Wednesday, Dec 9, 4.40-6.40, Churchill (building 54 on the map), room 101, Ivan's notes.

Thursday, Dec 10, 1-3, Shillman (building 30 on the map), room 315, Ivan's notes.

Friday, Dec 11, 10am-12, Shillman (building 30 on the map), room 415.

The lectures will be preceded by two lectures on Fourier-Mukai transforms by Benjamin Schmidt (Friday, Dec 4, 5.10-7, Location MIT, E17-133) and Xiaolei Zhao (Tuesday, Dec 8, 5.45-8, Location MIT, E17-129).

Benjamin Schmidt, Introduction to Derived Categories and Fourier Mukai Transforms.

Abstract: I will give a light introduction to the theory of bounded derived categories of coherent sheaves on smooth projective varieties. In particular, some of the issues arising from bad properties of the category of coherent sheaves will be pointed out. I will then talk about Fourier Mukai transforms in some more detail. One of the key results in this area due to Orlov says that every fully faithful functor between derived categories of coherent sheaves that admits right and left adjoints is a Fourier Mukai transform.

Xiaolei Zhao, Spherical objects, braid group actions and the Mukai flop, Ivan's notes.

Abstract: We will first introduce the notion of spherical objects and see how they induce autoequivalences of derived categories. When we have a configuration of spherical objects, this gives rise to a braid group action on the category. For the second part, we will construct the Mukai flop, and show that derived categories of varieties connected by a Mukai flop are equivalent. These will be prerequisites for Joel's lectures, and we will follow the streamline in section 8.1, 8.2, 11.4 of Huybrechts' book.