My research interests are centered around effective methods in arithmetic geometry, arithmetic statistics, and number theory.
Publications
-
Hypergeometric L-functions 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
)
to appear in Arithmetic geometry, number theory, and computation, Simons Symposia.
arXiv:2003.11037 -
Computing classical modular forms
(with
Alex Best,
Jonathan Bober,
Andrew R. Booker,
John Cremona,
Maarten Derickx,
David Lowry-Duda,
Min Lee,
David Roe,
Andrew V. Sutherland,
and
John Voight
)
to appear in Arithmetic geometry, number theory, and computation, Simons Symposia.
arXiv:2002.04717 -
Restrictions on Weil polynomials of Jacobians of hyperelliptic curves
(with
Ravi Donepudi,
Ravi Fernando,
Valentijn Karemaker,
Caleb Springer,
and
Mckenzie West)
to appear in Arithmetic geometry, number theory, and computation, Simons Symposia.
arXiv:2002.02067 -
Arithmetic invariants from Sato-Tate 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)
to appear in Arithmetic geometry, number theory, and computation, Simons Symposia.
pdf -
Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms
(with
Davide Lombardo and
John Voight
)
submitted
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), 1303-1339
DOI, arXiv:1705.09248, SageMath/Magma implementation -
On the arithmetic of a family of degree-two K3 surfaces
(with
Florian Bouyer,
Dino Festi,
Chris Nicholls, and
Mckenzie West
)
Mathematical Proceedings 166 (2018), no. 3, 523-542.
DOI, arXiv:1703.02127 -
On the distribution of the Picard ranks of the reductions of a
K3 surface
(with
Andreas-Stephan 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,
David Lowry-Duda
)
Mathematical Proceedings 162 (2018), no. 2, 225–248
DOI, arXiv:1610.00164. -
Effective computations of Hasse-Weil zeta functions
Ph.D. thesis pdf -
Variation of Néron-Severi ranks of reductions of K3 surfaces (with Yuri Tschinkel)
Experimental Mathematics 23 (2014), 475-481.
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), 141-148.
DOI, arXiv:1311.3469. -
A search for Wilson primes (with Robert Gerbicz
and David Harvey)
Mathematics of Computation 82 (2014), 3071-3091.
DOI, arXiv:1209.3436. -
Faster deterministic integer factorization (with David Harvey)
Mathematics of Computation 83 (2014), 339-345.
DOI, arXiv:1201.2116.
Software
- L-functions and Modular Forms Database (LMFDB) (Core developer and associate Editor)
- A new directory of seminars worldwide (Co-creator 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
-
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 Néron-Severi 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)
Maine-Québec 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, Québec-Maine 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 p-adic 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 Hasse-Weil zeta functions
(slides)
Explicit Methods for Modularity of K3 Surfaces and Other Higher Weight Motives, ICERM, Brown University, Oct 2015 -
Effective computations of Hasse-Weil zeta functions
Courant Institute of Mathematical Sciences, NYU, May 2015 -
Variation of Néron-Severi ranks of reductions of algebraic surfaces
Department of Mathematics, Rice University, Feb 2015 -
Variation of Néron-Severi ranks of reductions of algebraic surfaces
School of Mathematics and Statistics, UNSW, Oct 2014 -
Variation of Néron-Severi 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