Lorenzo Sillari (Erdos Center) will speak in the geometry seminar at 2pm on 23rd March. The talk will take place in the Salle des Profs (9th floor building NO). Lorenzo’s title is “Topological and geometric aspects of almost complex 4-manifolds in the spirit of Enriques-Kodaira classification” and his abstract is below.
In this talk I will discuss the possibility of extending parts of Enriques-Kodaira classification of compact complex surfaces to compact almost complex 4-manifolds. I will start by giving a broad perspective on the standard classification and on the main invariants used in it: the Kodaira dimension and the plurigenera. I will later move to the difficulties of working with non-integrable structures. In this case, one has to combine in a clever way techniques from symplectic topology and differential geometry to prove interesting results. We will conclude by speculating on what could be a possible shape of the classification, especially in relation with some recent conjecture by Chen and Zhang.