CHINA·77779193永利(集团)有限公司-Official website

度量几何暑期学术报告

Title: Complete solutions of Toda equations and cyclic Higgs bundles over non-compact surfaces

Speaker: 李琼玲 (南开大学)

Abstract

A Higgs bundle over a Riemann surface is a pair consisting of a holomorphic vector bundle E and a Higgs bundle as a End(E)-valued holomorphic 1-form. We want to study the Hitchin-Kobayashi correspondence for Higgs bundles over general non-compact Riemann surfaces. The most important direction of the correspondence is looking for a Hermitian-Yang-Mills metric for a given Higgs bundle. On a Riemann surface with a holomorphic $r$-differential, one can naturally define a Toda equation and a cyclic Higgs bundle with a grading. A solution of the Toda equation is equivalent to a Hermitian-Yang-Mills metric of the Higgs bundle for which the grading is orthogonal. In this talk, we focus on a general non-compact Riemann surface with an $r$-differential which is not necessarily meromorphic at infinity. We introduce the notion of complete solution of the Toda equation, and we prove the existence and uniqueness of a complete solution/metric. This is joint work with Takuro Mochizuki (RIMS).

北京时间：2021年7月13日（周二）上午9:00—11:00
线下报告教室：新教二楼808 

联系人：胥世成

线上腾讯会议ID：560 2435 5145
欢迎老师和同学们参加！