# May 31-June 1, 2018

## Titles and abstracts ▾

• Francesco Bastianelli Effective cycles on symmetric products of curves

TBA

• Vicente Cortés

TBA

• Jonathan Evans Bounding symplectic embeddings of rational homology balls in surfaces of general type

This is joint work with Ivan Smith. Developing ideas of T. Khodorovskiy and J. Rana, we prove that if the Milnor fibre of a Wahl singularity embeds symplectically in a (canonically polarised) surface of general type with $b^+>1$ then the length of the singularity is bounded above by $4K^2+7$, where the length is the number of components of the exceptional divisor of the minimal resolution and $K^2$ is the square of the canonical class. This implies the corresponding length bound for singularities of stable surfaces of general type, which is an improvement on the previous bound known to algebraic geometers ($400(K^2)^4$, due to Y. Lee). Our proof uses Seiberg-Witten theory and holomorphic curves.

• Alessandro Ghigi

TBA

• Victor Lozovanu

TBA

• Angela Ortega Generic injectivity of the Prym map for double ramified coverings

Given a finite morphism of smooth curves one can canonically associate it a polarized abelian variety, the Prym variety. This induces a map from the moduli space of coverings to the moduli space of polarized abelian varieties, known as the Prym map. In this talk we will consider the Prym map between the moduli space of double coverings over a genus g curve ramified at r points, and the moduli space of polarized abelian varieties of dimension $(g-1+r)/2$ with polarization of type D. We will show the generic injectivity of the Prym map in the cases (a) $g=2$, $r=6$ and (b) $g=5$, $r=2$. In the first case the proof is constructive and can be extended to the range $r > \max{6, 2(g+2)/3}$. This a joint work with Juan Carlos Naranjo.

• Tommaso Pacini Variations on the theme of volume

TBA

• Nicola Pagani Double ramification cycles from universal Jacobians

TBA

• Fabio Podestà (TBC)

TBA

• Luis Ugarte

TBA