Topological fluid mechanics From Gauss’ linking number to modern topological dynamics
Renzo Ricca University of Milano-Biccoca, Italy

Infos Complémentaires

13h30 - Conf IV
24 rue Lhomond, Paris
Contact : benjamin.huard@ens.fr, aleksandra.walczak@ens.fr
http://www.phys.ens.fr/

Jeudi 28 mars 2013

Contrary to common perception topological fluid mechanics is an old subject, rooted
in Helmholtz’s (1858) conservation laws and Kelvin’s (1870) vortex atom theory. In
this talk we would like to address some of the most recent developments in the field,
in the light of the original ideas rooted in the works of Kelvin and Tait. Since most of
the recent revival is based on the topological interpretation of helicity in terms of
linking number (Moffatt, 1969 ; Moffatt & Ricca, 1992), it seems appropriate to briefly
re-visit Gauss’ linking number formula of 1833, by offering a plausible derivation of
his statement (of mysterious origin) entirely based on Gauss’ own work. We then
review some recent results on vortex knots and on the energy groundstate of
magnetic knots and links based on the author’s own research. These results may
find useful applications in various physical contexts, providing further grounds to
establish a mathematical foundation of topological field theory based on a
one-to-one correspondence between energy and topology.

13h30 - Conf IV
24 rue Lhomond, Paris
Contact : benjamin.huard@ens.fr, aleksandra.walczak@ens.fr
http://www.phys.ens.fr/