# Logarithmic Gromov-Witten invariants

 Homological Mirror Symmetry (minicourse) Topic: Logarithmic Gromov-Witten invariants Speaker: Helge Ruddat Affiliation: Johannes Gutenberg-Universität 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.