Cristiano Bocci (Università di Siena)
Title. New objects to characterize dynamic Markov systems
Abstract. In this talk I will introduce some results on Dynamic Markov Systems, based on a collaboration with the group of Econophysicists of the University of Alessandria. Dynamic Markov Systems (DMS) have several applications in Economics, Computer Science and Biology (social networks, Petri Nets, speed date!) The vertices in the graph associated to the DMS represent „cooperation graphs“. In this work we try to characterize these graphs, using Tropical Mathematics, Linear Algebra and Statistics. This is a joint work with Luca Chiantini and Fabio Rapallo.
Further material. Slides of the talk
Ciro Ciliberto (Università di Roma Tor Vergata)
Title. Curves on general hypersurfaces in projective space
Abstract. This talk concerns the existence of curves with low gonality on smooth hypersurfaces $X\subset \mathbb{P}^{n+1}$. After reviewing a series of results on this topic, I will report on a recent progress on the subject in collaboration with F. Bastianelli, F. Flamini and P. Supino. In particular, we obtained that if $X\subset \mathbb{P}^{n+1}$ is a very general hypersurface of degree $d\geqslant 2n+2$, the least gonality of a curve $C\subset X$ passing through a general point of $X$ is $\gon(C)=d-\left\lfloor\frac{\sqrt{16n+1}-1}{2}\right\rfloor$, apart from some exceptions we list.
Rosa M. Miró-Roig (Universitat de Barcelona)
Title. On the existence of Ulrich bundles on smooth surfaces
Abstract. In my talk, I will discuss the existence of rank $r$ Ulrich bundles on a general surface $S\subset \PP^3$ of degree $d$. More concretely, I will address the problem of characterizing the set $\{ (r,d)\in \NN \mid \exits a rank $r4 Ulrich bundle on a general surface $S$ of degree $d$ in \PP^3 \}$ and I will summarize what it known so far.
Further material. Slides of the talk
Francesco Russo (Università di Catania)
Title. Resultants, discriminants, hessians III
Abstract. In the sixties Beniamino Segre published two notes with a similar title (I&II). We shall present a natural continuation of his results in the context of hypersurfaces with vanishing hessian. After reviewing the history of this subject, the known classification results and some examples, we shall present two new series of hypersurfaces with vanishing hessian with geometrical properties very different from the know ones (Gordan-Noether, Perazzo, Permutti, Ciliberto-Russo-Simis). The purpose of the talk is to put these new examples (and the previous ones) in the classical and modern framework of resultants, discriminants, Cayley Trick and Dual Cayley Trick, pursuing over the seminal approach of B. Segre. This is joint work with Rodrigo Gondim and Giovanni Staglianò.