All my papers are available from the arxiv at http://arxiv.org/a/kumar_a_4.html
- Inose's construction and elliptic K3 surfaces with Mordell-Weil rank 15 revisited (with M. Kuwata), 11 pages, arxiv, to appear in Contemporary Mathematics.
- The sphere packing problem in dimension 24 (with H. Cohn, S. D. Miller, D. Radchenko and M. Viazovska), 12 pages, arxiv, to appear in Annals of Mathematics.
- Elliptic K3 surfaces associated with the product of two elliptic curves:
Mordell-Weil lattices and their fields of definition (with M. Kuwata), 33 pages, arxiv, to appear in Nagoya Mathematical Journal.
- Algebraic models and arithmetic geometry of Teichmuller curves in genus two (with R. Mukamel), 43 pages, arxiv,
International Mathematics Research Notices 2016; doi:10.1093/imrn/rnw193.
- Real multiplication through explicit correspondences (with R. Mukamel), 16 pages, arxiv,
LMS Journal of Computation and Mathematics 19 (Special issue A) (2016), 29-42.
- Optimal simplices and codes in projective spaces (with H. Cohn and G. Minton), arxiv,
Geometry and Topology 20 (2016), no. 3, 1289-1357.
- 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.
- Examples of abelian surfaces with everywhere good reduction (with L. Dembele), arxiv,
Mathematische Annalen 364 (2016), no. 3, 1365-1392.
- Hilbert modular surfaces for square discriminants and elliptic subfields of genus 2 function fields, arxiv,
Research in the Mathematical Sciences 2:24 (2015).
- K3 surfaces and equations for Hilbert modular surfaces (with Noam Elkies), arxiv
Algebra and Number Theory 8 (2014), no. 10, 2297-2411.
- Metacommutation of Hurwitz primes (with Henry Cohn), 11 pages, arxiv
Proceedings of the American Mathematical Society 143 (2015), no. 4, 1459-1469.
- 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.
- Elliptic fibrations on a generic Jacobian Kummer surface arxiv
Journal of Algebraic Geometry 23 (2014), 599-667.
- 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.
- 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).
- Rigidity of Spherical Codes (with Henry Cohn, Salvatore Torquato and Yang Jiao) arxiv
Geometry and Topology 15 (2011), no. 4, 2235–2273.
- 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.
- 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
Proceedings of the National Academy of Sciences 106 (2009) no. 24, 9570–9575.
- Optimality and uniqueness of the Leech lattice among lattices (with Henry Cohn) arxiv
Annals of Mathematics 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 journal arxiv
International Mathematics Research Notices 2008, no. 6, Art. ID rnm165, 26 pp.
- Uniqueness of the (22,891,1/4) spherical code (with Henry Cohn) arxiv
New York Journal of Mathematics 13 (2007), 147–157.
- Universally optimal distribution of points on spheres (with Henry Cohn) arxiv
Journal of the American Mathematical Society 20 (2007), no. 1, 99–148.
- The D_4 root system is not universally optimal (with Henry Cohn, John Conway and Noam Elkies) arxiv
Experimental Mathematics 16 (2007), 313–320.
- The densest lattice in twenty-four dimensions (with Henry Cohn) arxiv
Electronic Research Announcements of the American Mathematical Society 10 (2004), 58–67.
- 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.