K3 surfaces & friends: Brauer groups and moduli

Application for this workshop is now open! The deadline for application is March 14, 2025. The decisions will be announced by March 28, 2025. Please apply via the Register button on the right.

K3 surfaces are fundamental objects in algebraic and arithmetic geometry, as well as neighbouring fields. This workshop focuses on two indispensable tools used in the study of K3 surfaces and related objects: Brauer groups and moduli spaces. Brauer groups serve as a bridge between algebraic invariants and geometry, and as such are frequently used in algebra, number theory and algebraic geometry. Moduli spaces classify and parametrize objects, making them central to both understanding the original objects and constructing new spaces. Brauer groups and moduli spaces are classical tools, which remain highly relevant and in fact form a very active area in modern research.

This workshop will bring together researchers with different backgrounds whose work involves K3 surfaces, Brauer classes and moduli spaces. We will focus on recent developments and future prospects, centred around the following classical and upcoming themes:

• Brauer groups of K3 surfaces, over fields and in families;
• Moduli spaces of Brauer twisted sheaves and hyperkähler varieties;
• Derived categories of varieties over arbitrary fields and rational points.

The workshop aims to offer a platform to foster collaboration, to showcase different perspectives on the topics of the workshop and to give early career researchers a chance to learn from the experts in the respective fields.

The workshop will feature three introductory talks:

- Brauer-Manin obstructions by Rachel Newton

- Hyperkähler varieties by Daniel Huybrechts

- Derived categories by Alexander Kuznetsov

Other speakers include (list not yet complete):

Nicolas Addington*

Chiara Camere

Bert van Geemen

Eyal Markman

Alexei Skorobogatov

Alan Thompson 

Anthony Várilly-Alvarado

*to be confirmed