Workshop: Hyperkahler quotients, singularities, and quivers: January 30 – February 3, 2023.

Participant List Schedule

Organized by:

Ljudmila Kamenova (Stony Brook University),
Giovanni Mongardi (University of Bologna),
Alexei Oblomkov (UMass Amherst)

Hyperkahler manifolds are higher-dimensional generalizations of K3 surfaces, and as such they are a perfect testing ground for central conjectures in algebraic geometry, like the Hodge conjecture, the Tate conjecture, Grothendieck’s standard conjectures, Bloch-Beilinson conjectures, etc. Exciting new insight has been obtained in recent years, but many new and old questions remain open. Recent developments put hyperkahler manifolds at a central place in the interaction between complex geometry, arithmetic algebraic geometry, derived category theory, and more. Bringing together people working on various specific problems of this sort and experts interested in the general geometry of hyperkahler varieties should trigger further results.

We intend to focus on a detailed understanding of the general conjectures for special classes of hyperkahler manifolds, e.g., those of K3[n]-type, which could lead to new insight into the conjectures in general. Of very high recent interest are also irreducible symplectic varieties, which are a singular analogue of hyperkahler manifolds and share with them most of the interesting properties. Studying these cases is relevant in order to understand general properties of hyperkahler geometry. As an example, general results linking their Hodge structure with their geometry have been recently proven by Bakker and Lehn, and in the case of orbifolds a twistor family structure was constructed by Menet.

This Workshop is also associated with a Program: Hyperkahler quotients, singularities, and quivers: January 2-February 24, 2023

 

Talk Schedule


Time Title Speaker Location
9:00am Breakfast N/A SCGP Cafe
9:30am Rational Hodge isometries of hyper-Kahler varieties of K3[n] and generalized Kummer type are algebraic Eyal Markman SCGP 102
10:30am Coffee Break N/A SCGP Cafe
11:00am A failed attempt at irrationality via algebraic K-theory Nicolas Addington SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:30pm The Matsushita alternative Benjamin Bakker SCGP 102
4:00pm Terminal singularities, Hyperkahler Quotients and Quiver N-ality Anindya Dey SCGP 102

Time Title Speaker Location
10:00am Breakfast N/A SCGP Cafe
11:00am Cycles in the K3 period domain and moduli of complex hyperkähler metrics Daniel Greb SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:30pm Parabolic automorphisms of hyperkähler manifolds Ekaterina Amerik SCGP 102
4:00pm Some open problems in order to construct compact hyperkähler orbifolds Gregoire Menet SCGP 102

Time Title Speaker Location
9:00am Breakfast N/A SCGP Cafe
9:30am Symplectic singularities and Coulomb branches Aminhay Hanany SCGP 102
10:30am Coffee Break N/A SCGP Cafe
11:00am Hitchin WKB-problem and P = W conjecture in lowest degree for rank 2 over the 5-punctured sphere Szilard Szabo SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:30pm Prym fibrations as irreducible symplectic varieties Chiara Camere SCGP 102
4:00pm Derived equivalent K3 surfaces and their motives as algebra objects. Lie Fu SCGP 102

Time Title Speaker Location
9:00am Breakfast N/A SCGP Cafe
9:30am A locally complete family of projective IHS orbifolds of Nikulin type Michal Kapustka SCGP 102
10:30am Coffee Break N/A SCGP Cafe
11:00am On the cone conjecture for Enriques manifolds. Gianluca Pacienza SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:30pm Recent progress on the study of automorphisms of K3 surfaces Alessandra Sarti SCGP 102
4:30pm Classification in algebraic geometry and the geometry of moduli spaces Workshop & Math Colloquium: Klaus Hulek SCGP 102

Time Title Speaker Location
9:00am Breakfast N/A SCGP Cafe
9:30am Strict nef divisor Daisuke Matsushita SCGP 102
10:30am Coffee Break N/A SCGP Cafe
11:00am Terminalizations of quotients of HK manifolds via symplectic actions. Annalisa Grossi SCGP 102
12:00pm Lunch N/A SCGP Cafe