The school will consist of five courses.
Courses
Pierrick Bousseau (University of Oxford): Log Gromov-Witten invariants, mirror symmetry, and applications
(new: slides available)
Alexander Kuznetsov (Steklov Mathematical Institute): Semiorthogonal Decompositions and Categorical Resolutions
Pat Lank (Università degli Studi di Milano): Relative Fourier-Mukai theory for noetherian schemes (link to lecture notes)
Laura Pertusi (Università degli Studi di Milano): Stability conditions on noncommutative schemes (link to arXiv notes)
Tony Yue Yu (Caltech, online course): F-bundles, mirror symmetry and birational invariants (new: slides available)
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.
Gabriel Abanades Joglar: Refined BCOV Mirror Symmetry
Alex Junior Gómez Saltachín: Derived Categories of the Canonical Stack of the Log del Pezzo Surface X_10 in the weighted projective space P(1, 2, 3, 4, 5)
Matthijs Holstege: Resolutions of near-thin quiver moduli
Riku Kurama: Flops, derived categories and liftability of threefolds
Irene Macías Tarrío: Wall-and-Chamber Theory in higher-dimensional varieties
Rodrigo Pereira: The moduli space of Higgs bundles: Lagrangians and mirror symmetry
Prajwal Samal: Construction of Fourier-Mukai Functors using GLSM
Saket Sha: Twisted Arinkin transforms and derived categories of moduli spaces on Kuznetsov components
Abstracts can be found here