seminar at SISSA

[Emanuele Tuillier Illingworth]

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MATHEMATICAL PHYSICS SECTOR SEMINAR
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Title:  Donaldson Thomas invariant of P^1 scroll

Speaker: Hua-Liang, Chang

Time: 14/ Nov/ 2007. 2:00-3:00.  Room D.

Abstract:

(2:00-2:50) I will review the definition of GW-invariants, give the definition of Donaldosn Thomas invariants and descibe the M.N.O.P. conjecture about them. The degeneration program raised by R.Pandharipande will be discussed, and thus the importance of "relative P^1 scroll" will be revealed. And then I will diverse to a new localization method for GW theory on p_g>0 kaehler surfaces: the two-form localization given by T.Parker and J.H, Li decides the complete factors that decides whole GW theory of p_g>0 surfaces.

(3:00-4:00) I will then go to J, Li and Y-H,Kiem's algebraic approach to the two-form localization. And then the two-form localization for Donaldson-Thomas invariant of P^1 scroll will be produced. In the end I will discuss some problems around this directions; and a new direction given by R, Pandharipande and R, Thomas on the enumerations via derived objects.
The remaining time will be left for questions and discussions.