Enumerative invariants in algebraic geometry and string theory
Cetraro, June 6-11, 2005

Open strings

Prof. Marcos Marino, CERN, Geneve, Switzerland


In these set of lectures I will present the main results of the theory of the topological vertex, which computes Gromov-Witten invariants of toric Calabi-Yau threefolds. I will emphasize its physical origins and in particular the connection to Chern-Simon theory and invariants of knots.
1. An overview of Chern-Simons theory.

2. Topological strings on Calabi-Yau threefolds: general aspects.

3. Chern-Simons theory and topological strings.

4. Toric geometry and the topological vertex.

The only prerequisite for these lectures is probably some familiariry with Gromov-Witten invariants. As for references, I will rely very much on

M. Marino, "Chern-Simons theory and topological strings", hep-th/0406005,

although my presentation will be much more mathematically oriented.

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