Logistics

  • Seminar begins: April 25th, 2017.
  • Seminar time: Tuesdays 16:00-18:00
  • Seminar location: M101
  • 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

  • 25.4.2017 (Christoph Eibl) Cartesian monoidal \(\infty\)-categories (DAG II.1.1-1.2)
  • 2.5.2017 (Justin Noel) \(\infty\)-operads.
  • 9.5.2017 (Matan Prasma) Formal properties of algebras (DAG II.1.4-1.5)
  • 16.5.2017 (TBD) Tensored \(\infty\)-categories and non-unital algebras / (DAG II.2.1 + Higher algebra 4.2.1).
  • 23.5.2017 (Kim Nguyen) Formal properties of modules (DAG II.2.2-2.4).
  • 30.5.2017 (Georgios Raptis) Monoidal model categories and modules (DAG II.1.6+2.5).
  • 6.6.2017 (Holiday) No seminar.
  • 13.6.2017 (Christoph Schrade) Presentably symmetric monoidal \(\infty\)-categories after Nikolaus-Sagave.
  • 20.6.2017 (Markus Land) The monoidal structure on presentable \(\infty\)<\li2>-categories (DAG II.4.1 + HA 4.8.1).
  • 27.6.2017 (TBD) The smash product monoidal structure (DAG II.4.2 + HA 4.8.2).
  • 4.7.2017 (TBD) \(A_\infy\)-rings, their modules, and tensor products (DAG II.4.3-4.5).
  • 11.7.2017 (Daniel Sch├Ąppi) Properties of modules (DAG II.4.6-4.7).
  • 18.7.2017 (Kim Nguyen) Enriched (\infty\)-categories
  • 25.7.2017 (TBD) TBD.