Logarithmic Gromov-Witten invariants

Homological Mirror Symmetry (minicourse)
Topic:Logarithmic Gromov-Witten invariants
Speaker:Helge Ruddat
Affiliation:Johannes Gutenberg-Universit├Ąt Mainz; Member, School of Mathematics
Date:Wednesday, October 26
Time/Room:10:45am - 12:00pm/S-101

Logarithmic Gromov-Witten invariants generalize usual and relative Gromov-Witten invariants and were first suggested by Siebert and then recently introduced by Gross-Siebert and Abramovich-Chen. Applications include more general degeneration formulas and the intrinsic construction of mirror duals to a log Calabi-Yau pair $(X,D)$. The key results so far are log stable reduction and the existence of a natural virtual fundamental class as well as by means of the notion of "basicness" the algebraicity and quasi-compactness of the associated moduli spaces. I will explain the key features of these interesting invariants that closely relate to tropical curves.