This is a talk I will give on Monday, December 15th, 2025 at the Seminar on Domain Theory, hosted by the TianYuan Mathematics Center in Kunming, Yunnan, PRC. The organizers are Hui Kou (寇辉, Sichuan University, Chengdu, Sichuan, PRC), Xiaodong Jia (贾晓东, Hunan University, Changsha, Hunan, PRC), and myself.
Abstract
I will give an introduction to barycentric algebras, the plain, the preordered and the (semi)topological. Those include all convex subsets of (plain, preordered, semitopological) cones, but there are a few more. Then I will turn to pointed barycentric algebras, the preordered and the (semi)topological. The leading examples are spaces of probability, and subprobability valuations (or measures).
Slides
The full slides, with animation steps; the shorter presentation, without them.
Videos
- Cones: what we know about them (9:48)
- Barycentric algebras: the plain, the preordered and the (semi)topological (24:32)
- Pointed barycentric algebras: the preordered and the (semi)topological (19:02)
