Sala Riunioni (Dip. Matematica).
Let k be a knot (i.e. an embedding of S^1into S^3). Once S^3is seen as the boundary of D^4, one can ask which kind of (properly) embedded surfaces in D^4have k as boundary. Finding the minimal genus of such a surfaces (called slice genus) is a central topic in low dimensional topology. In this talk I wish to describe some inequalities, arising from contact topology and quantum homologies. These inequalities, called Bennequin-type inequalities, can be used to estimate the slice genus of a knot in term of other invariants. The seminar will be organized as follows; first, I will give a brief overview of the history of this problem, and indicate some motivations to study it. Then, I will describe some known results that may help to determine the slice genus of a knot. In doing so, I will introduce some basic contact topology. Finally, I will describe how we can use some ”contact” knot invariant to estimate the slice genus.