Comparing Calabi-Yau and quasi-bisymplectic structures for multiplicative preprojective algebras

04.05.2023 13:15 – 14:15

Multiplicative preprojective algebras first appeared in the work of Crawley-Boevey and Shaw, in the course of their study of the Deligne-Simpson problem. Their representation varieties, known as multiplicative quiver varieties, naturally appear in various areas (character varieties, local systems on Riemann surfaces and perverse sheaves on nodal curves, integrable systems, etc...). Van den Bergh proved that these varieties can be obtained using a quasi-Hamiltonian reduction procedure (after Alekseev-Malkin-Meinreinken), and developed a noncommutative version of the quasi-Hamiltonian formalism so that all constructions actually hold directly at the level of the multiplicative preprojective algebras. In this talk I will explain that the moment map defining these multiplicative preprojective algebras carry a relative Calabi-Yau structure (a notion introduced by Brav and Dyckerhoff, following some earlier suggestion of Toën), and how the three notions (quasi-Hamiltonian structures, their non-commutative version, and relative Calabi-Yau structures) interact.
The talk is based on joint works with Tristan Bozec and Sarah Scherotzke.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Thursday 04.05.2023, Séminaire "Geometry and Topology" and "Lie groups and moduli spaces"

entrée libre