Aim & Scope

姚鴻澤教授1981 年畢業於臺灣大學數學系,2014 年獲選為臺大傑出校友,目前也是Distinguished NCTS Scholar 。他是數學物理、分析與機率論領域的領導者,研究成果影響了機率論、隨機過程、隨機矩陣、非平衡態統計物理和量子力學等,為當今世上影響層面最深最廣的數學家之一。

姚鴻澤教授曾獲龐加萊獎與參克阿瑟獎,也是美國國家科學院院士，最近也以在隨機矩陣的突破性研究，獲美國數學會頒發2026 Leroy P. Steele Prize for Seminal Contribution to Research。

國家理論科學研究中心有幸邀请姚院士於2026 年7 月2 日舉辦Meet with Prof. Horng-Tzer Yau, 介紹隨機矩陣和相關應用。歡迎有興趣的同學以及數學界同仁共同參與,故於lecture.結束設有一小時的交流活動,期望藉由Q&A、學術交流讓台灣數學界激盪出不同的火花。

Invited Speaker

Horng-Tzer Yau (Harvard University)

Agenda

13:45-14:00 Registration

14:00-15:00 Lecture (姚鴻澤院士主講)

15:00-15:30 Q&A

15:30-16:00 Tea Time

Title

 Random Matrices: Wigner Universality, Anderson Delocalization, and Beyond

Abstract

In this lecture we review developments in random matrix theory with an emphasis on progress over the past two decades. The guiding principle is Wigner's universality thesis, which asserts that the spectral statistics of highly correlated systems resemble those of classical random matrix ensembles. Anderson's localization--delocalization transition for the tight-binding model extends this vision to non-mean-field models. The main results covered in this lecture include the resolution of the Wigner--Dyson--Mehta conjecture; the Sarnak--Miller--Novikoff--Sabelli conjecture on Ramanujan graphs; and delocalization and universality for band matrices and block Anderson models in all dimensions.

We begin by reviewing the three-step strategy for establishing universality in mean-field random matrices, and the obstacles to extending this strategy to non-mean-field ensembles.

We then outline a new method based on the loop hierarchy and its tree approximation, which yields quantum diffusion.

Finally, we explain how quantum diffusion modifies the three-step strategy and leads to proofs of universality for non-mean-field models

Registration