The school will consist of five 4-hour courses and a complementary lecture.
Courses
Pierrick Bousseau (University of Oxford): Log Gromov-Witten invariants, mirror symmetry, and applications
Alexander Kuznetsov (Steklov Mathematical Institute): Semiorthogonal Decompositions and Categorical Resolutions
Pat Lank (Università degli Studi di Milano): Yoga sequences of integral transforms and singularity categories
Laura Pertusi (Università degli Studi di Milano): Stability conditions on noncommutative schemes
Tony Yue Yu (Caltech, online course): TBA
Lectures
Soheyla Feyzbakhsh (Imperial College): TBA
Description
The precise content of the 5 mini-courses will be established later, but the the main directions to be covered will be:
Semiorthogonal Decompositions and Categorical Resolutions: Foundations and applications of semiorthogonal decompositions in derived categories, together with categorical resolutions of singularities, and their role in rationality problems and the geometry of Fano varieties.
Stability Conditions and Wall-Crossing: Bridgeland stability on triangulated categories, its use in constructing moduli spaces of stable objects, and wall-crossing phenomena as a tool for understanding birational transformations.
Mirror Symmetry and Degenerations: Mirror constructions via tropical and logarithmic techniques, punctured Gromov–Witten theory, and their connections to moduli spaces and enumerative geometry.
Singularity Categories and Integral Transforms: The structure of singularity categories as quotients of derived categories, and the role of integral transforms in comparing different settings and measuring the complexity of singularities.
Hodge Theory and Birational Invariants: Recent developments combining Hodge theory with quantum structures, introducing new invariants with applications to rationality and the geometry of Calabi–Yau varieties.