## My name is Jie Han (韩杰, 韓傑 in traditional Chinese). 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. My research is partially supported by Simons Collaboration Grant for Mathematicians.## 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: - On Perfect Matchings in k-complexes, IMRN, to appear. We give new proofs of several characterization theorems for the existence of perfect matchings in dense simplicial complexes by Keevash and Mycroft [Mem. AMS, 2015]. In particular, our proof avoids the use of the hypergraph regularity lemma and the hypergraph blow-up lemma. Instead, we use the lattice-based absorbing method developed by Han and a recent probabilistic argument of Kohayakawa, Person and Han.
- 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. 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.
- Decision problem for Perfect Matchings in Dense k-uniform Hypergraphs, Trans. 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, Yulin Chang (2), Guantao Chen, Louis DeBiasio, Laihao Ding, Peter Frankl, Luyining Gan (2), Wei Gao (3), Hiep Han(2), Hao Huang, Matthew Jenssen, Peter Keevash, Jaehoon Kim, Yoshiharu Kohayakawa (12👑), Shoham Letzter, Allan Lo (2), Richard Montgomery, Patrick Morris(5), Guilherme Oliveira Mota(4), Suil O, Olaf Parczyk(2), Yury Person(4), Barnaby Roberts, Marcelo T. Sales(2), Nicolás Sanhueza-Matamala, Songling Shan, Xichao Shu, Henrique Stagni(2), Shumin Sun, Lubos Thoma, Andrew Treglown (3), Shoichi Tsuchiya, Guanghui Wang, Chuanyun Zang (2), Yi Zhao (13👑), Wenling Zhou.Last update: July 2020. |