Edoardo Fossati
SNS Pisa

Everything has been said about Stein fillings of lens spaces when they are endowed with their standard (tight) contact structure. Nevertheless, lens spaces support many more tight structures, that are all classified, but for which a complete list of their Stein fillings is still missing.

I will present a series of methods and techniques which can be used to investigate the topology of these fillings, giving constraints, for example, on their Euler characteristic and fundamental group.