My research interests lie in theoretical computer science. Currently, I am interested in the complexity of counting problems defined over graphs, especially those in the Holant framework. A central goal of this area is to prove dichotomy or trichotomy theorems.
My past research experience was mainly about bent functions, sequences and finite fields.
Past Research Projects
On the Hamming Weights of Ternary Sequences March 2014 -June 2014
Award: Excellent Bachelor's Thesis Prize (top 5%) Score: A+
This project was supervised by Prof. Xiutao Feng and Prof. Honggang Hu, and supported by AMSS.
We presented a general inequality about the hamming weights of ternary sequences. With this inequality, We solved a problem about sequences with three valued cross-correlation and simplified the proof of Welch’s Conjecture.
On the Symmetric 2-Adic Complexity May 2013 - May2014
Award: Excellent National Undergraduate Innovation Project Prize (top5%) Score: A+
This project was supervised by Prof. Yi Ouyang, and supported by National Innovation Fund.
We presented a lower bound on the expected value of the symmetric 2-adic complexity, and the lower bound means that a random sequence has large symmetric 2-adic complexity with high probability. On the other hand, we proved that in most cases, the 2-adic complexity is strictly bigger than the symmetric 2-adic complexity.
Research on the Lin's Conjecture April 2013 - October 2013
Award: Excellent Undergraduate Research Project Prize (top 5%) Score: A+
This project was supervised by Prof. Honggang Hu.
We presented a proof for the Lin's conjecture. The mathematical tools employed are the second order multiplexing decimation Hadamard transform, Stickelberger's theorem, the Teichmuller character, and combinatorial techniques for enumerating the Hamming weights of ternary numbers.