The proposal “Geometry at the tip of the global nilpotent cone” will be funded by the FWF 2022-2025. There will be post-doc positions funded by the grant, see more here: Here is the first paragraph of the abstract of the proposal.
“Here we propose a circle of problems related to mirror symmetry of Lagrangian upward flows at the tip of the global nilpotent cone in the Hitchin integrable system. The Hitchin integrable system is a general construction attaching a completely integrable Hamiltonian system to a curve and a complex reductive group G. The total space of the Hitchin system is the moduli space of Higgs bundles. We study this integrable system via the multiplicity algebras of the Hitchin map restricted to certain Lagrangian upward flows. Such multiplicity algebas – under the name of ”local algebra” – have been studied by the Arnold school on singularities of differential maps.”
The ICM 2022 contribution “Enhanced mirror symmetry for Langlands dual Hitchin systems” gives a good introduction to the problems in the proposal.
The talk “Hitchin map as spectrum of equivariant cohomology“, CMSA Colloquium, Harvard discusses some related issues