Titles and abstracts:
Victor Batyrev and Karin Schaller:
"Stringy Chern classes of singular toric varieties and their applications''
Let X be a normal projective Q-Gorenstein variety with at worst log-terminal singularities. We prove a formula expressing the total stringy Chern class of a generic complete intersection in X via the total stringy Chern class of X. This formula is motivated by its applications to mirror symmetry for Calabi-Yau complete intersections in toric varieties. We compute stringy Chern classes and give a combinatorial interpretation of the stringy Libgober-Wood identity for arbitrary projective Q-Gorenstein toric varieties. As an application we derive a new combinatorial identity relating d-dimensional reflexive polytopes to the number 12 in dimension d>=4.
"12-Formulas in symplectic geometry and combinatorics''
In this talk I will explain how many interesting combinatorial formulas can be derived from equivariant symplectic geometry, especially from the rigidity of some equivariant bundles and the existence of a moment map for Hamiltonian torus actions. This allows us to derive a generalisation of the ``12 and 24 formulas'' for reflexive polytopes of dimensions 2 and 3 to Delzant reflexive polytopes of every dimension.
Moreover the class of reflexive GKM graphs, which generalises that of Delzant reflexive polytopes, is introduced. For these graphs analogue
combinatorial formulas hold.
This talk is based on the paper ``12, 24 and beyond'' by L. Godinho, F. von Heymann and myself.