Video URL http://pirsa.org/18050053
Skew Howe duality is based on a very simple observation: the set of n by m matrices has commuting action of SL_n and SL_m. We can use this observation to study morphisms of GL_m representations using GL_n. This perspective has proven very useful in recent years for studying quantum knot invariants and their categorifications. I will survey work in this direction from the last 10 years, including more recent developments concerning annular skew Howe duality and annular knot invariants.