Homological Mirror Symmetry (Mini-Course)

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.