Homological Mirror Symmetry (Mini-Course)

Following Katz-Nishinou, we will compute the number of lines on a quintic threefold in $\mathbb P^4$ by degenerating the quintic to the union of coordinate hyperplanes. This motivates degeneration formulae in Gromov-Witten theory that I will give another application of sketching the proof idea for a simple relationship between local and relative Gromov-Witten invariants. For the second half, I will explain the key notion of "basicness" alias "minimality" for log stable maps.