## Logistics

• Seminar begins: April 11th, 2016.
• Seminar time: Mondays 16:00-18:00
• Seminar location: M101
• George Raptis and I are available by appointment for assisting with talk preparation.
• Detailed list of topics.
• Detailed schedule.

## 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

• 11.4.2016 (Justin Noel and Georgios Raptis) Introduction and program.
• 18.4.2016 (Daniel Schaeppi) The Riehl-Verity approach to quasicategories I.
• 25.4.2016 (Daniel Schaeppi) The Riehl-Verity approach to quasicategories II.
• 2.5.2016 (Kim Nguyen) Cartesian fibrations.
• 9.5.2016 (Tom Fiore) Adjoint functors between $$\infty$$-categories (notes).
• 23.5.2016 (Christoph Schrade) Presentable $$\infty$$-categories I.
• 30.5.2016 (Christoph Schrade) Presentable $$\infty$$-categories II.
• 6.6.2016 (Koen van Woerden) Homotopical algebra
• 13.6.2016 (Justin Noel) Marked simplicial sets and the cartesian model structure (notes).
• 20.6.2016 (Oriol Raventos) Monoidal $$\infty$$-categories
• 27.6.2016 (Kim Nguyen) The Ando-Blumberg-Gepner-Hopkins-Rezk approach to Thom spectra.
• 4.7.2016 (Christoph Eibl) Homotopical sheaf theory
• 11.7.2016 (Georgios Raptis) $$\infty$$-Topoi.