Appears in collection : Algèbre, Géométrie et Physique : une conférence en l'honneur

I will report on a program to construct Landau-Ginzburg mirrors to affine varieties from the perspective of the SYZ conjecture and prove homological mirror symmetry for these mirror pairs. The wrapped Fukaya categories that appear in the statement of homological mirror symmetry in this setting will be discussed, focusing especially on the simplest non-trivial example: the pair of pants.Parts of this work are joint with M. Abouzaid, A. Efimov, L. Katzarkov and D. Orlov.