Asymptotic geometry of the Higgs bundle moduli space

• Applicant: Professor Dr. Hartmut Weiß, since 4/2021
• Subject Area: Mathematics
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 339380321

Subject of this proposal are moduli spaces of Higgs bundles and their asymptotic geometry. Here we intend to come to a better understanding of the recent compactification by singular solutions of Hitchin's self-duality equations in the case of solutions which belong to holomorphic quadratic differentials with multiple zeroes. At the same time we seek to make further progress in the description of the asymptotic structure of the hyperKaehler metric these moduli spaces come equipped with. These results relate and will find possible applications to such diverse analytic-geometrical objects as gravitational instantons (which in some cases arise as Higgs bundle moduli spaces) and equivariant harmonic maps which play a crucial role in nonabelian Hodge theory.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2026: Geometry at Infinity
• Ehemaliger Antragsteller: Privatdozent Dr. Jan Swoboda, until 3/2021