Insects use flight as far more than a means of getting from A to B. Flight creates an aeiral theatre for interaction, whether between species or among members of the same species. For example, a male dragonfly must hunt for food, fend off rival males, and pursue evasive females in order to reproduce, tasks that all revolve around chasing fast-moving targets. Despite the remarkable diversity of insect species and their aerial behaviours, common patterns emerge in how they exploit speed and manoeuvrability to achieve these goals. Simple geometric guidance laws can describe these flight trajectories with surprising accuracy, revealing shared strategies that underpin insect aerial combat.

Core-annular flows are often proposed to reduce frictional losses in industrial pipeline transport processes. Traditionally, a low-viscosity lubricating film is placed around a more viscous core to reduce the drag on the core. However, maintaining stable pipelining, where the core and the lubricant remain separated has proved challenging.
In this talk we present an alternative approach using three-layer, horizontal core-annular pipe flow, in which two fluids are separated by a deformable elastic solid. In the experiments, an elastic solid created by an in-situ chemical reaction maintains the separation of the core and annular fluids. Corrugations of the elastic interface are observed and stable pipelining, where the elastic shell created separating the two fluids remains intact, is successfully demonstrated even when the core fluid is buoyant. We also develop a theoretical model combining lubrication theory for the fluids with standard shell theory for the elastic solid, to predict the buckling states resulting from radial compression of the shell.
The self-sculpting of the shell by buckling cannot by itself generate hydrodynamic lift owing to symmetry in the direction of flow. Instead, we demonstrate that hydrodynamic lift can be achieved by other elastohydrodynamic effects, when that symmetry becomes broken during the bending of the shell.

The dynamic nature of first order methods can be interpreted by means of continuous time models. In this survey talk, we explain how physical concepts like acceleration, inertia or momentum have been used to improve the performance of convex optimization algorithms. 

We give special attention to the historical evolution of complexity results, especially in the form of convergence rates, under the light of this connection. We also discuss different ways in which acceleration schemes can be applied when the smoothness or strong convexity parameters are unknown, and how these ideas extend to saddle point and constrained problems. 

 Given a group acting on a metric space X, one is often interested in the kernel of the action, consisting of those elements that fix every point of X. From a coarse geometric perspective, however, this notion is unsatisfactory, as the kernel is generally not invariant under G-equivariant quasi-isometries. To address this, one can instead consider the coarse kernel, defined as the collection of group elements that move every point of X by a uniformly bounded amount. In this talk, we study this coarse kernel under various assumptions on the action. 

When the action is geometric, we give a purely algebraic characterisation of the coarse kernel as the FC-centre of the group. We then specialise to actions on CAT(0) spaces, where we investigate the coarse kernel via the curtain model, a hyperbolic space associated to a CAT(0) space introduced by Petyt, Spriano, and Zalloum. Along the way, we will meet centralisers, boundaries, and actions on hyperbolic spaces! This is based on my summer project supervised by Davide Spriano and Harry Petyt.