The work was performed through 3 work packages:
The first one was designed to prove Donagi-Pantev's and Drinfeld's conjectures, which was fully achieved in the smooth moduli space (the former) and for rank three bundles (the latter).
In a second work package, a generalisations of wobbliness as defined by Hausel and Hitchin is explored, as well as applications to mirror symmetry. Criteria for wobbliness for higher fixed points are proven, which solves a conjecture by Hausel and Hitchin. This is important given their ongoing programme to compute some geometric properties (multiplicities) in the nilpotent cone, to which some obstructions exist which are totally identified by the results of GoH. Regarding mirror symmetry, this is a vast programme involving some dualities in mathematics and physics. These are equivalences of objects a priori totally different in nature. Hence, mirror symmetry is a powerful engine. The results by the researcher and secondment collaborators provide some branes flowing to wobbly bundles, of which few examples are known. These are moreover specially important, as they are related to global invariants of the moduli space.
The third work package studies wobbliness relative to some meaningful subspaces in mirror symmetry. We are able to classify wobbly fixed point components for U(p,q)-Higgs bundles and show that these are also wobbly components in the whole moduli space. We compute their equivariant multiplicities, which as applications yields obstructions to existence of very stable components and emptiness of fixed points.
The results have been disseminated through conferences and seminars (a total of 16 events in 17 months) including a the conferences Quantum Fields, Geometry and Representation Theory 2021 (Bangalore, India) and Quantisation of moduli spaces (Oberwolfach, 2022), COW seminar and Oxford seminar.
