Cluster algebras: from finite to infinite -- Sira Gratz
Abstract: Cluster algebras were introduced by Fomin and Zelevinsky at the beginning of this millennium. Despite their relatively young age, strong connections to various fields of mathematics - pure and applied - have been established; they show up in topics as diverse as the representation theory of algebras, Teichmüller theory, Poisson geometry, string theory, and partial differential equations describing shallow water waves. In this talk, following a short introduction to cluster algebras, we will explore their generalisation to infinite rank.
Modelling the effects of data streams using rough paths theory -- Hao Ni
Abstract: In this talk, we bring the theory of rough paths to the study of non-parametric statistics on streamed data and particularly to the problem of regression where the input variable is a stream of information, and the dependent response is also (potentially) a path or a stream. We explain how a certain graded feature set of a stream, known in the rough path literature as the signature of the path, has a universality that allows one to characterise the functional relationship summarising the conditional distribution of the dependent response. At the same time this feature set allows explicit computational approaches through linear regression. We give several examples to show how this low dimensional statistic can be effective to predict the effects of a data stream.