# Publications

Found 58 results

Universal optimality of the E_8 and Leech lattices and interpolation formulas."

"*Annals of Mathematics*(to appear).Matrix multiplication via matrix groups."

"*Preprint*(2022).Sign uncertainty principles and bounded-degree polynomials."

"*Preprint*(2022).Three-point bounds for sphere packing."

"*Preprint*(2022).The work of Maryna Viazovska."

"*Fields medal laudatio*(2022).Consistent nonparametric estimation for heavy-tailed sparse graphs."

"*Ann. Statist.*49 (2021): 1904-1930.Dual linear programming bounds for sphere packing via modular forms."

"*Math. Comp.*91 (2021): 491-508.Free partition functions and an averaged holographic duality."

"*J. High Energy Phys.*(2021): Paper No. 130, 42 pages.Sphere packing bounds via rescaling."

"*Preprint*(2021).High-dimensional sphere packing and the modular bootstrap."

"*J. High Energy Phys.*(2020): Paper No. 66, 44 pages.*Identifiability for graphexes and the weak kernel metric*." In

*Building Bridges II*, 29-157. Bolyai Soc. Math. Stud. Springer, Berlin, 2019.

An L^p theory of sparse graph convergence I: Limits, sparse random graph models, and power law distributions."

"*Trans. Amer. Math. Soc.*372 (2019): 3019-3062.An optimal uncertainty principle in twelve dimensions via modular forms."

"*Invent. Math.*217 (2019): 799-831.Sampling perspectives on sparse exchangeable graphs."

"*Ann. Probab.*47 (2019): 2754-2800.The Gaussian core model in high dimensions."

"*Duke Math. J.*167 (2018): 2417-2455.An L^p theory of sparse graph convergence II: LD convergence, quotients and right convergence."

"*Ann. Probab.*46 (2018): 337-396.On cap sets and the group-theoretic approach to matrix multiplication."

"*Discrete Anal.*(2017): Paper No. 3, 27 pages.A conceptual breakthrough in sphere packing."

"*Notices Amer. Math. Soc.*64 (2017): 102-115.*Packing, coding, and ground states*." In

*Mathematics and materials*, 45-102. IAS/Park City Math. Ser. Amer. Math. Soc., Providence, RI, 2017.

Sparse exchangeable graphs and their limits via graphon processes."

"*J. Mach. Learn. Res.*18 (2017): Paper No. 210, 71 pages.The sphere packing problem in dimension 24."

" "*Ann. of Math. (2)*185 (2017): 1017-1033.Optimal simplices and codes in projective spaces."

" "*Geom. Topol.*20 (2016): 1289-1357.Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding."

"*Adv. Math. Commun.*9 (2015): 311-339.Metacommutation of Hurwitz primes."

"*Proc. Amer. Math. Soc.*143 (2015): 1459-1469.Energy-minimizing error-correcting codes."

"*IEEE Trans. Inform. Theory*60 (2014): 7442-7450.*Formal duality and generalizations of the Poisson summation formula*." In

*Discrete geometry and algebraic combinatorics*, 123-140. Contemp. Math. Amer. Math. Soc., Providence, RI, 2014.

*The impossibility of obfuscation with auxiliary input or a universal simulator*." In

*Advances in Cryptology–-CRYPTO 2014*, 71-89. Lecture Notes in Comput. Sci. Springer, Heidelberg, 2014.

Sphere packing bounds via spherical codes."

"*Duke Math. J.*163 (2014): 1965-2002.*Approximate common divisors via lattices*." In

*ANTS X–-Proceedings of the Tenth Algorithmic Number Theory Symposium*, 271-293. Open Book Ser. Math. Sci. Publ., Berkeley, CA, 2013.

*Fast matrix multiplication using coherent configurations*." In

*Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms*, 1074-1087. SIAM, Philadelphia, PA, 2013.

Mathematicians take a stand."

"*Notices Amer. Math. Soc.*59 (2012): 828-833.Three-point bounds for energy minimization."

"*J. Amer. Math. Soc.*25 (2012): 929-958.Rigidity of spherical codes."

"*Geom. Topol.*15 (2011): 2235-2273.*Order and disorder in energy minimization*." In

*Proceedings of the International Congress of Mathematicians, Hyderabad, August 19–27, 2010, Volume IV*, 2416-2443. Hindustan Book Agency, New Delhi, 2010.

Point configurations that are asymmetric yet balanced."

"*Proc. Amer. Math. Soc.*138 (2010): 2863-2872.Algorithmic design of self-assembling structures."

"*Proc. Natl. Acad. Sci. USA*106 (2009): 9570-9575.Experimental study of energy-minimizing point configurations on spheres."

"*Experiment. Math.*18 (2009): 257-283.Ground states and formal duality relations in the Gaussian core model."

"*Phys. Rev. E (3)*80 (2009): 061116.Optimality and uniqueness of the Leech lattice among lattices."

"*Ann. of Math. (2)*170 (2009): 1003-1050.Counterintuitive ground states in soft-core models."

"*Phys. Rev. E (3)*78 (2008): 061113.The D_4 root system is not universally optimal."

"*Experiment. Math.*16 (2007): 313-320.Uniqueness of the (22,891,1/4) spherical code."

"*New York J. Math.*13 (2007): 147-157.Universally optimal distribution of points on spheres."

"*J. Amer. Math. Soc.*20 (2007): 99-148.A short proof of the simple continued fraction expansion of e."

"*Amer. Math. Monthly*113 (2006): 57-62.*Group-theoretic algorithms for matrix multiplication*." In

*Proceedings of the 46th Annual Symposium on Foundations of Computer Science*, 379-388. IEEE Computer Society, 2005.

The densest lattice in twenty-four dimensions."

"*Electron. Res. Announc. Amer. Math. Soc.*10 (2004): 58-67.Projective geometry over F_1 and the Gaussian binomial coefficients."

"*Amer. Math. Monthly*111 (2004): 487-495.*A group-theoretic approach to fast matrix multiplication*." In

*Proceedings of the 44th Annual Symposium on Foundations of Computer Science*, 438-449. IEEE Computer Society, 2003.

New upper bounds on sphere packings I."

"*Ann. of Math. (2)*157 (2003): 689-714.Generating a random sink-free orientation in quadratic time."

"*Electron. J. Combin.*9 (2002): Research Paper 10, 13 pages.New upper bounds on sphere packings II."

"*Geom. Topol.*6 (2002): 329-353.A variational principle for domino tilings."

"*J. Amer. Math. Soc.*14 (2001): 297-346.2-adic behavior of numbers of domino tilings."

"*Electron. J. Combin.*6 (1999): Research Paper 14, 7 pages.The shape of a typical boxed plane partition."

"*New York J. Math.*4 (1998): 137-165.Local statistics for random domino tilings of the Aztec diamond."

"*Duke Math. J.*85 (1996): 117-166.Symmetry and specializability in continued fractions."

"*Acta Arith.*75 (1996): 297-320.