Raymond Goldstein

November 28, 2025

Title: The Geometry of Multicellular Life

Abstract: One of the most fundamental issues in evolutionary biology is how unicellular life transitioned to multicellular life. How — and why — was it that the simplest single-celled organisms that emerged from the primordial soup evolved into organisms with many cells and cell types dividing up life’s processes? This talk will describe recent experimental and theoretical advances in understanding the architecture of organisms that serve as models of this evolutionary transition.
I will discuss the shape-shifting properties of certain choanoflagellates (the closest living relatives of animals), the recent discovery of common probability distributions of cellular neighborhood volumes in yeast and alga, as well as embryonic 'inversion' and the spontaneous curling of the extracellular matrix of green algae. These studies together shed light on the fundamental question, "How do cells produce structures external to themselves in an accurate and robust manner?"

Keywords: multicellularity, topological defects, embryonic inversion.

Andrew Gilbert

December 5, 2025

Title: The geometry of Lagrangian averaging in ideal fluid dynamics

Abstract: In seminal papers in the 1960s Vladimir Arnold introduced the idea that the motion of an ideal fluid can be considered as a geodesic in the space of volume-preserving maps from the fluid domain to itself. This viewpoint places fluid dynamics, on any Riemannian manifold, in an abstract setting which also incorporates Lie group structure. Although this theory is profound and beautiful, at first sight it has little bearing for the everyday applications of fluid dynamics. However it turns out that the process of Lagrangian averaging (namely averaging over fluid parcels in an ensemble of fluid flows, contrasted with Eulerian averaging at a fixed point), is best understood using the ideas of pull-backs and Lie derivatives on a general manifold, even though one ultimately applies these notions in ordinary three-dimensional space.

This talk will be very much aimed at fluid dynamicists rather than professional geometers, and will outline Arnold’s ideas, and applications to the Generalised Lagrangian Mean Theory put forward by David Andrews and Michael McIntyre, and subsequent related theories, particularly of Andrew Soward and Paul Roberts.

This is joint work with Jacques Vanneste (University of Edinburgh).

Keywords: fluid dynamics, geometry, generalised lagrangian mean.