DWIC: Dg With Infty Categories Seminar (Fall 2021)

The main topics for this seminar are dg categories and infinity categories. Our main references for dg categories are [K] and [T], and our main references for infinity categories are ???

Schedule

Week 1: Triangulated/derived categories
Week 2: Dg categories part I: basic definitions, functors, examples, and pretriangulated dg categories
Week 3: Previous talk continued
Week 4: Dg categories part II: symmetric monoidal structure, homotopy category of dg category, and localization
Week 5: Infty categories part I
Week 6: Infty categories part II
Week 7: Infty categories part III
Week 8: ???
Week 9: ???
Week 10: ???
Week 11: ???
Sept 27
Fan Zhou
Review of triangulated and derived categories, notes
I will introduce the basic language of triangulated and derived categories, along with applications to derived functors.
Oct 04
Matthew Hase-Liu
Introduction to dg categories
I will talk about dg categories, dg functors, and why we care about these constructions in the context of triangulated categories. To this end, we'll discuss pretriangulated dg categories, which generalize the shift and mapping cone operations on the level of complexes.
Oct 11
Matthew Hase-Liu
Introduction to dg categories continued
I will finish off what I didn't cover last time.
Oct 18
Ivan Zelich
Derived Morita Equivalence
We discuss generalising Morita Equivalence in the DG-category setting. Consequently, we will introduce suitable notions of projectivity, i.e. Tilting complexes, and how all this relates to the homotopy theory of dg categories.