Detecting structural complexity: new results and applications


Il 27 Marzo 2007 alle ore 16:00 in aula 1A/150 della Torre Archimede il Professor Renzo Ricca dell'Universita' di Milano Bicocca terra' la sesta conferenza della serie Colloquia Patavina.

Trovate qui sotto un sommario della conferenza ed una breve biografia.

La Commissione Colloquia (Garuti, Pavon, Pitteri, Rossi).

- Titolo
Detecting structural complexity: new results and applications

- Conferenziere
Renzo Ricca (Univ. Milano Bicocca)

Martedi' 27 Marzo 2007, ore 16:00
Aula: 1A/150, Torre Archimede

- Riassunto
We present and discuss recent results obtained from applications of differential geometry of space curves and knot theory to detect morphological complexity of tangles of physical filaments in three-dimensional space, relating this complexity to dynamical aspects of the physical tangle. By introducing concepts such as tropicity, writhing, alignment, linking and crossing numbers of vector fields, we show how to use these measures to detect and analyse structural complexity. By extracting information from projected graphs we show how to estimate fundamental properties associated with the physical system. In particular we present new results and review progress made on a research programme
based on vortex tangle simulations, to show how these quantities are related to dynamical information, including linear and angular momentum, helicity and kinetic energy of the tangle. Applications may be as disparate as the analysis of complex patterns of scalar and vector fields, such as intricate networks of streamlines, vortex and magnetic fields, or filamentary structures such as biopolymers and neural systems. Our results are very promising and highlight a call for new progress in mathematical analysis of structural complexity as well as in visiometrics and graphics diagnostics.

- Breve curriculum

Personal Details
Birth date: 24.01.1960
Status: married to Pia Truc
One child: Joel

Office Address
Department of Mathematics and Applications, Universita di Milano-Bicocca, Via Cozzi 53, 20125 Milano,Italy. Telephone: +39.02.6448 5762. Fax: +39.02.6448 5705. E-mail: renzo.

Recent Appointments
2003-to date Professor of Mathematical Physics (Fixed-Term), U. Milano-Bicocca. 1998-2003 Senior Research Fellow and Lecturer (Fixed-Term), University College London.

Ph.D. (16.07.1994). University of Cambridge, Trinity College. Title: Geometric and topological aspects of vortex filament motion. Supervisor: Professor H.K. Moffatt.
M.Sci. (Mathematics) (10.10.1990). University of Cambridge, Trinity College.

Research Interests
Application of geometric and topological techniques to study vortex dynamics, magnetohydrodynamics of flux tubes and energy relaxation of elastic filaments. Mathematical study of structural complexity and applications to DNA biology.

Recent International Recognitions and Awards
* 2003 MIUR Project Competition ("Incentivazione alla mobilita di studiosi stranieri e italiani residenti all'estero"), Italian Ministry of Education, Italy.
* 2001 JSPS Invitation Fellowship, Japan Society for the Promotion of Science, Japan.

Organization and Direction of International Programmes
* 2001 (June) CIME Summer School: Topological Fluid Mechanics. Scientific Director. International Mathematical Summer Center, CIME Foundation, UMI, Italy.
* 2000 (September-December) IN1 programme: Geometry and Topology of Fluid Flows. Programme organizer (with H. Aref, T. Kambe, R. Pelz). Isaac Newton Institute for Mathematical Sciences, Cambridge.

Recent Publications and Edited Volumes
* 2007 (Editor) Lectures on Topological Fluid Dynamics. CIME Lecture Notes in Mathematics. Springer-Verlag. To appear.
* 2006 Writhing and coiling of closed filaments. (With F. Maggioni). Proc. R. Soc. A 462, 3151-3166.
* 2005 Structural complexity. In Encyclopedia of Nonlinear Science (ed. A. Scott), pp. 885-887.Routledge, New York and London.
* 2005 Inflexional disequilibrium of magnetic flux tubes. Fluid Dyn. Res. 36, 319-332.
* 2001 (Editor) An Introduction to the Geometry and Topology of Fluid Flows. NATO AS1 Series 11, 47.Kluwer.

Rif. M. A. Garuti, M. Pavon, M. Pitteri, F. Rossi

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