(i) Structural complexity and dynamical systems
Relationships between dynamical features and evolution of complex fluid systems such as vortex tangles and magnetic fields in terms of geometric, algebraic and topological information.
Aims: to establish relations between dynamical aspects and morphological information by analytical means.
(ii) Energy lower bounds on magnetic knots and links
Identification of minimum energy states of magnetic knots and links in terms of topological complexity.
Aims: to establish relations between energy lower bounds and topological complexity.
(iii) Critical surfaces spanning quantum knots
Characterisation of minimal Seifert surfaces spanning quantum knots and links, change of topology through reconnection and relation with energy.
Aims: to establish relations between geometric properties and energy content of surfaces of physical interest.
(iv) Geodesics in knot polynomial space
Interpretation of optimal decay pathways of fluid knots as geodesics in a knot polynomial space and relation with energy.
Aims: to establish new theoretical framework for the topological cascade of physical knots and links.