Spin structures in enumerative geometry
Workshop in Leiden, 16-18 June 2025

Overview. The goal of the workshop is to gather different points of view on spin structures, especially from a modular and enumerative geometry perspective. In particular, this includes the following topics:

• FJRW theory;
• Topological recursion of Ω-classes;
• Refinement of invariants according to sign/parity;
• Choice of spin structures in Oh-Thomas formalism (e.g. DT4 invariants);
• Invariants of surfaces of positive genus;
• BKP hierarchy;
• Birationnal geometry of connected components of moduli spaces defined by parity

• Andrei Bud (Goethe-Universität, Frankfurt). The Kodaira dimension of strata of differentials
  Abstract: The Kodaira dimension is a fundamental invariant that measures the birational complexity of algebraic varieties. In this talk, we will investigate the Kodaira dimension of strata of Abelian differentials, highlighting differences between even and odd spin parities, as well as between low and high genera. This is based on joint work with Dawei Chen and Martin Möller.
  
  
• Alessandro Chiodo (Sorbonne Université, Paris). title tba
  Abstract: tba
  
  
• Elba Garcia-Failde (Sorbonne Université, Paris). title tba
  Abstract: tba
  
  
• Alessandro Giacchetto (ETH, Zürich). A new spin on Gromov–Witten and Hurwitz
  Abstract: Spin Gromov–Witten invariants were introduced by Kiem and Li to determine the ordinary Gromov–Witten invariants of surfaces with smooth canonical divisors. Conjecturally, these invariants can be expressed as linear combinations of spin Hurwitz numbers, which are themselves computable via representation theory—a relationship known as the spin GW/Hurwitz correspondence. In this talk, I will present a proof of the correspondence in the case of target P^1, and explain how the general case follows from a conjectural degeneration formula for spin GW invariants. Time permitting, I will also discuss new directions related to the Virasoro conjecture for such targets, as well as connections to the GW/PT correspondence. Based on joint works with R. Kramer, D. Lewański, and A. Sauvaget.
  
  
• Nick Kuhn (University of Oxford). title tba
  Abstract: tba
  
  
• Melissa Liu (Columbia University, New-York). title tba
  Abstract: tba
  
  
• Sergej Monavari (EPFL, Lausanne). The refined local Donaldson-Thomas theory of curves
  Abstract: The Maulik-Nekrasov-Okounkov-Pandharipande correspondence predicts an equivalence between the partition functions of (numerical) Gromov-Witten and Donaldson-Thomas invariants of smooth projective threefolds. It was recently proposed by Pardon a solution of this conjectural correspondence by reducing to the simpler case of local curves, which are more amenable for computations by means of TQFT methods. Even more recently, inspired by the seminal work of Nekrasov-Okounkov on the index in M-theory, Brini-Schuler proposed a refined GW/DT correspondence. In this talk, I will present a full solution for the Donaldson-Thomas side of the refined GW/DT correspondence in the case of local curves. In particular, I will explain how to derive the refined DT partition function without relying on degeneration techniques and TQFT methods, and how our formulas recover string-theoretic prediction of Aganagic-Schaeffer. Based on work in progress.
  
  
• Riccardo Ontani (Imperial College, London). title tba
  Abstract: tba
  
  
• Paolo Rossi (Università di Padova, Padova). title tba
  Abstract: tba
  
  
• Ran Tessler (Weizmann Institute, Tel-Aviv). Open FJRW theory-geometry, integrable hierarchies and mirror symmetry
  Abstract: We will start by reviewing FJRW theory, and then define its open-string analogue. We will show that the resulting intersection theories satisfy interesting mirror symmetry statements and are closely related to integrable hierarchies.
  Based on joint works with A. Buryak, E. Clader, M. Gross, T. Kelly and Y. Zhao.
  
  
• Markus Upmeier (University of Aberdeen). Stable homotopy methods for studying spin structures on moduli spaces
  Abstract: I will introduce a new framework for analyzing and constructing spin structures on moduli spaces using tools from stable homotopy theory. Unlike orientations, which could be treated using ordinary category theory (specifically, Picard groupoids, which model stable homotopy 1-types), the case of spin structures requires working with stable homotopy 2-types.
  
  After reviewing the algebraic topology background that underlies this approach, I will discuss my ongoing research project and some preliminary results.
  
  

• 13h30-14h30: Nick Kuhn
• 14h30-15h30: Alessandro Giacchetto
  Break
• 16h00-17h00: Sergej Monavari

• 9h00-10h30: Melissa Liu
  Break
• 11h00-12h30: Ran Tessler
  Lunch
• 14h00-15h00: Andrei Bud
  Break
• 15h30-16h30: Paolo Rossi
• 16h30-17h30: Markus Upmeier

• 9h00-10h00: Alessandro Chiodo
• 10h00-11h00: Elba Garcia-Failde
  Break
• 11h30-12h30: Riccardo Ontani