【学术报告】Toda equations and cyclic Higgs bundles over non-compact surfaces

• 主讲人：Qiongling Li
• 时间：Nov. 19, 2021 (17:00-18:00 Beijing time, 12:00-13:00 Moscow time))
• 地点：online

Abstract: For Higgs bundles over compact Kahler manifods, it is known by Hitchin and Simpson that the existence of Hermitian-Einstein metric is equivalent to the polystability of the Higgs bundle. There are some generalizations to non-compact cases. 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-Einstein 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. In particular, we discuss the Hermitian-Einstein metrics on the cyclic Higgs bundles determined by r-differentials. This is joint work with Takuro Mochizuki (Kyoto University).

Bio: Qiongling Li got her Ph.D. from Rice University in 2014. She is currently a research fellow at Chern Institute of Mathematics, Nankai University. Her main research fields are Higgs bundles, harmonic maps, and higher Teichmuller theory. Her recent works have been focused on understanding the non-abelian Hodge correspondence over Riemann surfaces.