|Speaker:||Jacopo Stoppa (Cambridge)|
|Title:||D0-D6 states counting and Gromov-Witten invariants.|
|Date:||Tue, Mar 16, 2010, 13:15 - 14:45|
|Place:||Seminar Room A|
Part 1 (20 min):
In the physics literature Donaldson-Thomas invariants denote the virtual counts of certain instantons, which correspond mathematically to ideal sheaves of points and curves on a Calabi-Yau 3-fold. A corresponding mathematical theory counting higher rank vector bundles and sheaves was initiated by Thomas and recently completed by Joyce-Song. After a brief introduction to this circle of ideas I will concentrate on counting D0-D6 states, showing that this is already quite subtle, and outlining the connection with work of Toda and previous physical computations of Szabo and others.
Part 2 (60 min):
I will describe a correspondence between the above D0-D6 Donaldson-Thomas invariants on a Calabi-Yau 3-fold (essentially counting 0-dimensional perturbations of the trivial vector bundle of arbitrary rank) and Gromov-Witten invariants counting rational curves on blowups of a weighted projective plane. This correspondence extends one found by Gross-Pandharipande where instead of sheaves one has representations of Kronecker quivers. The proof is based on the Kontsevich-Soibelman wall-crossing formula. A possible physical background for this result is given by work of Denef and Moore.