AbstractAround 2008, de Cataldo, Hausel, and Migliorini proposed the P=W conjecture, which predicts aconnection between the topology of the Hitchin system and the Hodge theory of the charactervariety under the non-abelian Hodge correspondence. Since then, much effort has been devoted tounderstanding this myterious phenomenon, leading to the discovery of new geometric structures onboth the Higgs...
The DonovaThe Donovan-Wemyss Conjecture via the Derived Auslander-Iyama CorrespondenceAbstractThe Donovan-Wemyss Conjecture predicts that the isomorphism type of an isolated compound Du Val singularity R that admits a crepant resolution is completely determined by the derived-equivalence class of any of its contraction algebras. Crucial results of August and Hua-Keller reduced the conjecture to...