27 March 2025, 13:15 (EET), Hall 300, INRNE

• Mikhail (Misha) Shkolnikov (IMI-BAS)
• Title: An affine convex flow
• Abstract: Which geometry describes physical reality? From a common everyday perspective, it is Euclidean geometry, with such familiar invariant notions as distances, angles, volumes, and areas. From a standpoint of special relativity, one needs to unify space and time, obtaining Minkowski space. From Erlangen program perspective, the first geometry is characterized by the usual rotational group of symmetries, and the second is by the group of Lorentz transformations. A more general framework is provided by affine geometry, where distances and angles lose their relevance since the symmetries are now all linear transformations preserving the volume -- in particular, any notion natural to affine geometry descends to geometries with smaller symmetry groups. In this talk based on a joint project with Nikita Kalinin and Ernesto Lupercio, I will report on a recent discovery of a convex smoothing flow in affine geometry. This new development stems from our study of the tropical scaling limit of strings in the context of self-organized criticality, the history and motivation of which will be thoroughly covered.
• Slides