Tuesday 18 October, 11:00 - 12:00, IMPAN, room 321 - Discussion group
Wednesday 19 October, 11:00 - 12:00, IMPAN, room 403 - Giovanni Moreno, Secant varieties in hydrodynamic integrability.
Wednesday 19 October, 14:30 - 15:30, IMPAN, room 403 - Kristian Ranestad, Convex hull of surfaces in R^4.
Thursday 20 October, 16:10 - 18:00, hybrid: IMPAN room 405 and on zoom - Preworkshop teach-in on geometry of secants.
Friday 21 October, 11:00 - 12:00, IMPAN, room 321 - Luca Chiantini, On the coarse and fine structure of secant varieties part I.
Friday 21 October, 14:30 - 15:30, IMPAN, room 321 - Luca Chiantini, On the coarse and fine structure of secant varieties part II.
Giovanni Moreno, Secant varieties in hydrodynamic integrability
The first case of a PDE of physical interest which has been successfully integrated by the method of hydrodynamics reductions dates back to B. Riemann (1860). More than one century later, this very method has been generalised, by the work of several authors (J. Gibbon, S.P. Tsarev, D.J. Benney, E.V. Ferapontov et al.), to vaster classes of PDEs: those that turn out to be hydrodynamically integrable possess some peculiar geometric features, that admit a natural interpretation in terms of secant varieties of the cone of rank-one vertical tangent vectors to jet spaces.
Kristian Ranestad, Convex hull of surfaces in R^4
If S is a compact algebraic surface in a real 4-space, the boundary of its convex hull is a hypersurface. What is its equation and degree? I will present some results for surfaces of small degree, from recent work with Meroni and Sinn.
Luca Chiantini, On the coarse and fine structure of secant varieties
I will give a survey on some (classical and recent) geometric tools that characterize the study of the structure of secant varieties. I will start by describing with classical methods and recent advances on the behaviour of generic points. Then I will introduce some new methods for the study of specific points of secant varieties, with special focus on Veronese and Segre embeddings.
We will discuss some basic notions, notations and properties related to geometry of secants, in preparation to the workshop next week. Anyone is welcome to attend, but the primary focus will be on the participants of the workshop, who have not enough experience with the subject. The scope of the discussion should be limited to (not much more than) the content of the cheat-sheet (ściąga) for the workshop.