Topic: arithmetic geometry

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 wi

This workshop examines the fifty-year influence of Barry Mazur’s work on modular curves and the Eisenstein ideal. It connects congruences between modular forms with Diophantine problems, elliptic-curve torsion, arithmetic geometry and the Langlands programme, then considers subsequent advances and open conjectures. Graduate students, postdoctoral researchers and faculty should know algebraic number theory, elliptic curves and modular forms; experience with Galois representations or Iwasawa theory is helpful. Accommodation is provided for participants travelling to ICTS.