Gromov�Witten invariants and topological strings: a progress report

• Autores: Marcos Mariño
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé, Javier Soria de Diego, Juan Luis Varona Malumbres, Joan Verdera, Vol. 3, 2006, ISBN 978-3-03719-022-7, págs. 409-420
• Idioma: inglés
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• Resumen

  • In this talk I summarize recent progress in the theory of Gromov�Witten invariants from topological string theory and string dualities. On the one hand, large N dualities have led to the theory of the topological vertex, which solves Gromov�Witten theory to all genera on toric, noncompact Calabi�Yau threefolds. On the other hand, heterotic/type II duality and the holomorphic anomaly equations can be used to analyze Gromov�Witten theory in some simple compact examples. I sketch the physical ideas behind these results and connect the results obtained in physics with the results obtained in algebraic geometry.