FLOERTHINLOWDIM

Floer theoretical invariants of low dimensional manifolds

Coordinatore	KING'S COLLEGE LONDON    more  Organization address address: Strand city: LONDON postcode: WC2R 2LS contact info Titolo: Mr. Nome: Paul Cognome: Labbett Email: send email Telefono: 442078000000
Nazionalità Coordinatore	United Kingdom [UK]
Totale costo	100˙000 €
EC contributo	100˙000 €
Programma	FP7-PEOPLE Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	FP7-PEOPLE-2010-RG
Funding Scheme	MC-IRG
Anno di inizio	2010
Periodo (anno-mese-giorno)	2010-10-01   -   2014-09-30

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	KING'S COLLEGE LONDON  Organization address address: Strand city: LONDON postcode: WC2R 2LS contact info Titolo: Mr. Nome: Paul Cognome: Labbett Email: send email Telefono: 442078000000	UK (LONDON)	coordinator	33˙333.33
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: Mr. Nome: Keith Cognome: Cann Email: send email Telefono: +44 1223 333543 Fax: +44 1223 332988	UK (CAMBRIDGE)	participant	66˙666.67

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 Obiettivo del progetto (Objective)

'My main research interests are in low dimensional topology, symplectic geometry and gauge theory. Over the past 20 years, these fields has seen an explosion of activity due to its relevance to string theory. As part of my PhD thesis, I proved an equivalence between two 3-manifold invariants coming from Floer theory. These are Perutz's Lagrangian matching invariants and Ozsvath and Szabo's Heegaard Floer theory. Although, Heegaard Floer theory has been studied extensively, Lagrangian matching invariants is a relatively recent theory and it remains to be explored more thoroughly. The set-up of Lagrangian matching invariants gives more emphasis on symplectic techniques, and this offers a different approach to Heegaard Floer theory. My goal is to explore these invariants in more depth and bring in new symplectic techniques to the study of 3-manifolds. As a concrete project along these lines, I have been working with Perutz in extending these invariants to bordered three manifolds for which we apply techniques used in the study of Fukaya categories of symplectic manifolds. As a byproduct, we obtain categorical mapping class group actions. Another main part of my research is the study of Fukaya categories of Lefschetz fibration on the Hilbert schemes of the A_n type Milnor fibre, a special type quiver variety. This involves Floer theoretic calculations of non-compact Lagrangian submanifolds. The applications of this research has deep connections with conjectures involving the relation of the Fukaya category to geometric representation theory, in particular to Khovanov's combinatorial link invariants. In addition to the projects described above, I am interested in various structures in low dimensional topology. For example, I proved that every smooth 4-manifold admits a broken Lefschetz fibration. This gives a new calculus of 4-manifolds, which I plan to apply to solve old conjectures about 4-manifolds.'