Programme
11:00
João Nunes (Instituto Superior Técnico, Lisboa)
Quantization and tropical geometry for toric manifolds
Let X be a toric manifold. We will describe families of Kahler
structures on X which are interesting from the point of view
of geometric quantization. Along each family,
the Kahler metric collapses in the Gromov-Hausdorff sense
to a Hessian metric on the moment polytope P.
Moreover, as the Kahler structure degenerates,
the amoebas for hypersurfaces in X tropicalize under
an appropriate Legendre transformation of P.
This is based on joint work with T.Baier, C.Florentino and J.Mourao.
14:00 Lothar Göttsche (ICTP, Trieste and MPI, Bonn)
Refined curve counting and refined Severi degrees.
This is report on joint works with Vivek Shende, Florian Block and Sam Payne.
An old conjecture of mine gives a generating function for the numbers of
$\delta$-nodal curves in linear systems on surfaces. In this talk we want
to propose a refinement of the conjecture, where the numbers of curves are
replaced by polynomials in a variable $y$, which for $y=1$ specialize to
the numbers of curves. For rational surfaces these refined invariants are
related to Welschinger invariants and have an
interpretation in tropical geometry.
15:00 Tea
15:30 Sergey Galkin (Universität Wien)
Mutations of potentials and their upper bounds
We introduce Berenstein's notion of upper bounds to theory
of mutations of potentials and prove an excessive
Laurent phenomenon (which now says - upper bounds are preserved
by mutations) using this new technique. The statement is quite general
and can be applied in different contexts where Laurent polynomials
and their mutations appear (e.g. Auroux's wall-crossing
in symplectic geometry and mirror symmetry).
This is a joint work with John Alexander Cruz Morales
(preprint IPMU 12-0110).
Organisers : Benoît Bertrand, Erwan Brugallé, Ilia Itenberg, Grigory Mikhalkin
Max Planck Intitute, Bonn, July 13th 2012
Max-Planck-Institut für Mathematik