Seminar: Diagram Categories
in Homotopy Theory

This is the website for an online seminar on the general topic of Diagram Categories in Homotopy Theory. The seminar meets approximately once per month in term time.

The time of the meeting is 1pm Pacific Time, unless otherwise stated.

The seminar is affiliated with a Collaborative Research Group (CRG) sponsored by PIMS.

The Zoom link for this seminar is circulated by email and through departmental seminar announcements.

• To join the mailing list for this seminar, use the web interface for UBC mailing lists.

• In case of difficulty, contact the administrator of the mailing list: Ben Williams tbjw@math.ubc.ca

Past Talks

Recordings of talks are posted within a week of the talk itself, provided we have permission.

• October 28, 2025 Maxine Calle (U Penn): Cut-and-paste K-theory of manifolds and SK-automorphisms
  Abstract: Given two manifolds M and N, one can ask whether it is possible to cut M up into pieces and reassemble them to obtain N. This “cut-and-paste” (SK) relation fits into the framework of scissors congruence K-theory, which is an extension of higher algebraic K-theory to more general settings. In this talk, we will discuss a new model for the cut-and-paste K-theory of manifolds, modeled on Waldhausen’s S-dot construction, and describe how the first K-group is related to SK-automorphisms of manifolds, i.e. the ways a manifold can be SK-equivalent to itself. This talk is based on joint work with Maru Sarazola.

No recording was made of this talk. Slides are available here.

• October 7, 2025 Niall Taggart (Queen's University Belfast): Algebraic models for functor calculus
  Abstract: There is a striking and useful analogy between equivariant homotopy theory and functor calculus. In the equivariant setting, Greenlees conjectured that the category of rational G-spectra has an algebraic model - meaning it is equivalent to the derived category of an abelian category with desirable finiteness properties. This talk will examine the functor calculus counterpart of this conjecture in (potentially) more than one flavour of functor calculus. (Joint work with D. Barnes and M. Kedziorek.)

Recording: https://www.mathtube.org/lecture/video/algebraic-models-functor-calculus