In preparation

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

  1. Algebraic models for Teichmuller curves in Hilbert modular surfaces (with R. Mukamel), 43 pages, arxiv.

  2. Orbit parametrizations for K3 surfaces (with M. Bhargava and W. Ho), 62 pages, arxiv.

  3. Examples of abelian surfaces with everywhere good reduction (with L. Dembele), 27 pages, arxiv

  4. Simplices and optimal codes in projective spaces (with H. Cohn and G. Minton), 50 pages, arxiv

  5. K3 surfaces and equations for Hilbert modular surfaces (with Noam Elkies), 83 pages, arxiv
    to appear in Algebra Number Theory.

  6. Metacommutation of Hurwitz primes (with Henry Cohn), 11 pages, arxiv
    to appear in Proc. Amer. Math. Soc.

  7. 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.

  8. Elliptic fibrations on a generic Jacobian Kummer surface, 45 pages arxiv
    to appear in J. Algebraic Geom.

  9. Multiplicative excellent families of elliptic surfaces of type E7 or E8 (with Tetsuji Shioda) arxiv
    Algebra Number Theory 7 (2013), no. 7, 1613–1641.

  10. 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).

  11. Rigidity of Spherical Codes (with Henry Cohn, Salvatore Torquato and Yang Jiao) arxiv
    Geom. Topol. 15 (2011), no. 4, 2235–2273.

  12. 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.

  13. Ground states and formal duality relations in the Gaussian core model (with Henry Cohn and Achill Schürmann) arxiv
    Physical Review E 80 (2009), 061116.

  14. Algorithmic design of self-assembling structures (with Henry Cohn) arxiv
    Proc. Nat. Acad. Sci. 106 (2009) no. 24, 9570–9575.

  15. Optimality and uniqueness of the Leech lattice among lattices (with Henry Cohn) arxiv
    Ann. of Math. 170 (2009), No. 3, 1003–1050.

  16. Counterintuitive ground states in soft-core models (with Henry Cohn) arxiv
    Physical Review E 78 (2008), 061113.

  17. K3 surfaces associated with curves of genus two journal arxiv
    Internat. Math. Res. Notices 2008, no. 6, Art. ID rnm165, 26 pp.

  18. Uniqueness of the (22,891,1/4) spherical code (with Henry Cohn) arxiv
    New York J. Math. 13 (2007), 147–157.

  19. Universally optimal distribution of points on spheres (with Henry Cohn) arxiv
    J. Amer. Math. Soc. 20 (2007), no. 1, 99–148.

  20. The D_4 root system is not universally optimal (with Henry Cohn, John Conway and Noam Elkies) arxiv
    Experiment. Math. 16 (2007), 313–320.

  21. The densest lattice in twenty-four dimensions (with Henry Cohn) arxiv
    Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 58–67.

  22. A Proof of Pieri's formula using generalized Schensted insertion algorithm for RC-graphs (with Mikhail Kogan) pdf arxiv
    Proc. Amer. Math. Soc. 130 (2002), 2525–2534.