Antonio Alfieri

Lattice cohomology is a combinatorial invariant of isolated singularities of complex surfaces introduced by Ozsvath Stipsicz and Szabo, and independently by Nemethi. The construction, inspired by Heegaard Floer homology, was recently employed by...

Plumbed three-manifolds are those three-manifolds that can be be realized as links of isolated complex surface singularities. Inspired by Heegaard Floer theory Nemethi introduced a combinatorial invariant of complex surface singularities (lattice...

I will introduce deformations of lattice cohomology corresponding to the knot homologies found by Ozsváth, Stipsicz and Szabó in https://arxiv.org/abs/1407.1795. If time permits I will show that by means of holomorphic triangles counting, one can...

A classical problem in algebraic geometry asks what rational cuspidal curves can be realised in the complex projective plane. In the last few years some substantial advancement regarding this problem have been made, also based on the methods of...