# Jerusalem Mathematics Colloquium

Thursday, 10th January 2008, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Jake Solomon

(Princeton University)

"Open Gromov-Witten Theory and the structure of real enumerative
geometry"

** Abstract: **
I plan to illustrate the application of open Gromov-Witten theory to real
enumerative geometry through examples in the real projective plane. Lines
in the projective plane are algebraic curves of degree 1 and genus 0. The
beginning of plane geometry is the problem of determining the number of
lines through 2 points. In 1870, Zeuthen generalized this problem to the
problem of enumerating genus 0 plane curves of degree d through 3d-1
points. Recently, Welschinger introduced an analogous problem for signed
counts of real curves. Open Gromov-Witten theory explicitly relates the
real enumerative problem with its classical complex analog, simultaneously
solving both problems. The formulas are most naturally expressed as a PDE
very similar to the WDVV equation. Moreover, like the WDVV equation, the
PDE of open Gromov-Witten theory holds for arbitrary target manifolds.

Light refreshments will be served in the faculty lounge at 3:30.

List of talks, 2007-08

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