Academic Report of School of Mathematical Sciences [2026] No. 078

(Series Report for High-Level University Construction No. 1337)

Title：Prime-detecting quasi-modular forms

Speaker：Xujin Liu, Professor (The University of Hong Kong)

Time：15:00-16:00, July 15, 2026

Location：Room 2433, Huiwen Building, Yuehai Campus, Shenzhen University

Abstract: A Diophantine set is a collection of tuples that are positive integer solutions of a Diophantine equation. The set of primes is known to be Diophantine. A question of Schneider asks whether the set of primes is partition-theoretic, i.e., whether it consists of solutions to equations in partition functions. In this talk, we will give an exposition of the work of Craig, van Ittersum, and Ono, which answers this question affirmatively, as well as subsequent joint work with Kane, Krishnamoorthy and the speaker.

Speaker Profile：Xujin Liu is a professor in the Department of Mathematics at the University of Hong Kong and a doctoral advisor. Professor Liu Xujin’s research spans several fields, including classical analytic number theory, automorphic forms, and L-functions. To date, he has published more than 50 papers in mathematical journals both in China and abroad.

Faculty and students are welcome to attend!

Invited by: Yingnan Wang

School of Mathematical Sciences

July 10, 2026