Logistics

• Seminar begins: April 9th, 2018.
• Seminar time: Tuesdays 16:00-18:00
• Seminar location: M311
• George Raptis and I are available by appointment for assisting with talk preparation (we encourage speakers to take advantage of this).
• Detailed preliminary schedule with references.
• Previous seminars:
  • Summer 2016.
  • Winter 2016.
  • Summer 2017.
  • Winter 2017.

  Specialized Plan for the 2018 Summer Semester

  This semester we will focus on models for \((\infty,n)\)-categories. This will include comparisons and applications. Of special interest are internal category objects in \((\infty,n-1)\)-categories (i.e., higher Segal categories and Segal spaces) and small models (e.g., stratified simplicial sets, \(\theta_n\)-sets). The primary application of interest for us will be the rigorous formulation and the sketch proof of the Baez-Dolan cobordism hypothesis by Jacob Lurie.

  General Plan

  The general 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

  • 10.4.2018 (Justin Noel) Introduction, motivation, and overview of the program.
  • 17.4.2018 (Justin Noel) Rezk's complete Segal spaces.
  • 24.4.2018 (Kim Nguyen) The Joyal-Tierney equivalences between complete Segal spaces and quasicategories.
  • 8.5.2018 (OPEN) Segal \((\infty,n)\)-categories and comparisons.
  • 15.5.2018 (Daniel Schäppi) Higher Segal spaces and comparisons.
  • 29.5.2018 (Ulrich Bunke) Cobordism categories and topological field theories.
  • 5.6.2018 (Daniel Schäppi) Fully dualizable objects and the cobordism hypothesis.
  • 12.6.2018 (Georgios Raptis) The sketch proof of the cobordism hypothesis.
  • 19.5.2018 (Harry Gindi) The \(\theta\)-construction.
  • 26.5.2018 (Harry Gindi) Ara's theory of \(\theta_n\)-sets.
  • 3.7.2018 (Kim Nguyen) Equivalence of models for \((\infty,n)\)-categories
  • 10.7.2018 (OPEN) The unicity theorem of Barwick-Schommer-Pries.