Homological Projective Duality for determinantal varieties

In this talk, I will describe pairs of homologically projective dual determinantal varieties, and some applications of this result. The varieties in question are cut out by minors of an $n \times m$ matrix of linear forms on a given projective space. As one application, we obtain new pairs of derived-equivalent Calabi-Yau manifolds. This is a joint work with M. Bolognesi and D. Faenzi.