|Location:||MSRI: Simons Auditorium|
Yanki Lekili: "Broken Lefschetz fibrations"
Tristram Bogart: "Tropical rational curves on tropical hypersurfaces (II)"
In the 1980's, Herbert Clemens proved that a general hypersurface in P^n of degree at least 2n-1 contains no rational curves and conjectured that a general quintic threefold in P3 contains only finitely many rational curves of fixed degree. In ongoing work with Erwan Brugallé and Ethan Cotterill, we develop a tropical approach to these problems, using the technique of floor diagrams. In this talk I will describe our proof strategy for the tropical analogue of Clemens' result in dimension three.