In this talk we will first define refined tropical invariants (Following Block-Goettsche and
Goettsche-Schroeter) which are Laurent polynomials in one variable y, that under some some
appropriate conditions, for y=1 yield Gromov Witten invariants, and for y=-1 yield Welschinger
invariants of toric del Pezzo surfaces, that count complex, resp. real
plane tropical curves
passing through a generic configuration of points.
Then we will define a refinement of arbitrary rational tropical descendant invariants, that
count plane tropical curves that pass through a more generic configuration of points.
Joint work with E. Shustin.
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