Explore advanced enumerative geometry through this comprehensive summer school featuring lectures and talks by leading mathematicians from prestigious institutions worldwide. Delve into the fundamental principles of counting geometric objects, a field with over 2,000 years of history that has experienced remarkable breakthroughs in recent decades. Master key topics including Gromov-Witten theory, Donaldson-Thomas theory, and the counting of curves and sheaves through structured lecture series by experts like Richard Thomas on Vafa-Witten invariants, Eugene Gorsky on link homology algebra and geometry, and Joel Kamnitzer on symplectic resolutions and Coulomb branches. Discover connections between enumerative geometry and mathematical physics through gauge theory applications, including 3d and 4d gauge theories and their invariants. Examine applications to categorification and low-dimensional topology, while exploring Hall algebras and their refined versions in cohomological, K-theoretic, and derived category contexts. Benefit from invited lectures by renowned mathematicians including Davesh Maulik on stable pairs and Gopakumar-Vafa invariants, Rahul Pandharipande on curves, maps, and sheaves, and Markus Reineke on cohomological Hall algebras. Engage with advanced research presentations covering topics from skein algebras and continued fractions to quantum super-groups and pseudoperiodic topology, delivered by experts from institutions including MIT, University of Toronto, ETH Zürich, and IHES.

Syllabus

Richard Thomas - Vafa-Witten Invariants of Projective Surfaces 1/5
Eugene Gorsky - Algebra and Geometry of Link Homology 1/5
Joel Kamnitzer - Symplectic Resolutions, Coulomb Branches, and 3d Mirror Symmetry 1/5
Pierrick Bousseau - The Skein Algebra of the 4-punctured Sphere from Curve Counting
Richard Thomas - Vafa-Witten Invariants of Projective Surfaces 2/5
Eugene Gorsky - Algebra and Geometry of Link Homology 2/5
Joel Kamnitzer - Symplectic Resolutions, Coulomb Branches, and 3d Mirror Symmetry 2/5
Lothar Gottsche - SU(r) Vafa-Witten Invariants and Continued Fractions
Richard Thomas - Vafa-Witten Invariants of Projective Surfaces 3/5
Eugene Gorsky - Algebra and Geometry of Link Homology 3/5
Joel Kamnitzer - Symplectic Resolutions, Coulomb Branches, and 3d Mirror Symmetry 3/5
Georg Oberdieck - Multiple Cover Formula for the Stable Pairs Theory of K3xE
Richard Thomas - Vafa-Witten Invariants of Projective Surfaces 4/5
Eugene Gorsky - Algebra and geometry of link homology 4/5
Joel Kamnitzer - Symplectic Resolutions, Coulomb Branches, and 3d Mirror Symmetry 4/5
Alexander Braverman - Gaiotto Conjectures for Quantum Super-groups
Richard Thomas - Vafa-Witten Invariants of Projective Surfaces 5/5
Eugene Gorsky - Algebra and Geometry of Link Homology 5/5
Joel Kamnitzer - Symplectic Resolutions, Coulomb Branches, and 3d Mirror Symmetry 5/5
Tudor Dimofte - 3d SUSY Gauge Theory and Quantum Groups at Roots of Unity
Rahul Pandharipande - Enumerative Geometry of Curves, Maps, and Sheaves 1/5
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 1/4
Dimitri Zvonkine - Generalized Airy Functions...
Davesh Maulik - Stable Pairs and Gopakumar-Vafa Invariants 1/5
Rahul Pandharipande - Enumerative Geometry of Curves, Maps, and Sheaves 2/5
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 2/4
Michael Groechenig - Complex K-theory of Dual Hitchin Systems
Davesh Maulik - Stable Pairs and Gopakumar-Vafa Invariants 2/5
Rahul Pandharipande - Enumerative Geometry of Curves, Maps, and Sheaves 3/5
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 3/4
Richard Rimanyi - Stable Envelopes, Bow Varieties, 3d Mirror Symmetry
Davesh Maulik - Stable Pairs and Gopakumar-Vafa Invariants 3/5
Peng Shan - Cohomology of Affine Springer Fibres and Centre of Small Quantum Groups
Rahul Pandharipande - Enumerative Geometry of Curves, Maps, and Sheaves 4/5
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 4/4
Davesh Maulik - Stable Pairs and Gopakumar-Vafa Invariants 4/5
Rahul Pandharipande - Enumerative Geometry of Curves, Maps, and Sheaves 5/5
Maxim Kontsevich - BPS Counting and Pseudoperiodic Topology
Davesh Maulik - Stable Pairs and Gopakumar-Vafa Invariants 5/5