arithmetic reflection groups and crystallographic packings, Mar 7 11, 2022. I coorganized (with Alla Detinko, Misha Kapovich, Peter Sarnak, and Rich Schwartz) the virtual ICERM workshop Computational Aspects of Discrete Subgroups of Lie Groups, Jun 14  18, 2021. I coorganized (with Hee Oh and Alireza Salehi Golsefidy) an Oberwolfach Arbeitsgemeinschaft ("Study Group") on Thin groups and superapproximation, I coorganized (with Alice Mark and Misha Belolipetsky) the virtual AIM workshop Arithmetic reflection groups and crystallographic packings, Dec 1418, 2020. I coorganized (with Dubi Kelmer and Min Lee) the ICERM workshop Lattice Point Distribution and Homogeneous Dynamics, Jun 22  26, 2020. I coorganized (with Alice Mark and Daniel Allcock) the AIM workshop Arithmetic reflection groups and crystallographic packings, I coorganized (with Kate Stange, Ellen Eischen, and Joel Kamnitzer) the ICERM workshop Illustrating Number Theory and Algebra, Oct 21  25, 2019. 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. 