The kernel for stratified Mukai flops

I will revisit the derived equivalence for stratified Mukai flops, which was established by Cautis-Kamnitzer-Licata (2009) and Halpern-Leistner--Sam (2016) using different methods. Using matrix factorizations of coherent sheaves, we show that these two approaches coincide and obtain a new, simpler Fourier-Mukai kernel for the equivalence (joint work with E. Segal).