Renzo L. Ricca

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Renzo Ricca
MIUR Return Scholarship (2003)
Scientific career
Fieldstopological fluid dynamics, structural complexity,
vortex dynamics and magnetohydrodynamics
InstitutionsUniversity of Milano-Bicocca
Doctoral advisorH. Keith Moffatt

Renzo Luigi Ricca (24 January 1960) is an Italian-born applied mathematician (naturalised British citizen), professor of mathematical physics at the

kinetic and magnetic helicity, and physical knot theory
in general.

Education

Ricca was born and educated first in

Ph.D. work was conducted under the guidance of H. Keith Moffatt on the subject of topological fluid dynamics. In 1991 while completing his doctoral studies he was awarded the J.T. Knight's Prize
in Mathematics for work on geometric interpretation of soliton conserved quantities, obtaining the Ph.D. in Applied Mathematics for work on geometric and topological aspects of vortex filament dynamics.

Career

In 1992, after visiting the Institute for Theoretical Physics (UC Santa Barbara) and the Institute for Advanced Study (Princeton), Ricca returned to Europe joining the faculty of the mathematics department of the University College London, first as a research fellow. and then as a senior research fellow and part-time lecturer. From 1993 to 1995 he also held a joint position as university researcher at the Politecnico di Torino. In 2003 he moved to the Department of Mathematics and Applications of the University of Milano-Bicocca, first as a visiting scholar and then as associate professor of mathematical physics. He held many visiting positions in various institutions worldwide, and from 2016 he is also guest professor of the Beijing University of Technology (BJUT) in China.

Research

Ricca's main research interests lie in ideal

braids.[1] Aspects of potential theory of knotted fields, structural complexity and energy
of filament tangles are also at the core of his research.

Geometric aspects of dynamical systems

In the context of classical vortex dynamics Ricca's main contributions concern the geometric interpretation of certain conserved quantities

integrable systems and the first study of three-dimensional effects of torsion on vortex filament dynamics.[3] In ideal magnetohydrodynamics Ricca has demonstrated the effects of inflexional instability of twisted magnetic flux tubes[4] that trigger braid formation in solar coronal loops
. In more recent years Ricca has been concerned with the role of minimal
Bose-Einstein condensates
and critical energy.

Topological fluid dynamics

In 1992, relying on earlier work by Berger and Field,[6] Moffatt and Ricca [7] established a deep connection between topology and classical field theory extending the original result by Keith Moffatt on the topological interpretation of hydrodynamical helicity[8] and providing a rigorous derivation of the linking number of an isolated flux tube from the helicity of classical fluid mechanics in terms of writhe and twist. He also derived explicit torus knot solutions[9] to integrable equations of hydrodynamic type, and he contributed to determine new relations between energy of knotted fields and topological information in terms of crossing and winding number information.[10] In collaboration with Xin Liu, Ricca derived the Jones and HOMFLYPT

Aharonov-Bohm effect for the formation of new defects in condensates,[13] and provided analytical and topological proofs of the zero helicity condition for Seifert framed defects.[14]

Dynamical models in high-dimensional manifolds

In the context of high-dimensional manifolds in 1991 Ricca derived the intrinsic equations of motion of a string[15] as a model for the then emerging string theory of high-energy particle physics, proposing a connection between the hierarchy of integrable equations of hydrodynamic type and the general setting of intrinsic kinematics of one-dimensional objects in (2n+1)-dimensional manifolds. Recently he contributed to extend the hydrodynamic description of the Gross-Pitaevskii equation to general Riemannian manifolds,[16] with possible applications to analog models of gravity in cosmological black hole theory

Origin and development of mathematical concepts

With a comprehensive review work

Karl Friedrich Gauss' own possible derivation of the origin of the linking number concept, and the independent derivation done by James Clerk Maxwell
.

Research-Related Activities

In the year 2000 he co-organised and directed a 4-month research programme on geometry and topology of fluid flows held at the

Scuola Normale Superiore
in Pisa. In 2016 he organised an
IUTAM Symposium on helicity (hosted by the Istituto Veneto di Scienze, Lettere ed Arti in Venice) that gathered more than 100 scientists from 20 different countries, and in September 2019 he organised and directed at the Beijing University of Technology (BJUT) the first programme in China devoted to topological aspects of knotted fields. He is a founding member of GEOTOP-A, an international web-seminar series that was launched in 2018 to promote applications of geometry and topology in science. He is also a founding member of The Association for Mathematical Research (AMR)
, a non-profit organisation launched in 2021 to support mathematical research and scholarship through a broad spectrum of services to the mathematical community.

Awards and Distinctions

Edited Volumes

  • Ricca, R.L. (Editor) An Introduction to the Geometry and Topology of Fluid Flows. NATO ASI Series II 47. Kluwer, Dordrecht, The Netherlands (2001).
    ISBN 978-1402002069
  • Ricca, R.L. (Editor) Lectures on Topological Fluid Mechanics. Springer-CIME Lecture Notes in Mathematics 1973. Springer-Verlag, Heidelberg, Germany (2009).
    ISBN 9783642008368
  • Adams, C.C., Gordon, C.McA., Jones, V.F.R., Kauffman, L.H., Lambropoulou, S., Millett, K.C., Przytycki, J.H., Ricca, R.L., Sazdanovic, R. (Editors) Knots, Low-Dimensional Topology and Applications. Springer-Nature, Switzerland (2019).
    ISBN 978-3-030-16030-2

Sources

References

  1. S2CID 225115899
    .
  2. doi:10.1063/1.858274
    .
  3. S2CID 123188269
    ..
  4. S2CID 120375559
    .
  5. PMC 3009808
    .
  6. S2CID 39276012
    .
  7. S2CID 122310895
    .
  8. S2CID 121478573
    .
  9. S2CID 17656338
    .
  10. doi:10.1016/S0167-2789(01)00304-9
    .
  11. S2CID 55344424
    .
  12. hdl:10281/393628
    .
  13. S2CID 225115899
    .
  14. S2CID 258687991
    .
  15. PMID 9905529
    .
  16. S2CID 235719999
    .
  17. S2CID 120535907
    .
  18. doi:10.1142/S0218216511009261
    .
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