Topology of real algebraic varieties near the tropical limit

Abstract: Describing all the possible topologies of real projective hypersurfaces of fixed degree and dimension is a very difficult problem, going back to Hilbert's sixteenth problem. We will show some progress on this problem when assuming that the variety is closed to some degeneration, called tropical limit. We will recall some basics on real algebraic geometry and tropical geometry and then relate the Betti numbers of a real variety near the tropical limit to the dimension of some tropical homology groups (by the way of a spectral sequence). It is based on joint works with Kris Shaw and Johannes Rau and Kris Shaw.

Mathematics

Audience: researchers in the topic

Geometry Seminar - University of Florence

Series comments: If you are interested in attending, please send a message to daniele.angella@unifi.it or francesco.pediconi@unifi.it.