Special Year 2016-17: Homological Mirror Symmetry

This talk will prove formality results for Fukaya categories in some examples following "The symplectic arc algebra is formal" by Abouzaid--Smith.

This talk will cover sections 2 and 3 of "The symplectic arc algebra is formal" by Abouzaid-Smith

I will explain the case of log Calabi-Yau surfaces, based on my previous works and my work in progress with Sean Keel.

I will explain the construction and the geometry of the non-archimedean SYZ fibration.

I will attempt to explain Costello's set up of the problem of perturbative quantization of a gauge theory in the Batalin-Vilkovisky formalism, thus allowing us to formulate the main results of Costello and Li.