Landscaping wobbly Higgs bundles

Time: 16:30 (Vietnam time), July 10, 2025

Venue: Room 612, A6, Institute of Mathematics-VAST

Online (Join Zoom Meeting) tại link:

https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1

Abstract: The origin of wobbly Higgs bundles dates back to Drinfeld, who in unpublished work proved that, in rank two, these objects are a pure codimension one subscheme of the moduli space of vector bundles. The term wobbly is due to Donagi—Pantev, in whose work towards a proof of geometric Langlands via Higgs bundles the wobbly divisor plays a key role. Hausel and Hitchin generalised these results to other Hodge bundles, showing that wobbly Higgs bundles are key towards understanding the geometry of the nilpotent cone. These applications have placed wobbly bundles at the center of today's research.

In this talk, after some motivational introduction, I will explain the proof of Donagi—Pantev's conjecture on the equality of wobbly and shaky loci, as well as the classification of Hodge bundle components into wobbly and very stable.