Dates: September 11 - 15, 2023
Venue: HIM lecture hall (Poppelsdorfer Allee 45, Bonn)
Organizers: Sarah Frei (Dartmouth),  Richard Haburcak (Dartmouth), Genki Ouchi (Nagoya), Jack Petok (Dartmouth), and Xuqiang Qin (UNC)

Lecturers:

• Chiara Camere (Milano)
• Daniel Huybrechts (Bonn)
• Christian Lehn (TU Chemnitz)
• Sofia Tirabassi (Stockholm)

Description:

The focus of the school will be K3 surfaces, hyperkähler manifolds, and cubic fourfolds.  A major problem in the geometry of classical algebraic varieties is the rationality problem for cubic hypersurfaces of dimension 4. While it remains to be seen whether all cubic fourfolds are rational, a rich framework of theorems and conjectures has been developed to study this problem, relating cubic fourfolds with K3 surfaces as well as other hyperkähler manifolds. Some of these relationships are described by classical algebraic geometric constructions, and in the last few decades tools such as Hodge theory, derived categories, and moduli theory have proven indispensable in studying these connections.

The school aims to introduce participants to this circle of ideas, and will consist of 4 expository mini-courses and short introductory talks from some participants of the Junior Trimester Program. The lectures will be aimed at advanced graduate students and postdocs with a background in algebraic geometry.

Click here for the abstract.

Click here for the schedule.

Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this school, are eligible to attend this event.

Daniel Huybrechts: Brauer groups and twisted sheaves on K3 surfaces 1

Chiara Camere: Finite Group actions on hyperkähler manifolds 1

Cristian Lehn: Lagrangian Fibrations of Holomorphic Symplectic Varieties 1

Sofia Tirabassi: Lieblich-Olsson deformation technique and applications 1

Daniel Huybrechts: Brauer groups and twisted sheaves on K3 surfaces 2

Chiara Camere: Finite group actions on hyperkähler manifolds 2

Cristian Lehn: Lagrangian Fibrations of Holomorphic Symplectic Varieties 3

Sasha Viktorova: The defect of a cubic threefold

Christian Lehn: Lagrangian Fibrations of Holomorphic Symplectic Varieties 4

Daniel Huybrechts: Brauer groups and twisted sheaves on K3 surfaces 3

Chiara Camere: Finite group actions on hyperkähler manifolds 3

Unfortunately, due to a power outage, this video was corrupted while recording it.

Sofia Tirabassi: Lieblich-Olsson deformation technique and applications 3

Chiara Camere: Finite group actions on hyperkähler manifolds 4

Stevell Muller: On symplectic transformations of OG10-type hyperkähler manifolds via cubic fourfolds