Seminarium: Geometry and physics
- Datum: –16.00
- Plats: Ångströmlaboratoriet Häggsalen, Ångströmlaboratoriet
- Föreläsare: (1) Arkady Vaintrob (University of Oregon), (2) Robert Berman (Chalmers)
- Arrangör: Avdelningen för teoretisk fysik, institutionen för fysik och astronomi
- Kontaktperson: Tobias Ekholm, Maxim Zabzine
(1) I will discuss a cohomological field theory related to a quasihomogeneous singularity W with a group G of its diagonal symmetries (a Landau-Ginzburg A-model). The state space of this theory is the equivariant Milnor ring of W and its correlators are analogs of the Gromov-Witten invariants for the non-commutative space associated with the pair (W,G). In the case of simple singularities of type A they control the intersection theory on the moduli space of higher spin curves. The construction is based on categories of equivariant matrix factorizations.
(2) In this talk I will describe a statistical mechanical approach to the construction of Kähler-Einstein metrics on a complex algebraic variety X, i.e. Kähler solutions to Einstein's vacuum field equations. The microscopic theory is given by a canonical fermion gas on X whose one-particle states are pluricanonical holomorphic sections on X. The convergence problem in the case of a positive cosmological constant (i.e. the case when X is a Fano manifold) is still open and turns out to be closely connected to the Yau-Tian-Donaldson conjecture in Kähler geometry. Some intriguing relations to the AdS/CFT correspondence will also be pointed out.