Research Experiences
When I was an undergraduate student, I learned Combinatorics and was surprised by the grace of this branch of mathematics. I conducted my undergraduate research about extending Baranyai’s Theorem, fortunately supervised by Prof. Hao Huang and Prof. Jie Ma.
An Extension Baranyai’s Theorem
- Baranyai’s Theorem states that a complete $k$-uniform hypergraph on $n$ vertices is $1$-factorable if and only if $k\mid n$. This project try to extend this theorem into non-uniform settings. We finally determined all n, k, such that the family $K_n^{\le k}$ consisting of subsets of $[n]$ of size up to k is 1-factorable, and thus extend Baranyai’s Theorem to the non-uniform setting.
As my master’s dissertation, I paid my attention on the breakthrough of Kahn-Kalai Conjecture by Jinyoung Park and Huy Tuan Pham. My supervisor is Prof. Paul Balister.
A survey of Kahn-Kalai Conjecture
- Park and Pham successfully proved the renowned Kahn-Kalai conjecture, offering an elegant upper bound for thresholds which is a core problem in random discrete structures. This survey focuses on the Kahn-Kalai conjecture, offering many examples to make the conjecture more motivated and various applications to vividly illustrate the profound significance of this conjecture.
During my studying time at Oxford, I took some courses in Number Theory and was introduced to Cryptography. I took a course of Cryptography and wrote a course project about blind signature. I was attracted by Cryptography since it combines both real-world applications and an elegant mathematical theoretical foundation. Now, I am begining my new journey of research in Cryptography under the guidance of Prof. Jiaheng Zhang.
