Speaker: Nianzi Li（Tsinghua University）
Time: 09:00-11:00, Aug 6, 2025
Room: Tencent Meeting ID: 382 322 632, no password
The moduli space of Higgs bundles is endowed with a complete hyperkähler metric, known as the Hitchin metric. The Hitchin fibration gives the moduli space the structure of a completely integrable system and defines a simpler hyperkähler metric on the smooth locus of the fibration, called the semiflat metric. It is a fundamental result that on the smooth locus, the Hitchin metric converges exponentially to the semiflat metric. We extends this exponential decay result to the singular locus of the Hitchin fibration. Our proof has two main components. First, we use a gluing construction to control the limiting behavior of the harmonic metric for a ray of Higgs bundles in the singular locus. Second, we use Mochizuki's techniques of metric comparison via harmonic one-forms to this degenerate setting. Based on joint work with Siqi He and Johannes Horn.
