Topics

The following is a list of potential topics for lectures by the seminar participants. It is not exhaustive; you are welcome to propose your own topic! You are also welcome to email us with suggested references for any given topic.

Topics claimed by a participant:

• Weighted limits and colimits.
  • Claimed by James Macpherson, who will tell us about weighted joins.
  • Ref: Max Kelly – Basic concepts of enriched category theory, Section 3.1; Martina Rovelli – Weighted limits in an (∞,1)-category.
• (∞,n)-categories.
  • Claimed by Björn Gohla, who will tell us about Segal n-categories.
  • Ref: Julia Bergner and Charles Rezk - Comparison of models for (∞,n)-categories, I and Comparison of models for (∞,n)-categories, II, Carlos Simpson - Homotopy theory of higher categories (draft version).
• The hypotheses: cobordism, tangle, homotopy, and/or stabilization.
  • Claimed by Rui Peixoto, who will tell us about the cobordism hypothesis.
  • Ref: John Baez and James Dolan - Higher-dimensional Algebra and Topological Quantum Field Theory, John Baez - The homotopy hypothesis.
  • Note: In the Baez-Dolan reference, the cobordism hypothesis is called “The Extended TQFT Hypothesis, Part I”.
• Operads and ∞-operads.
  • Claimed by João Candeias.
  • Ref: Jacob Lurie - Higher algebra, Chapter 2.
• Topological field theories or other functorial field theories.
  • Claimed by Nino Scalbi.
  • Ref: Jacob Lurie - On the classification of topological field theories, among others.

Topics still available:

• Straightening and unstraightening.
• Symmetric monoidal structures.
• The panorama of models for ∞-categories.
• Homotopy limits and colimits vs ∞-limits and ∞-colimits.
• Model categories vs ∞-categories.
• Enriched ∞-categories.
• (∞,2)-categories.
• Functor calculus.
• Embedding calculus.
• Derived deformation theory.
• Stable ∞-categories.