Talk

AG Preprint Seminar (Reading Seminar Group SAG of Prof. D. Huybrechts)

In Lurie's article on the Cobordism Hypothesis, he discusses a description of symmetric monoidal (∞,n)-categories with duals for objects and certain adjoints as "chain complexes" of symmetric monoidal ∞-categories with duals, but does not give a proof. I will discuss an approach to proving this based on a general description of closed symmetric monoidal V-enriched ∞-categories as lax symmetric monoidal functors to V. This is work in progress with Thomas Nikolaus.

Homological mirror symmetry (HMS), proposed by Kontsevich, conjectures a categorical equivalence between the Fukaya category of a symplectic manifold and the derived category of coherent sheaves on its mirror scheme. We recall the basic formulation of HMS together with several classical examples that illustrate this correspondence.

Infinitesimal Einstein deformations  are solutions of the linearised Einstein equation. They can be considered as potential tangent vectors to curves of Einstein metrics. An important question is to decide for a given infinitesimal Einstein deformations whether it is integrable, i.e. indeed tangent to such a curve.  In 1981 Koiso introduced an obstruction against integrability of infinitesimal Einstein deformations. However, so far the obstruction was computed only in very few cases.