Emory forest  Hao Huang
  • Email: hao.huang at emory dot edu



 

I am currently a tenure-track Assistant Professor in the Math & CS Department at Emory University.


My previous position was a postdoctoral fellow at the Institute for Mathematics and its Applications at UMN, participating in the annual program: Thematic Year on Discrete Structures: Analysis and Application. From Sep 2012 to Aug 2014, I was a postdoctoral member at the School of Mathematics at Institute for Advanced Study, Princeton and DIMACS at Rutgers University. Prior to that, I received the Ph.D degree in Jun, 2012, from Department of Mathematics, UCLA. My thesis advisor was Professor Benny Sudakov.  (Click for a nice photo of our combinatorics group at UCLA).

I completed my B.S. degree in School of Mathematical Sciences, Peking University back in 2007.


 


Research interest


My research interests include extremal combinatorics, probabilistic/algebraic methods, spectral graph theory, structural graph theory, and theoretical computer science.


Here is a list of my favorite open problems, created when I was in the graduate school. Two of them have been solved already!


See Discover Magazine, Quanta Magazine, Combinatorics and More, Computational Complexity, Gödel’s Lost Letter and P=NP, Live Science, Shtetl-Optimized, What's new, Windows on Theory, and most interestingly, El Pais for coverage of my recent proof of the Sensitivity Conjecture. The proof has also been simplified and nicely TeXed in one page!



Co-authors

 

Noga Alon, Y. Anbalagan, Harout Aydinian, Tom Bohman, Alexander Clifton, Shagnik Das, Jacob Fox, Peter Frankl, Jie Han, Oleksiy Klurman, Choongbum Lee, Tong Li, Nati Linial, Po-Shen Loh, Shachar Lovett, Jie Ma, Humberto Naves, Sergey Norin, Yuval Peled, Cosmin Pohoata, Vojtech Rodl, Andrzej Rucinski, Asaf Shapira, Benny Sudakov, Adrian Vetta, Guanghui Wang, Hehui Wu, Alexander Yu, Raphy Yuster, Yi Zhao.



Publications & Preprints

  1. A counterexample to the Alon-Saks-Seymour conjecture and related problems (with B. Sudakov), Combinatorica 32 (2012), 205-219.
  2. Bandwidth theorem for random graphs (with C. Lee and B. Sudakov), Journal of Combinatorial Theory, Series B 102 (2012), 14-37.
  3. Quasi-randomness of graph balanced cut properties (with C. Lee), Random Structures & Algorithms, 41 (2012), 124-145.
  4. Nonnegative k-sums, fractional covers, and probability of small deviations (with N. Alon and B. Sudakov), Journal of Combinatorial Theory, Series B, 102 (2012), 784-796.
  5. Large matchings in uniform hypergraphs and the conjectures of Erdos and Samuels (with N. Alon, P. Frankl, V. Rodl, A. Rucinski, and B. Sudakov), Journal of Combinatorial Theory, Series A, 119 (2012), 1200-1215.
  6. The size of a hypergraph and its matching number (with P. Loh, B. Sudakov), Combinatorics, Probability and Computing, 21 (2012), 442-450.
  7. Large feedback arc sets, high minimum degree subgraphs, and long cycles in Eulerian digraphs (with J. Ma, A. Shapira, B. Sudakov, and R. Yuster), Combinatorics, Probability and Computing, 22 (2013), 859-873.
  8. A problem of Erdos on the minimum number of k-cliques (with S. Das, J. Ma, H. Naves, and B. Sudakov), Journal of Combinatorial Theory, Series B, 103 (2013), 344-373.
  9. On the 3-local profiles of graphs (with N. Linial, H. Naves, Y. Peled, and B. Sudakov), J. Graph Theory, 76 (2014), 236-248.
  10. On the maximum induced density of directed stars and related problems, SIAM Journal on Discrete Mathematics, 28-1 (2014), 92-98.
  11. The minimum number of nonnegative edges in hypergraphs (with B. Sudakov), The Electronic Journal of Combinatorics, 21(3) (2014), P3.7.
  12. Maximizing the number of nonnegatives subsets (with N. Alon, H. Aydinian), SIAM Journal on Discrete Mathematics, 28-2 (2014), 811-816.
  13. Large supports are required for well-supported Nash equilibria (with Y. Anbalagan, S. Lovett, S. Norin, A. Vetta, and H. Wu), Proceedings of 18th on Approximation Algorithms for Combinatorial Optimization Problems (APPROX), 2015.
  14. On the densities of cliques and independent sets in graphs (with N. Linial, H. Naves, Y. Peled, and B. Sudakov), Combinatorica 36(5) (2016), 493-512.
  15. More on the bipartite decomposition of random graphs (with N. Alon, T. Bohman), Journal of Graph Theory, 84(1) (2017), 45-52.
  16. On graphs decomposable into induced matchings of linear sizes (with J. Fox, B. Sudakov), Bull. London Math. Soc., 49(1) (2017), 45-57.
  17. A note on the double-critical graph conjecture (with A. Yu), submitted.
  18. Degree versions of the Erdos-Ko-Rado Theorem and Erdos hypergraph matching conjecture (with Y. Zhao), Journal of Combinatorial Theory, Series A, 150 (2017) 233-247.
  19. A degree version of the Hilton-Milner Theorem (with P. Frankl, J. Han and Y. Zhao), Journal of Combinatorial Theory, Series A, 155 (2018), 493-502.
  20. On tight cycles in hypergraphs (with J. Ma), to appear in SIAM Journal on Discrete Mathematics.
  21. Two extremal problems on intersecting families, European Journal of Combinatorics, 76 (2019), 1-9.
  22. Rainbow matchings in properly-colored hypergraphs (with T. Li, G. Wang), The Electronic Journal of Combinatorics, 26(1) (2019), P1.4.
  23. On subsets of the hypercube with prescribed Hamming distances (with O. Klurman, C. Pohoata), Journal of Combinatorial Theory, Series A, 171 (2020), Article 105156.
  24. On almost k-covers of hypercubes (with A. Clifton), to appear in Combinatorica.
  25. Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture, Annals of Mathematics, 190 (2019), 949-955.
  26. On local Turan problems (with P. Frankl and V. Rodl), preprint.

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This webpage was last updated on Feb 14, 2020.