All my papers are available from the arxiv at http://arxiv.org/a/kumar_a_4.html

Preprints/Submitted papers

  1. ​Universal optimality of the E8 and Leech lattices and interpolation formulas 
    (with H. Cohn, S. D. Miller, D. Radchenko and M. Viazovska), arxiv.

Published Papers

  1. Inose's construction and elliptic K3 surfaces with Mordell-Weil rank 15 revisited (with M. Kuwata), arxiv,
    ​Higher Genus Curves in Mathematical Physics and Arithmetic Geometry, 131–141, Contemporary Mathematics 703.
  2. Elliptic K3 surfaces associated with the product of two elliptic curves:
      Mordell-Weil lattices and their fields of definition (with M. Kuwata), arxiv,
    Nagoya Mathematical Journal 228 (2017), 124-185.
  3. The sphere packing problem in dimension 24 (with H. Cohn, S. D. Miller, D. Radchenko and M. Viazovska), arxiv,
    ​​Annals of Mathematics 185 (2017), 1017–1033.
  4. Algebraic models and arithmetic geometry of Teichmuller curves in genus two (with R. Mukamel), arxiv,
    International Mathematics Research Notices 2016; doi:10.1093/imrn/rnw193.
  5. Real multiplication through explicit correspondences (with R. Mukamel), arxiv,
    LMS Journal of Computation and Mathematics 19 (Special issue A) (2016), 29-42. 
  6. Optimal simplices and codes in projective spaces (with H. Cohn and G. Minton), arxiv,
    Geometry and Topology 20 (2016), no. 3, 1289-1357.
  7. Orbit parametrizations for K3 surfaces (with M. Bhargava and W. Ho), arxiv,
    Forum of Mathematics Sigma Vol. 4, e18, 86 pages, doi:10.1017/fms.2016.12.
  8. Examples of abelian surfaces with everywhere good reduction (with L. Dembele), arxiv,
    Mathematische Annalen 364 (2016), no. 3, 1365-1392. 
  9. Hilbert modular surfaces for square discriminants and elliptic subfields of genus 2 function fields, arxiv,
    Research in the Mathematical Sciences 2:24 (2015).
  10. K3 surfaces and equations for Hilbert modular surfaces (with Noam Elkies), arxiv 
    Algebra and Number Theory 8 (2014), no. 10, 2297-2411. 
  11. Metacommutation of Hurwitz primes (with Henry Cohn), 11 pages, arxiv 
    Proceedings of the American Mathematical Society 143 (2015), no. 4, 1459-1469.
  12. Formal duality and generalizations of the Poisson summation formula, (with H. Cohn, C. Reiher and A. Schurmann), arxiv 
    Discrete Geometry and Algebraic Combinatorics, 123–140, Contemporary Mathematics 422.
  13. Elliptic fibrations on a generic Jacobian Kummer surface arxiv 
    Journal of Algebraic Geometry 23 (2014), 599-667.
  14. Multiplicative excellent families of elliptic surfaces of type E7 or E8 (with Tetsuji Shioda) arxiv 
    Algebra and Number Theory 7 (2013), no. 7, 1613–1641. 
  15. Using Elimination Theory to construct Rigid Matrices (with Satya Lokam, Vijay Patankar and Jayalal Sarma) arxiv 
    Computational Complexity (2013) 10.1007/s00037-013-0061-0 (online first link). 
  16. Rigidity of Spherical Codes (with Henry Cohn, Salvatore Torquato and Yang Jiao) arxiv 
    Geometry and Topology 15 (2011), no. 4, 2235–2273.  
  17. Point configurations that are asymmetric yet balanced (with Henry Cohn, Noam Elkies and Achill Schürmann) arxiv 
    Proceedings of the American Mathematical Society 138 (2010), no. 8, 2863–2872. 
  18. Ground states and formal duality relations in the Gaussian core model (with Henry Cohn and Achill Schürmann) arxiv 
    Physical Review E 80 (2009), 061116. 
  19. Algorithmic design of self-assembling structures (with Henry Cohn) arxiv 
    Proceedings of the National Academy of Sciences 106 (2009) no. 24, 9570–9575. 
  20. Optimality and uniqueness of the Leech lattice among lattices (with Henry Cohn) arxiv 
    Annals of Mathematics 170 (2009), No. 3, 1003–1050. 
  21. Counterintuitive ground states in soft-core models (with Henry Cohn) arxiv 
    Physical Review E 78 (2008), 061113. 
  22. K3 surfaces associated with curves of genus two journal arxiv 
    International Mathematics Research Notices 2008, no. 6, Art. ID rnm165, 26 pp. 
  23. Uniqueness of the (22,891,1/4) spherical code (with Henry Cohn) arxiv 
    New York Journal of Mathematics 13 (2007), 147–157. 
  24. Universally optimal distribution of points on spheres (with Henry Cohn) arxiv 
    Journal of the American Mathematical Society 20 (2007), no. 1, 99–148. 
  25. The D_4 root system is not universally optimal (with Henry Cohn, John Conway and Noam Elkies) arxiv 
    Experimental Mathematics 16 (2007), 313–320. 
  26. The densest lattice in twenty-four dimensions (with Henry Cohn) arxiv 
    Electronic Research Announcements of the American Mathematical Society 10 (2004), 58–67. 
  27. A Proof of Pieri's formula using generalized Schensted insertion algorithm for RC-graphs (with Mikhail Kogan) arxiv
    Proceedings of the American Mathematical Society 130 (2002), 2525–2534. ​