## My name is Jie Han (韩杰). I am a tenure-track assistant professor in Department of Mathematics, University of Rhode Island, RI, USA. I am a member of the discrete math group.## Before moving (back) to the US, I was a postdoc research fellow at the Universidade de Sao Paulo (USP) working with Prof. Yoshiharu Kohayakawa from March 2015 to August 2018 and a visiting research fellow of the University of Birmingham in the academic year 2015 - 2016. I stayed at IMA (the Institute for Mathematics and its Applications, Minneapolis, MN) in Fall 2014. I finished my Ph. D. in Georgia State University (GSU) (2010 - 2015) under the supervision of Prof. Yi Zhao. I finished my B. S. in Beijing Institute of Technology (2004 - 2008).## Research: Online papers，ArXivMy research is on graph theory and combinatorics, especially in extremal (hyper)graph theory. Selected papers: - Two-regular subgraphs of odd-uniform hypergraphs, with Jaehoon Kim, JCTB, 128 (2018) 175-191. We determine the maximum number of edges in an odd uniform hypergraph which does not contain any 2-regular subgraphs and characterize the unique extremal example. This verifies a conjecture of Mubayi and Verstraete.
- Maximum size of a non-trivial intersecting uniform family that is not a subfamily of the Hilton-Milner family, with Yoshiharu Kohayakawa, Proc. of AMS, 145-1 (2017), 73–87. We determine the maximum size of an intersecting uniform family that is not a subfamily of the EKR family or the HM family, and characterize all extremal families that achieve the maximum size.
- Forbidding Hamilton cycles in uniform hypergraphs, with Yi Zhao, JCTA, 143 (2016) 107-115. We establish a new lower bound for the minimum d-degree thresholds for uniform hypergraphs containing Hamilton l-cycles. In particular, this disproves a conjecture of Rodl and Rucinski.
- Decision problem for Perfect Matchings in Dense k-uniform Hypergraphs, Trans. of AMS, 369-7(2017), 5197-5218. We show that the decision problem for the containment of perfect matchings in k-uniform hypergraphs with minimum codegree at least n/k can be solved in polynomial time. This solves a problem of Karpinski, Rucinski and Szymanska completely and improves the work of Keevash, Knox and Mycroft.
- Minimum codegree threshold for Hamilton l-cycles in k-uniform hypergraphs, with Yi Zhao. JCTA, 132 (2015) 194-223. We determine the minimum codegree threshold for Hamilton l-cycles in k-uniform hypergraphs for all l<k/2. This is best possible and improves the result by Han and Schacht.
## Coauthors: Josefran O. Bastos, Fabricio Benevides, Wiebke Bedenknecht, Julia Böttcher, Guantao Chen, Louis DeBiasio, Peter Frankl, Wei Gao (2), Hao Huang, Matthew Jenssen, Jaehoon Kim, Yoshiharu Kohayakawa (10), Allan Lo (2), Richard Montgomery, Patrick Morris(3), Guilherme Oliveira Mota(2), Suil O, Olaf Parczyk, Yury Person(4), Barnaby Roberts, Marcelo T. Sales(2), Nicolás Sanhueza-Matamala, Songling Shan, Henrique Stagni(2), Andrew Treglown (3), Shoichi Tsuchiya, Chuanyun Zang (2), Yi Zhao (11).Last update: April 2019. |