Past Algebraic Geometry Seminar

17 October 2017
Thomas Prince

Given a Fano manifold we will consider two ways of attaching a (usually infinite) collection of polytopes, and a certain combinatorial transformation relating them, to it. The first is via Mirror Symmetry, following a proposal of  Coates--Corti--Kasprzyk--Galkin--Golyshev. The second is via symplectic topology, and comes from considering degenerating Lagrangian torus fibrations. We then relate these two collections using the Gross--Siebert program. I will also comment on the situation in higher dimensions, noting particularly that by 'inverting' the second method (degenerating Lagrangian fibrations) we can produce topological constructions of Fano threefolds.

  • Algebraic Geometry Seminar
28 March 2007
David Eisenbud, MSRI
    One natural question in interpolation theory is: given a finite set of points in R^n, what is the least degree of polynomials on R^n needed to induce every function from the points to R? It turns out that this "interpolation degree" is closely related to a fundamental measure of complexity in algebraic geometry called Castelnuovo-Mumford regularity. I'll explain these ideas a new application to projections of varieties.  
  • Algebraic Geometry Seminar