An afternoon of complete intersections

                    17 November 2021, ETH Zürich (Zoom)


13:30-14:45   Xiaowen Hu (Sun Yat-Sen University, Guangzhou)

On the big quantum cohomology of Fano complete intersections   slides,   lecture

I will report on recent progress on the quantum cohomology of Fano complete intersections in projective spaces. I will introduce the square root recursion conjecture, a puzzle in odd dimensions, and some ad hoc methods for cubic hypersurfaces. For even dimensional complete intersections of two quadrics, a kind of exceptional complete intersection, I will explain the special feature of a genus 0 invariant of odd length, and, in 4 dimension, the relationship to enumerative geometry. [arxiv:1501.03683], [arxiv:2109.11469]

15:00-16:15   Pierrick Bousseau (CNRS and University of Paris-Saclay)   slides,   lecture

Gromov-Witten theory of complete intersections

I will describe an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. The main idea is to show that invariants with insertions of primitive cohomology classes are controlled by their monodromy and by invariants defined without primitive insertions but with imposed nodes in the domain curve. To compute these nodal Gromov-Witten invariants, we introduce the new notion of nodal relative Gromov-Witten invariants. This is joint work with Hülya Argüz, Rahul Pandharipande, and Dimitri Zvonkine. [arxiv:2109.13323]