Wochenplan des Fachbereichs Mathematik und Informatik

Abstract: Let M be a Riemannian manifold and let G be a compact Lie group acting on M effectively and by isometries. It is well known that a lower bound of the sectional curvature of M is again a bound for the curvature of the quotient space of the action, which is an Alexandrov space of curvature bounded below. Moreover, the analogous stability property holds for metric foliations and submersions. Although this does not hold for Ricci curvature, a corresponding stability property does hold for synthetic Ricci curvature lower bounds. Specifically, for quotients of RCD*(K,N)-spaces under isomorphic compact group actions and, more generally, under metric-measure foliations and submetries. In this talk I will discuss the proof of this result as well as some geometric applications. This is joint work with Martin Kell, Andrea Mondino and Gerardo Sosa.

A first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition. Equationality is a strengthening of stability yet so far only two examples of non-equational stable theories are known. We construct non-equational stable theories by a suitable colouring of the free pseudospace, based on Hrushovski and Srour's original example.