Date:
Wed, 10/12/202511:00-13:00
Zoom link: https://huji.zoom.us/j/84891772698?pwd=Z3u0rPdbxCnMy23fJr2SXto9FaL3WW.1
Meeting ID: 848 9177 2698
Passcode: 346819
Title: The Bauer-Poulsen dichotomy for simplicial theories
Abstract: Affine logic is the fragment of continuous logic where the only allowed connectives are affine combinations. An affine theory is called simplicial if all of its type spaces are Choquet simplices. Many important examples of affine theories turn out to be simplicial, including the theory of measure-preserving systems of a countable group, the theory of tracial von Neumann algebras, and the affine parts of many classical and continuous first-order theories.
I will present results on simplicial theories in affine logic, obtained in joint work with Ben Yaacov and Tsankov. Our main focus will be on the following dichotomy result: for a complete simplicial theory, the extreme types form either a closed set or a dense set.
If time permits, I will also discuss the link between this result and a celebrated dichotomy theorem by Glasner and Weiss on simplices of invariant measures, as well as preliminary results toward a common generalization and applications.
Meeting ID: 848 9177 2698
Passcode: 346819
Title: The Bauer-Poulsen dichotomy for simplicial theories
Abstract: Affine logic is the fragment of continuous logic where the only allowed connectives are affine combinations. An affine theory is called simplicial if all of its type spaces are Choquet simplices. Many important examples of affine theories turn out to be simplicial, including the theory of measure-preserving systems of a countable group, the theory of tracial von Neumann algebras, and the affine parts of many classical and continuous first-order theories.
I will present results on simplicial theories in affine logic, obtained in joint work with Ben Yaacov and Tsankov. Our main focus will be on the following dichotomy result: for a complete simplicial theory, the extreme types form either a closed set or a dense set.
If time permits, I will also discuss the link between this result and a celebrated dichotomy theorem by Glasner and Weiss on simplices of invariant measures, as well as preliminary results toward a common generalization and applications.