## Logistics

• Seminar begins: October 18th, 2016.
• Seminar time: Tuesdays 16:00-18:00
• Seminar location: M103
• George Raptis and I are available by appointment for assisting with talk preparation (we encourage speakers to take advantage of this).
• Detailed list of topics.
• Previous seminar: homepage.

## Plan

The purpose of this seminar is to study the general theory of higher categories and its applications. Higher category theory, especially the theory of $$(\infty,n)$$-categories, provides a powerful language for handling the complexity of encoding relations, relations between relations, and "so on".

This language has been applied to questions in homotopy theory, derived algebra, derived algebraic geometry, topological field theory, and computer science. In addition to conceptualizing classical results by placing them in a more general context, they have proven essential for studying homotopy theories themselves.

The exact subject matter of the seminar will be determined by the participants and their interests. In particular, participants are encouraged to speak about related topics arising in recent research papers. We also encourage participants to give talks on various foundational topics including, but not limited to, models for $$(\infty,n)$$-categories, presentable $$\infty$$-categories, higher topoi, stable $$\infty$$-categories, (higher) operad theory, derived schemes, (derived) stacks, the cobordism hypothesis, bicategories, higher Picard and Brauer groups...and beyond!

Participants should have some familiarity with the theory of $$\infty$$-categories.

## Schedule

• 18.10.2016 (Justin Noel and Georgios Raptis) Introduction and program.
• 25.10.2016 (Kim Nguyen) Giraud axioms.
• 8.11.2016 (Georgios Raptis) Sheaves and Grothendieck topologies in $$\infty$$-category theory.
• 15.11.2016 (Georgios Raptis) Sheaves and Grothendieck topologies in $$\infty$$-category theory part II.
• 22.11.2016 (Christoph Schrade) Kan extensions.
• 29.11.2016 (Daniel Schaeppi) Kan extensions part II
• 6.12.2016 No seminar (winter school)
• 13.12.2016 (Justin Noel) Equivariant homotopy theory.
• 20.12.2016 (Justin Noel) More equivariant homotopy theory.
• 10.1.2017 (Markus Land) Spectrum objects and stabilization
• 17.1.2017 (Markus Land) More spectrum objects and stabilization
• 24.1.2017 (Daniel Schaeppi) T-structures and the Dold-Kan-Lurie correspondence for stable -categories
• 31.1.2017 (Christoph Eibl) Derived $$\infty$$-categories.
• 7.2.2017 (Kim Nguyen) Enriched $$\infty$$-categories after Gepner-Haugseng.