We begin a new reading group this term, on microlocal sheaves in symplectic geometry. The first talk will be given on Tuesday 25 October at 9:30 am. The room is not yet fixed, but we will meet in the differential geometry corridor shortly before. The speaker is Misha Verbitsky. His title is *“Derived categories”* and his abstract is below. We will also discuss the different sources we will read on the topic and arrange speakers.

I will say a couple of words about abelian categories, injective and projective objects. Then I would give a formal definition of a derived category and explain how it relates to injective and projective resolutions. I would end with a brief introduction to triangulated categories. The talk is supposed to be very elementary and I would prefer to go slowly and have more discussions in class.