The mini-course will take place in Edinburgh, the week of May 11-15, 2026.
Title: A mini-course on global Kuranishi charts for pseudo-holomorphic stable maps
Description: The aim of this workshop is to explain the construction of global Kuranishi charts in detail. We will introduce the basic definitions and concepts and then focus on the case of moduli spaces of stable maps in order to showcase and motivate the ingredients that go into such a construction. Time permitting, the use of such presentations, such as in proving the Gromov-Witten axioms, will be discussed at the end of the week. Lectures will be given by Amanda Hirschi, Kai Hugtenburg, and Nick Sheridan. Ample time will be devoted to discussions.
While the moduli space of stable curves will be discussed, standard pseudo-holomorphic curve theory such as Gromov compactness and basics of Cauchy-Riemann operators (as covered in [McDuff-Salamon, J-holomorphic Curves and Symplectic Topology] or [Salamon, Lectures on Floer Homology]) will be assumed.Â
The schedule will be posted on this page in due course. We expect to have lectures in the mornings, followed by discussion sessions in the afternoons.
Monday:
Nick: Review of transversality issues. Notes.
Amanda: Overview of construction of global Kuranishi chart. Notes.
Tuesday:
Kai: Global Kuranishi charts. Notes.
Amanda: Auxiliary data and constructions I. Notes.
Wednesday:
Kai: Manifold structure. Notes.
Amanda: Auxiliary data and construction II. Notes. Nick's notes.
Thursday:
Kai: Uniqueness (up to equivalence/cobordism). Notes.
Amanda: Relative smooth structures. Notes.
Amanda: Higher genus Gromov-Witten invariants. Notes.
Friday:
Nick: Stabilizing divisors. Notes.
Amanda: Proving properties of Gromov-Witten invariants. Notes.