Semiorthogonal decompositions of derived categories of Fano varieties and Ulrich bundles

After its discovery, semiorthogonal decomposition has been one of the most important tools to understand derived categories of coherent sheaves on algebraic varieties. In this talk, I will discuss semiorthogonal decompositions of derived categories of Fano varieties and their applications to the study of Ulrich bundles on them. This talk is based on joint works with Yonghwa Cho, Young-Hoon Kiem, In-Kyun Kim, Yeongrak Kim, Hwayoung Lee and Kyeong-Dong Park.