SYMPTEICH

Towards symplectic Teichmueller theory

Coordinatore	THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	United Kingdom [UK]
Totale costo	650˙000 €
EC contributo	650˙000 €
Programma	FP7-IDEAS-ERC Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	ERC-2007-StG
Funding Scheme	ERC-SG
Anno di inizio	2008
Periodo (anno-mese-giorno)	2008-07-01   -   2013-06-30

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE  Organization address address: The Old Schools, Trinity Lane city: CAMBRIDGE postcode: CB2 1TN contact info Titolo: Dr. Nome: Ivan Cognome: Smith Email: send email Telefono: -765456 Fax: -339187	UK (CAMBRIDGE)	hostInstitution	0.00
2	THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE  Organization address address: The Old Schools, Trinity Lane city: CAMBRIDGE postcode: CB2 1TN contact info Titolo: Ms. Nome: Renata Cognome: Schaeffer Email: send email Telefono: +44 1223 333543 Fax: +44 1223 332988	UK (CAMBRIDGE)	hostInstitution	0.00

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 Obiettivo del progetto (Objective)

'Over the last decade, homological algebra has entered symplectic topology, largely thanks to the appearance of Fukaya categories in homological mirror symmetry. Applications of these new methods and ideas are still scarce. We propose a fundamentally new approach to studying symplectic dynamics, by studying the action of the symplectic mapping class group on the complex manifold of stability conditions on its Fukaya category. This can be seen as a first attempt to generalise classical Teichmueller theory to higher-dimensional symplectic manifolds. Many invariants arising in low-dimensional topology, including Khovanov cohomology for knots, are governed by the Fukaya categories of associated moduli spaces. We propose an 'uncertainty principle' in topology, in which these invariants are intrinsically constrained by rigidity of this underlying categorical structure. Besides applications in topology, this suggests a framework for studying the sense in which topological complexity is the shadow of dynamical complexity.'