Title: Complete solutions of Toda equations and cyclic Higgs bundles over non-compact surfaces
Speaker: Qiongling Li (Chern institute, Nankai)
Date: 14 December 2020
Time: 4:00 pm
Venue: MS teams (team code hiq1jfr)
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 harmonic 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 by using techniques for both Toda equations and
harmonic bundles. Moreover, we show some quantitative estimates of the complete solution. This is joint work with Takuro Mochizuki (RIMS).