Abstract:  This is a series of two lectures on categorifying quantum group U_q(g) using Fukaya categories proposed by Mina Aganagic. In the first lecture, we will give an introduction to the theory, focusing on the geometric setup, basic calculations and connection to representation theory; in the second lecture we will discuss the TQFT structures underlying our theory, proposing the definition of Hopf(ish) category as a categorication of Kapranov-Schechtmann’s factorizable perverse sheaf and primitive bialgebra.