ERC starting
Spin Curves Enumeration
Overview. Enumerative geometry of curves is the branch of mathematics that aims at counting complex curves, or Riemann surfaces, satisfying specific algebraic constraints.
This field has ancient roots, but gained significant interest in the 90s when physicists showed that solutions to enumerative problems of curves could be used to describe several theoretical models in string theory and quantum gravity.
In mathematics, the modern approach to enumerative problems involves the study of moduli spaces of curves, and the main difficulty is to describe the structure of their cohomology rings. In the present project, we intend to use spin curves to adress this problem. A spin curve is an enhancement of a curve obtained by choosing a square root of the co-tangent space. Curves have only one topological invariant (the genus), but spin curves carry an extra sign + or -, that allows for the definition of more refined enumerative problems. These refinements provide new classes and techniques to investigate the cohomology of moduli spaces of curves.
When? 1 January 2025 - 31 December 2029.
Where? The project is currently carried at the Laboratoire Analyse, Géometrie et Modélisation (AGM) in Cergy-Pontoise. The AGM has an algebra and geometry group that meets twice per month at the seminar. It is located about 45-55 mins away from the other universities of Paris (Jussieu, Diderot, or Ecole normale supérieure), where the "Séminaire de géométrie algébrique" and the "Séminaire de géométrie énumérative" take place.
Open position(s). One post-doc position (of 2 years) is open. The starting date is 1 February 2025. The applications should be sent before 30 November 2024, and contain : a CV (with list of publications), a short research statement (presentation of past and planned research), and 2 recommendation letters. The gross salary will depend on the experience of the candidate (years after PhD) and range from 36k to 57k per year (see here).
Events. TBA
(Pre-)Publications associated with the project.
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The master relation for polynomiality and equivalences of integrable systems (X. Blot, A. Sauvaget, and S. Shadrin)
arXiv: 2406.16632, 2024. arXiv -
The Spin Gromov-Witten/Hurwitz correspondence for P^1 (A. Giacchetto, R. Kramer, D. Lewański, and A. Sauvaget)
arXiv: 2208.03259, 2022. arXiv -
Integrals of ψ-classes on twisted double ramification cycles and spaces of differentials (M. Costantini, A. Sauvaget, and J. Schmitt)
arXiv: 2112.04238, 2021. arXiv -
Cylinder counts and spin refinement of area Siegel-Veech constants (J.W. van Ittersum, and A. Sauvaget)
Accepted for publication at Commentarii Mathematici Helvetici, 2024. arXiv -
Towards logarithmic GLSM: the r-spin case (with Q. Chen, F. Janda, Y. Ruan, and A. Sauvaget)
Geometry & Topology, 26(7):2855–2939, 2022. arXiv / journal
(Front page painting : Automne , Sonia Delaunay, 1965)
adrien.sauvaget@math.cnrs.fr
Laboratoire AGM, bureau 502
Université de Cergy Pontoise
2 avenue Adolphe Chauvin,
95302 Cergy-Pontoise Cedex (France)