Cubic Fourfolds, Gushel-Mukai Fourfolds, and Hyperkahler Manifolds

Cubic and Gushel–Mukai fourfolds connect to K3 surfaces through geometry and Hodge theory, while hyperkähler manifolds extend many K3 techniques to higher dimensions. This workshop brings algebraic and arithmetic geometry together to examine how these connections inform computations over finite fields, automorphisms in positive characteristic, rational points and Brauer–Manin obstructions. The programme investigates Lagrangian fibrations, birational geometry, degenerations of Kummer varieties, cohomology, and noncommutative deformations of abelian surfaces, combining geometric constructions with arithmetic questions.

The workshop runs from 26 to 30 October 2026. Monday check-in is 08:30–08:50, the welcome begins at 08:50 and the first research talk at 09:00. Talks start at 09:00 on the remaining days. Times are EDT (America/New_York). Applications are welcomed from faculty, postdoctoral researchers, graduate students, industry scientists and other researchers through ICERM's Cube account system. Graduate applicants require an advisor's supporting statement; some travel and lodging support may be available.