[geometry-ml:01035] Seminar at IPMU 3/16 Stoppa

[Satoshi Kondo]

Dear colleagues:

We announce the following seminar at IPMU
(the Institute for the Physics and Mathematics of the Universe).

Regards,

Satoshi Kondo (IPMU)
http://ipmu.jp/

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Speaker: Jacopo Stoppa (Cambridge)

Date: Mar.16 (Tue) 2010, 13:15-14:45

Place:  Seminar Room A

Title: D0-D6 states counting and Gromov-Witten invariants

Abstract:

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.
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You can check the location from
http://www.ipmu.jp/access/img/KashiwaCampusMap.png

The schedule of the seminar can be checked from
http://db.ipmu.jp/seminar/