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.
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