Description
It is widely believed that there is a close connection between
automorphic L-functions and random matrices. In particular, the
Katz-Sarnak philosophy predicts that for any suitable family of
automorphic L-functions $\mathcal{L}$, there exists a corresponding
symmetry type $G$, such that the distribution of low-lying zeros of
members in $\mathcal{L}$ can be modeled by the distribution of low-lying
eigenvalues of random matrices of type $G$. In this talk, I will give a
brief survey on this problem in the context of spinor/standard
L-functions attached to genus 2 Siegel modular forms. Then I will focus
on my own results on the harmonic-weighted distribution of low-lying
zeros of standard L-functions. Finally, I will discuss a few future
directions and applications.