Abstract:

In this talk, I’ll explain our upcoming work on Fukaya categories of complexified complements of polarized hyperplane arrangements. We proved that the partially wrapped Fukaya category of a simple hyperplane arrangement, stopped by the polarization, is derived Morita equivalent to the derived category of modules over the B-algebra of this hyperplane arrangement constructed by Braden-Licata-Proudfoot-Webster, hence verifying a conjecture proposed by Lauda, Licata and Manion. If time permits, I'll also talk about how to prove the conjecture without simpleness assumption. This is based on joint work in preparation with S. Lee, Y. Li and C.-Y. Mak.