CRM: Centro De Giorgi
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Entanglement and Linking

18 May 2011 - 19 May 2011

This event is part of an intensive research period:
Knots and Applications.


The Gauss integral formula for the linking number of two wires (“Zur Elektrodynamik”, 1833) emblematically illustrates the fascinating intermingling of topology, geometry and physics rooted in knot theory from its very birth. Its “diffuse” version, namely helicity, measures the mutual wrapping and coiling of the field lines of a solenoidal field, providing, in particular, a lower bound to the energy it stores, thereby playing a fundamental role in fluid mechanics, magnetohydrodynamics and plasma physics. However, the linking number alone is not sufficient for assessing triviality of a link (Whitehead link, Borromean rings, etc.) and finer higher order analogues thereof (Milnor, Massey) have been devised, together with companion diffuse versions (generalized helicities).

This workshop will be mainly devoted to differential geometric, topological and hydrodynamical aspects of ordinary and higher-order linking, braiding and their asymptotic versions (helicity and its higher order analogues); the following topics will be addressed: integral formulae for higher order linking numbers and the quest for generalized “helicity bounds energy” results and generalizations of Whitehead products (Arnold's problem), link-homotopy invariants of links and the homotopy invariants of associated maps to configuration space (Koschorke's conjecture), with applications, among others, to magnetohydrodynamics of plasmas, vortices, and relaxations of braided magnetic fields.

This event is part of the 3-month intensive research period program on “Knots and Applications”, that takes place at the Centro di Ricerca Matematica "Ennio De Giorgi" of the Scuola Normale Superiore di Pisa, Italy, and that is organised in collaboration with INdAM.

Invited Speakers

Peter Akhmetiev, Izmiran, Russia
Mitchell Berger, Exeter U., UK
Bertrand Duplantier, CEA & KITP, France
Gunnar Hornig, Dundee U., UK
Chun-Chung Hsieh, Academia Sinica, Taiwan
Louis Kauffman, U. Illinois, Chicago, USA
Rafal Komendarczyk, Tulane U., USA
Marc Lefranc, Lille U., France
Jason Parsley, Wake Forest U., USA
Renzo Ricca, U. Milano-Bicocca, Italy

Short Talks

Alberto Benvegnù, U. Verona, Italy
Francesca Maggioni, U. Bergamo, Italy
Clayton Shonkwiler, Haverford College, USA

Participants willing to contribute with a talk are encouraged to submit title and abstract to Mauro Spera at The local expenses of speakers will be covered by the organization. Young participants can apply for financial support, even if they are not submitting a talk.


All prospective participants and attendees are kindly requested to register here before 13 May, 2011.

Financial Support

Prospective participants should seek grant/university support towards travel expenses from local sources. Limited funding towards participant local expenses may be provided by CRM and INdAM upon application.

Request of Financial Support

Qualified junior participants and prospective attendees are invited to submit their request of financial support towards local expenses by sending their CV and list of publications to, before 13 March, 2011.


Publicize this Event: Please notify this event in your Department/Research Unit by downloading and posting the attached poster; please click here to download it.


All lectures, oral contributions and posters will be held in the lecture room Aula Dini (via del Castelletto 11 Pisa) that is at only 2 minutes walk from Centro De Giorgi.

Practical information

How to Get There: From outside Pisa to CRM, read the instructions here

Shopping times and holidays

Typical shopping times are 8:30-12:30 and 15:30-19:30. National holidays: 1 May, 2 June, 17 June