An algebraic Gromov-Witten type theory from D-strings


Chien-Hao Liu

15:30:00 - 17:00:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

From Witten's work on topological strings that related fundamental string world-sheet instantons with Gromov's J-holomorphic curves in symplectic geometry, which then was recast by Kontsevich to stable maps in algebraic geometry, it is very natural to anticipate a similar theory for D-strings in both the sympletic and the algebraic geometry. In this lecture, I'll explain a new algebraic Gromov-Witten type theory based on D-string world-sheet instantons in the compactification of Type IIB string theory on a Calabi-Yau 3-fold. (1) How the works of D.S. Nagaraj and C.S. Seshadri on vector bundles on nodal curves in 1990s motivate what candidate objects to add in order to compactify the related moduli spaces and (2) how the techniques of Jun Li and Baosen Wu in their study of degenerations of relative coherent sheaves in 2011 are adapted to prove a compactness theorem for the moduli space will be highlighted. Time permits, I'll comment on a few key questions beyond.

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