Mathematics

Dr. Umesh Dubey
Indian Institute of Science, Bangalore

The bounded derived category of coherent sheaves on a smooth projective variety provides many interesting relations between varieties. An important tool in the study of structure of such categories is semi-orthogonal decompositions which also give rise to Homological projective duality.
 The theory of Homological projective duality was introduced and developed by Kuznetsov. This categorical level duality captures some interesting geometric relations like relation between quadrics and hyper elliptic curves, exploited in the work of Desale and Ramanan, based on some ideas of A. Weil.
 In this talk we first introduce basic notions and then discuss some examples of Homological projective dual varieties.