4 papers
Balancing tautological intersection numbers
Kefeng Liu, Hao Xu
We prove the three balancing inequalities conjectured by the authors about 20 years ago: moving one unit from a larger index to a smaller one cannot decrease a mixed tautological i…
Uniform asymptotics and the Weil--Petersson constant
Kefeng Liu, Hao Xu
In their celebrated work on the large-genus asymptotic expansion of Weil--Petersson volumes, Mirzakhani and Zograf left open the question of whether the Weil--Petersson constant sa…
Local Laplacian: theory and models for data analysis
Jian Liu, Hongsong Feng, Kefeng Liu
While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are f…
Higher Weil-Petersson volumes of the moduli space of super Riemann surfaces
Xuanyu Huang, Kefeng Liu, Hao Xu
Inspired by the theory of JT supergravity, Stanford-Witten derived a remarkable recursion formula of Weil-Petersson volumes of moduli space of super Riemann surfaces. It is the sup…