Renzo L. Ricca

(i) Structural Complexity and Dynamical Systems

Work on relationships between energy and structural complexity of dynamical systems, such as vortex tangles and networks of magnetic fields, in terms of geometric, algebraic and topological information.

Aims: to establish relationships between energy contents and morphological information by analytical means.

(ii) Energy lower bounds of magnetic knots and links

Work on the energy groundstate spectrum of magnetic knots and links of increasing topological complexity in ideal magnetohydrodynamics.

Aims: to establish new lower bounds in terms of the topology of minimum energy states.

(iii) Minimal Surfaces Bounded by Knots

Work on the characterization of the minimal area surface of a thin film under tension, bounded by a knot.

Aims: to establish the effects of geometry and topology on the minimal surface as the knot change shape.