Geometry

Ivo Düntsch presents an algebraic treatment of the ternary betweenness relation familiar from geometry. The talk introduces betweenness algebras and the logic K^#, which uses two complementary binary modalities. Its algebraic models are Boolean algebras equipped with two binary modal operators linked by a connecting condition. This extends unary mixed logic and increases the expressive power of classical modal logic. The presentation develops properties of these structures from joint work with R. Gruszczyński and P. Menchón at Nicolaus Copernicus University. Online via Chapman University GALAI Zoom. Wednesday 30 September 2026, 14:30 PDT (America/Los_Angeles; UTC−7). Use the current Zoom link at the top of the organizer’s seminar page. Organized by Peter Jipsen at Chapman’s Center of Excellence in Computation, Algebra and Topology. The usual seminar slot ends at 15:45; no event-specific end time is given. This listing advertises the remote option.

Oden Institute Seminar by Rex Ying (Yale University) on how non-Euclidean geometries, particularly hyperbolic geometry, can enhance foundation models by better capturing hierarchies and symmetries in real-world data, with applications across Transformers, language model training, multimodal systems, and recommender systems.

Ivo Düntsch presents an algebraic treatment of the ternary betweenness relation familiar from geometry. The talk introduces betweenness algebras and the logic K^#, which uses two complementary binary modalities. Its algebraic models are Boolean algebras equipped with two binary modal operators linked by a connecting condition. This extends unary mixed logic and increases the expressive power of classical modal logic. The presentation develops properties of these structures from joint work with R. Gruszczyński and P. Menchón at Nicolaus Copernicus University. Online via Chapman University GALAI Zoom. Wednesday 30 September 2026, 14:30 PDT (America/Los_Angeles; UTC−7). Use the current Zoom link at the top of the organizer’s seminar page. Organized by Peter Jipsen at Chapman’s Center of Excellence in Computation, Algebra and Topology. The usual seminar slot ends at 15:45; no event-specific end time is given. This listing advertises the remote option.

Michael Hutchings introduces Reeb vector fields and explains why their periodic orbits are substantially better understood in three dimensions through Seiberg-Witten theory. The colloquium develops Irie's closing lemma, which creates a periodic orbit through a selected region after a small perturbation, and discusses a quantitative refinement connecting the perturbation size to an upper bound on the orbit period.