Elliptic K3 surfaces associated with the product of two elliptic curves: Mordell-Weil lattices and their fields of definition (with M. Kuwata).
Published/Submitted papers
Algebraic models for Teichmuller curves in Hilbert modular surfaces (with R. Mukamel), 43 pages, arxiv.
Orbit parametrizations for K3 surfaces (with M. Bhargava and W. Ho), 62 pages, arxiv.
Examples of abelian surfaces with everywhere good reduction (with L. Dembele), 27 pages, arxiv submitted.
Simplices and optimal codes in projective spaces (with H. Cohn and G. Minton), 50 pages, arxiv submitted.
K3 surfaces and equations for Hilbert modular surfaces (with Noam Elkies), 83 pages, arxiv
to appear in Algebra Number Theory.
Metacommutation of Hurwitz primes (with Henry Cohn), 11 pages, arxiv to appear in Proc. Amer. Math. Soc.
Formal duality and generalizations of the Poisson summation formula, (with H. Cohn, C. Reiher and A. Schurmann), 17 pages, arxiv to appear in Contemp. Math.
Elliptic fibrations on a generic Jacobian Kummer surface, 45 pages arxiv
to appear in J. Algebraic Geom.
Multiplicative excellent families of elliptic surfaces of type E7 or E8 (with Tetsuji Shioda) arxiv Algebra Number Theory 7 (2013), no. 7, 1613–1641.
Using Elimination Theory to construct Rigid Matrices (with Satya Lokam, Vijay Patankar and Jayalal Sarma), 25 pages, arxiv Comput. Complexity (2013) 10.1007/s00037-013-0061-0 (online first link).
Rigidity of Spherical Codes (with Henry Cohn, Salvatore Torquato and Yang Jiao) arxiv Geom. Topol. 15 (2011), no. 4, 2235–2273.
Point configurations that are asymmetric yet balanced (with Henry Cohn,
Noam Elkies and Achill Schürmann) arxiv Proc. Amer. Math. Soc. 138 (2010), no. 8, 2863–2872.
Ground states and formal duality relations in the Gaussian core model (with Henry Cohn and Achill Schürmann) arxiv Physical Review E 80 (2009), 061116.
Algorithmic design of self-assembling structures (with Henry Cohn) arxiv Proc. Nat. Acad. Sci. 106 (2009) no. 24, 9570–9575.
Optimality and uniqueness of the Leech lattice among lattices (with Henry Cohn) arxiv Ann. of Math. 170 (2009), No. 3, 1003–1050.
Counterintuitive ground states in soft-core models (with Henry Cohn)
arxiv Physical Review E 78 (2008), 061113.
K3 surfaces associated with curves of genus two journalarxiv Internat. Math. Res. Notices 2008, no. 6, Art. ID rnm165, 26 pp.
Uniqueness of the (22,891,1/4) spherical code (with Henry Cohn)
arxiv New York J. Math. 13 (2007), 147–157.
Universally optimal distribution of points on spheres (with Henry Cohn)
arxiv J. Amer. Math. Soc. 20 (2007), no. 1, 99–148.
The D_4 root system is not universally optimal (with Henry Cohn, John
Conway and Noam Elkies) arxiv Experiment. Math. 16 (2007), 313–320.
The densest lattice in twenty-four dimensions (with Henry Cohn) arxiv Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 58–67.
A Proof of Pieri's formula using generalized Schensted insertion
algorithm for RC-graphs (with Mikhail Kogan) pdfarxiv Proc. Amer. Math. Soc. 130 (2002), 2525–2534.