My research interests are centered around effective methods in arithmetic geometry, arithmetic statistics, and number theory.
Publications

Counting points on smooth plane quartics
(with
David Harvey
and
Andrew V. Sutherland
)
to appear Research in Number Theory, Fifteenth Algorithmic Number Theory Symposium (ANTS XV)
arXiv:2208.09890 
Abelian varieties of prescribed order over finite fields
(with
Raymond van Bommel,
Wanlin Li,
Bjorn Poonen,
and
Alexander Smith)
submitted
arXiv:2106.13651 
Hypergeometric Lfunctions in average polynomial time
(with
Kiran Kedlaya
and
David Roe)
Fourteenth Algorithmic Number Theory Symposium (ANTS XIV), Open Book Series 4 (2020), 143–159
DOI, arXiv:2005.13640 
Effective obstruction to lifting Tate classes from positive characteristic
(with
Emre Sertöz)
Arithmetic geometry, number theory, and computation, Simons Symposia
DOI, arXiv:2003.11037 
Computing classical modular forms
(with
Alex Best,
Jonathan Bober,
Andrew R. Booker,
John Cremona,
Maarten Derickx,
David LowryDuda,
Min Lee,
David Roe,
Andrew V. Sutherland,
and
John Voight)
Arithmetic geometry, number theory, and computation, Simons Symposia
DOI, Errata, arXiv:2002.04717 
Restrictions on Weil polynomials of Jacobians of hyperelliptic curves
(with
Ravi Donepudi,
Ravi Fernando,
Valentijn Karemaker,
Caleb Springer,
and
Mckenzie West)
Arithmetic geometry, number theory, and computation, Simons Symposia
DOI, arXiv:2002.02067 
Arithmetic invariants from SatoTate moments
(with Francesc Fité and
Andrew V. Sutherland)
Comptes Rendus Mathematique
DOI, arXiv:1910.00518 
Zen and the Art of Database Maintenance
(with David Roe)
Arithmetic geometry, number theory, and computation, Simons Symposia
DOI, pdf 
Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms
(with
Davide Lombardo and
John Voight)
Research in Number Theory 7, 46 (2021)
DOI, arXiv:1906.02803 
Computing Zeta Functions of Cyclic Covers in Large Characteristic
(with
Vishal Arul,
Alex Best,
Richard Magner,
and
Nicholas Triantafillou)
Thirteenth Algorithmic Number Theory Symposium (ANTS XIII), Open Book Series 2 (2019), 37–53.
DOI, arXiv:1806.02262, SageMath implementation 
Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in $p$adic cohomology
(with
David Harvey
and
Kiran Kedlaya
)
Thirteenth Algorithmic Number Theory Symposium (ANTS XIII), Open Book Series 2 (2019), 221–238.
DOI, arXiv:1806.00368 
Rigorous computation of the endomorphism ring of a Jacobian
(with
Nicolas Mascot,
Jeroen Sijsling, and
John Voight)
Mathematics of Computation 88 (2019), 13031339
DOI, Errata, arXiv:1705.09248, SageMath/Magma implementation 
On the arithmetic of a family of degreetwo K3 surfaces
(with
Florian Bouyer,
Dino Festi,
Chris Nicholls, and
Mckenzie West)
Mathematical Proceedings 166 (2018), no. 3, 523542.
DOI, arXiv:1703.02127 
On the distribution of the Picard ranks of the reductions of a
K3 surface
(with
AndreasStephan Elsenhans
and
Jörg Jahnel
)
Research in Number Theory 6, 27 (2020)
DOI, arXiv:1610.07823. 
Traces, High powers and one level density for families of curves over finite fields
(with
Alina Bucur,
Chantal David,
João Guerreiro,
and
David LowryDuda)
Mathematical Proceedings 162 (2018), no. 2, 225–248
DOI, arXiv:1610.00164. 
Effective computations of HasseWeil zeta functions
Ph.D. thesis pdf 
Variation of NéronSeveri ranks of reductions of K3 surfaces (with Yuri Tschinkel)
Experimental Mathematics 23 (2014), 475481.
DOI, arXiv:1405.2265, raw data. 
Asymptotic expansions, $L$values and a new Quantum Modular Form (with Korneel Debaene and João Guerreiro)
The Ramanujan Journal 35 (2014), 141148.
DOI, arXiv:1311.3469. 
A search for Wilson primes (with Robert Gerbicz
and David Harvey)
Mathematics of Computation 82 (2014), 30713091.
DOI, arXiv:1209.3436. 
Faster deterministic integer factorization (with David Harvey)
Mathematics of Computation 83 (2014), 339345.
DOI, arXiv:1201.2116.
Software
 Lfunctions and Modular Forms Database (LMFDB) (Core developer and associate Editor)
 A new directory of seminars worldwide (Cocreator and administrator)
 Controlled reduction: Computation of zeta functions of projective hypersurfaces (C++) and its SageMath wrapper
 Endomorphisms: Rigorous computation of the endomorphism ring of a Jacobian (SageMath/Magma)
 Bean Theory: Number Theory seminars in the Boston area
Talks

Computing isogeny classes of principally polarized abelian surfaces over the rationals
(slides)
Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting, January 2023 
Computing isogeny classes of principally polarized abelian surfaces over the rationals
(slides)
Joint Mathematics Meetings, January 2023 
Computing isogeny classes of principally polarized abelian surfaces over the rationals
Palmetto Number Theory Series (PANTS), December 2023 
Computing isogeny classes of principally polarized abelian surfaces over the rationals
Department of Mathematics, University of Washington, December 2023 
Counting points on smooth plane quartics
(slides)
Algorithmic Number Theory Symposium XV, University of Bristol, August 2022 
Geometric invariants from counting points
(slides)
Connecticut Summer School in Number Theory, June 2022 
The Lfunctions and modular forms database
(slides)
William & Mary Mathematics Colloquium, December 2021 
Effective obstruction to lifting Tate classes from positive characteristic
(slides)
Columbia CUNY NYU number theory seminar, April 2021 
From counting points to rational curves on K3 surfaces
(slides, video)
Vantage seminar, January 2021 
Effective obstruction to lifting Tate classes from positive characteristic
(slides)
Saarland University, December 2020. 
Bounding Picard numbers
(slides)
Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation monthly meeting, October 2020. 
From Frobenius polynomials to geometry
(slides)
Around Frobenius distributions and related topics, May 2020. 
Frobenius Distributions
(slides)
Department of Mathematics, University of California San Diego, February 2020. 
Computing central endomorphisms of an abelian variety via reductions modulo p
(slides)
JMM, AMS Special Session on Arithmetic Galois actions, January 2020 
Variation of Néron–Severi ranks of reductions of K3 surfaces
(slides)
JMM, Rational points on Algebraic varieties: Theory and Computation, January 2020 
Rigorous computation of the endomorphism ring of a Jacobian
(slides)
School of Mathematics and Statistics, UNSW, Nov 2019 
Variation of NéronSeveri ranks of reductions of K3 surfaces
(slides)
Department of Mathematics, The University of Tennessee, Knoxville, May 2019. 
Frobenius Distributions
(slides)
Department of Mathematics, University of Washington, April 2019. 
Upper bounds for the endomorphism algebra of an abelian variety
(slides)
JMM, AMS Special Session on Number Theory, Arithmetic Geometry, and Computation, January 2019 
Randomness in number theory
(slides)
Department of Mathematics, Colorado Sate University, November 2018 
Frobenius Distributions
(slides)
Colóquio de Geometria e Aritmética Rio de Janeiro, October 2018. 
Frobenius Distributions
(slides)
Department of Mathematics, Massachusetts Institute of Technology, September 2018. 
Computing zeta functions of nondegenerate hypersurfaces in toric varieties
(slides)
Algorithmic Number Theory Symposium XIII, University of Wisconsin, Madison, July 2018. 
Distributions in arithmetic geometry
(slides)
Communicating Mathematics Effectively, University of Washington, June 2018. 
Computing zeta functions of nondegenerate hypersurfaces in toric varieties
(slides)
Birational Geometry and Arithmetic, ICERM, Brown University, May 2018. 
Computing zeta functions of nondegenerate toric hypersurfaces
(slides)
Department of Mathematics & Statistics, Boston University, December 2017. 
Computing zeta functions of nondegenerate toric hypersurfaces
(slides)
MaineQuébec Number Theory Conference, October 2017 
Computing zeta functions of nondegenerate toric hypersurfaces
(slides, video)
Banff International Research Station, $p$adic Cohomology and Arithmetic Applications, October 2017 
Toric point counting and applications (slides, video)
Banff International Research Station, New Trends in Arithmetic and Geometry of Algebraic Surfaces, March 2017 
Toric point counting and applications
Department of Mathematics & Statistics, University of Vermont, February 2017 
Counting points on curves (slides)
Université Laval, Québec, QuébecMaine Number Theory Conference, October 2016 
Counting points on curves (slides)
University of New South Wales, School of Mathematics and Statistics, July 2016 
Zeta functions of quartic K3 surfaces over $\mathbf{F}_3$
(slides)
Sage Days 71: Explicit padic methods in number theory, Oxford University, March 2016 
Equidistributions in arithmetic geometry
(slides)
Department of Mathematics, Dartmouth College, Jan 2016 
Equidistributions in arithmetic geometry
(slides)
Departamento de Matemática, Instituto Superior Técnico, Dec 2015 
Effective computations of HasseWeil zeta functions
(slides)
Explicit Methods for Modularity of K3 Surfaces and Other Higher Weight Motives, ICERM, Brown University, Oct 2015 
Effective computations of HasseWeil zeta functions
Courant Institute of Mathematical Sciences, NYU, May 2015 
Variation of NéronSeveri ranks of reductions of algebraic surfaces
Department of Mathematics, Rice University, Feb 2015 
Variation of NéronSeveri ranks of reductions of algebraic surfaces
School of Mathematics and Statistics, UNSW, Oct 2014 
Variation of NéronSeveri ranks of reductions of algebraic surfaces
Courant Institute of Mathematical Sciences, NYU, Oct 2014 
The point counting problem
Courant Institute of Mathematical Sciences, NYU, Dec 2012 
Faster deterministic integer factorization
Courant Institute of Mathematical Sciences, NYU, Jan 2012 
Étale Cohomology
Courant Institute of Mathematical Sciences, NYU, Mar 2011 
Étale Cohomology
Departamento de Matemática, Instituto Superior Técnico, July 2010