Seminar on infinity categories

The student seminar on infinity categories is a continuation of last year's seminar on the same topic. The seminar meets Thursdays at 10:30 am-12:00 pm in Math 731 during Fall 2019.

The goal for this semester is to study the basics of stable infinity categories, in particular understand the infinity-enhancements of derived categories.

References

J. Lurie, Higher Algebra - primary reference for the seminar, more precisely, its first chapter.
J. Lurie, Higher Topos Theory - a thorough reference for the topic of quasi-categories.
M. Groth, A short course on infinity categories - a concise and non-technical survey on quasi-categories.
Ch. Rezk, Stuff about quasi-categories - stuff about quasi-categories.
V. Hinich, Lectures on infinity categories - lecture notes aiming at model-free description of infinity categories.

Program

1.	Aug 29	(P. Čoupek) Review of the basics of quasi-categories.
2.	Sep 5	(J. Knight) Joins, initial (final) objects and (co-)limits.
3.	Sep 12	(J. Knight) Pointed infinity categories, fibers, cofibers, triangles, definition of a stable category.
4.	Sep 26	(P. Čoupek) Review of additive, Abelian and triangulated categories.
5.	Oct 3	(P. Čoupek) Suspension and loop functor on a stable infinity category.
6.	Oct 18	(P. Čoupek) Additivity of the homotopy category of a stable infinity category and distinguished triangles on it.
7.	Oct 25	(P. Čoupek) Homotopy category of a stable infinity category is triangulated.
8.	Oct 31	(Z. Himes) exact functors and closure properties of stable infinity categories, t-structures on triangulated category.