Many dynamical systems arise naturally as parametrised families. One can then study the associated parameter space and ask how qualitative properties of the dynamics are reflected geometrically within it. In this talk I will discuss three examples where classification problems lead to intricate subsets of parameter space: the Mandelbrot set in complex dynamics, the Rauzy gasket arising from interval exchange transformations, and a tiling structure associated with the topological classification of a family of self-similar sets. Although these examples arise in very different settings, they exhibit striking parallels in how parameter spaces organise qualitative changes in the underlying dynamics.

Venue: Fulton G20

Former residents of West Park Hall during the academic year October 1992 to May 1993 are meeting up for a reunion to mark 30 years since (most of us) graduated. The main reunion activity will take place on Saturday, 6 June 2026.

Plans for the reunion are as follows:

Saturday daytime 

Although the Mansion House at West Park is not accessible, you are welcome to visit the grounds of West Park for more nostalgia and a few photo opportunities. It’s about 15 minutes’ walk from the Invercarse Hotel along the Perth Road. 

You can also  catch up with friends or visit Dundee’s various attractions (or pubs).

Saturday evening 

Later on Saturday, you are invited to meet for informal drinks in the bar or lawn area (weather dependent) before dinner is served at 19:30. We ask you to be there by 19:00. More information about the table arrangements will follow – you’ll have the opportunity to tell us if there’s anyone you particularly want to sit near to! We’ll also circulate menus but, in the meantime, please tell us about any special dietary or accessibility requirements.

Chemically-propelled particles are an artificial prototype for active matter. These submerged objects self-propel by consuming a fuel in the surrounding fluid: surface chemical reactions alter the local solute concentration, and solute-surface interactions cause any resulting concentration gradients to drive slip flows across its surface. The subsequent propulsion depends on both the swimmer geometry and the chemical patterning across its surface. 

I will present recent work on Slender Phoretic Theory, which asymptotically simplifies the solute concentration problem to calculating line integrals along the filament’s centreline. We use this theory to expand the library of known solutions, including to looped filaments such as tori and knots. By combining our theory with a model for elastic filaments, we investigate chemo-elastohydrodynamic filaments in simulations across a wide range of material stiffnesses. As the filament becomes more deformable, we find that the dynamic behaviour progresses from rigid motion, through buckling and out-of-plane transitions, towards chaos.

Venue: Fulton G20