See also my Google Scholar profile page

Books

• The Surprising Mathematics of Longest Increasing Subsequences. Cambridge University Press, 2015.
• Topics in Complex Analysis. De Gruyter, 2023.
• An Invitation to MadHat and Mathematical Typesetting. Association for Mathematical Research, 2023. Visit the MadHat website for more information.

                  

Selected journal papers

• On Viazovska's modular form inequalities. Proceedings of the National Academy of Sciences USA 120 (2023), article e2304891120.
• Gravitational allocation to Poisson points. With Sourav Chatterjee, Ron Peled and Yuval Peres. Annals of Mathematics. 172 (2010), 617-671.
• Improved upper bounds in the moving sofa problem. With Yoav Kallus. Advances in Mathematics. 340 (2018), 960-982.
• Absorbing time asymptotics in the oriented swap process. With Alexey Bufetov and Vadim Gorin. Annals of Applied Probability 32 (2022), 753-763.
• The oriented swap process. With Omer Angel and Alexander Holroyd. Annals of Probability 37 (2009), 1970-1998.

Journal papers (complete list)

1. On Viazovska's modular form inequalities. Proceedings of the National Academy of Sciences USA 120 (2023), article e2304891120.
2. The oriented swap process and last passage percolation. With Elia Bisi, Fabio Deelan Cunden and Shane Gibbons. Random Struct. Algor. 60 (2022), 690-715. See here for a Mathematica companion file. (This paper is the full version of the extended abstract "Sorting networks, staircase Young tableaux and last passage percolation" listed below.)
3. Absorbing time asymptotics in the oriented swap process. With Alexey Bufetov and Vadim Gorin. Ann. Appl. Probab. 32 (2022), 753-763.
4. Orthogonal polynomial expansions for the Riemann xi function in the Hermite, Meixner-Pollaczek, and continuous Hahn bases. Acta Arithmetica 200 (2021), 259-329.
   Note: this paper exists in two different versions with different titles. See this page for additional information and related resources.
38. Alternative summation orders for the Eisenstein series G₂ and Weierstrass ℘-function (joint with Robert Scherer). Rocky Mountain J. Math. 50 (2020), 1473-1482.
39. The Taylor coefficients of the Jacobi theta constant θ₃.  Ramanujan Journal. 52 (2020), 275-290. See here for a Maple package written by Doron Zeilberger that implements some of the formulas in the paper.
40. Improved upper bounds in the moving sofa problem. With Yoav Kallus. Adv. Math. 340 (2018), 960-982. See here for the SofaBounds companion software package.
35. Differential equations and exact solutions in the moving sofa problem. Experimental Math. 27 (2018), 316-330. See below for a Mathematica companion file.
34. On the number of n-dimensional representations of SU(3), the Bernoulli numbers, and the Witten zeta function. Acta Arithmetica 180 (2017), 111-159. See below for a Mathematica companion file.
33. Bijective combinatorial proof of the commutation of transfer matrices in the dense O(1) loop model. With Ron Peled. Séminaire Lotharingien de Combinatoire. 73 (2015), B73b.
34. Limit shapes of bumping routes in the Robinson-Schensted correspondence. With Piotr Sniady. Random Struct. Algor. 48 (2016), 171-182.
35. Connectivity patterns in loop percolation I: the rationality phenomenon and constant term identities. Commun. Math. Phys. 330 (2014), 499-538.
36. Jeu de taquin dynamics on infinite Young tableaux and second class particles. With Piotr Sniady. Ann. Probab. 43 (2015), 682-737.
37. New enumeration formulas for alternating sign matrices and square ice partition functions. With Arvind Ayyer. Adv. Math. 235 (2013), 161-186. (See below for 2 companion files.)
38. Arctic circles, domino tilings and square Young tableaux. Ann. Probab. 40 (2012), 611-647.
39. Phase transitions in gravitational allocation. With Sourav Chatterjee, Ron Peled and Yuval Peres. Geom. Funct. Anal. 20 (2010), 870-917.
40. A formula for a doubly refined enumeration of alternating sign matrices. With Matan Karklinsky. Adv. Appl. Math. 45 (2010), 28-35.
41. More refined enumerations of alternating sign matrices. With Ilse Fischer. Adv. Math. 222 (2009), 2004-2035. (See below for companion file.)
42. The oriented swap process. With Omer Angel and Alexander Holroyd. Ann. Probab. 37 (2009), 1970-1998.
43. Enumeration formulas for Young tableaux in a diagonal strip. With Yuliy Baryshnikov. The Israel J. of Math. 178 (2010), 157-186.
44. Gravitational allocation to Poisson points. With Sourav Chatterjee, Ron Peled and Yuval Peres. Annals of Math. 172 (2010), 617-671.
45. Random sorting networks. With Omer Angel, Alexander Holroyd and Balint Virag. Adv. Math. 215 (2007), 839-868.
46. The dynamics of Pythagorean triples. Trans. Amer. Math. Soc. 360 (2008), 6045-6064.
47. Integrals, probability, and MacMahon’s theorem. With George Andrews, Henrik Eriksson and Fedor Petrov. J. Comb. Theory Ser. A 114 (2007), 545-554.
48. Universal finitary codes with exponential tails. With Nate Harvey, Alexander Holroyd and Yuval Peres. Proc. London Math. Soc. 94 (2007), 475-496.
49. Shortest paths in the Tower of Hanoi graph and finite automata. SIAM J. Disc. Math. 20 (2006), 610-622.
50. The number of guillotine partitions in d dimensions. With Eyal Ackerman, Gill Barequet and Ron Pinter. Inform. Proc. Lett. 98 (2006), 162-167.
51. Random walks with k-wise independent increments. With Itai Benjamini and Gady Kozma. Elec. Comm. Prob. 11 (2006), 100-107.
52. Limit shapes for random square Young tableaux. With Boris Pittel. Adv. Appl. Math. 38 (2007), 164-209.
53. Permutations with short monotone subsequences. Adv. Appl. Math. 37 (2006), 501-510. An extended abstract also appeared in Proceedings of EuroComb 2005, Discr. Math. Theor. Comp. Sci. Proceedings Series Volume AE, 57-62.
54. Waiting for a bat to fly by (in polynomial time). With Itai Benjamini, Gady Kozma, Laszlo Lovasz and Gabor Tardos. Comb., Prob. and Computing 15 (2006), 673-683.
55. Roots of the derivative of a polynomial. Amer. Math. Monthly 112 (2005), 66-68.
56. Some formulas for the central trinomial and Motzkin numbers. J. of Integer Sequences 6 (2003), article 03.2.3.
57. The number of steps in the Robinson-Schensted algorithm. Funct. Anal. Appl. 39 (2005), 152-155.
58. On distributions computable by random walks on graphs. With Guy Kindler. SIAM J. Disc. Math. 17 (2004), 624-633. Also appeared in Proc. of the Fifteenth ACM-SIAM Symposium on Discrete Algorithms (SODA04), 124-131.
59. Integrals, partitions and cellular automata. With Alexander Holroyd and Thomas Liggett. Trans. Amer. Math. Soc. 356 (2004), 3349-3368.
60. Partitions of n into t n^1/2 parts. Europ. J. Combin. 26 (2005), 1-17.
61. Explicit formulas for hook walks on continual Young diagrams. Adv. Appl. Math. 32 (2004), 625-654.
62. Projecting the surface measure of the sphere of l_p^n. With Assaf Naor. Ann. Inst. Henri Poincare Prob. Stat. 39 (2003), 241-261.
63. Some comments on Euler’s series for pi^2/6. Math. Gazette, July 2002, 281-284.
64. Stirling’s approximation for n!: the ultimate short proof? Amer. Math. Monthly 107 (2000), 556-557.
65. Sharp entropy bounds for discrete statistical simulation. Statist. Probab. Lett. 42 (1999), 219-227.

Publications in conference proceedings

• Local extrema in random permutations and the structure of longest alternating subsequences. Disc. Math. Theor. Comp. Sci., Proceedings Vol. AO (2011), 825-834. (Proceedings of the 23rd International Conference on Formal Power Series and Algebraic Combinatorics – FPSAC 2011).
• Sorting networks, staircase Young tableaux and last passage percolation (joint with Elia Bisi, Fabio Deelan Cunden and Shane Gibbons). Proceedings of the 32nd Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2020). Séminaire Lotharingien de Combinatoire 84B.3, 12 pp. See here for a Mathematica companion file. (This paper is an extended abstract. Its full version is the paper "The oriented swap process and last passage percolation" listed above.)

Unpublished

• Identities arising from limit shapes of constrained random partitions. Unpublished preprint, 2003.

Patents

• Method and apparatus for filtering data packets. United States Patent 8,355,324. Y. Baryshnikov, D. Romik, E. H. Grosse, F. X. Zane.

Companion files

• A Mathematica package OrientedSwaps. Companion to the paper "Staircase Young tableaux, sorting networks and last passage percolation" with Elia Bisi, Fabio Cunden and Shane Gibbons.
• A software package SofaBounds (command line tool, written in C++). Companion to the paper "Improved upper bounds in the moving sofa problem" with Yoav Kallus.
• A Mathematica package MovingSofas. Companion to the paper "Differential equations and exact solutions in the moving sofa problem". If you don't have Mathematica, you can download the PDF version.
• A Mathematica notebook SU3-ASYM.nb. Companion to the paper "On the number of n-dimensional representations of SU(3), the Witten zeta function, and the Bernoulli numbers". If you don't have Mathematica, you can download the PDF version.
• A Maple package RefinedASM1234.txt. Companion to the paper "New enumeration formulas for alternating sign matrices and square ice partition functions" with Arvind Ayyer.
• A Mathematica notebook GammaDelta.nb. Companion to the paper "New enumeration formulas for alternating sign matrices and square ice partition functions" with Arvind Ayyer. This notebook verifies a claim added in the revised version of the paper.
• A Mathematica notebook RefinedASM.nb. Companion to the paper "More refined enumerations of alternating sign matrices" with Ilse Fischer.

Coauthors

Eyal Ackerman, George Andrews, Omer Angel, Arvind Ayyer, Gill Barequet, Yuliy Baryshnikov, Itai Benjamini, Elia Bisi, Alexey Bufetov, Sourav Chatterjee, Fabio Deelan Cunden, Henrik Eriksson, Ilse Fischer, Vadim Gorin, Nate Harvey, Alexander Holroyd, Shane Gibbons, Yoav Kallus, Guy Kindler, Gady Kozma, Thomas Liggett, Laszlo Lovasz, Matan Karklinsky, Assaf Naor, Ron Peled, Yuval Peres, Fedor Petrov, Ron Pinter, Boris Pittel, Robert Scherer, Piotr Śniady, Gabor Tardos, Bálint Virág