TQFT

The geometry of topological quantum field theories

Coordinatore	ALBERT-LUDWIGS-UNIVERSITAET FREIBURG    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Germany [DE]
Totale costo	750˙000 €
EC contributo	750˙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	2009
Periodo (anno-mese-giorno)	2009-01-01   -   2014-06-30

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	UNIVERSITAET AUGSBURG  Organization address address: UNIVERSITAETSSTRASSE 2 city: AUGSBURG postcode: 86159 contact info Titolo: Mr. Nome: Alois Cognome: Zimmermann Email: send email Telefono: +49 821 5985200 Fax: +49 821 5985505	DE (AUGSBURG)	beneficiary	0.00
2	ALBERT-LUDWIGS-UNIVERSITAET FREIBURG  Organization address address: FAHNENBERGPLATZ city: FREIBURG postcode: 79085 contact info Titolo: Prof. Nome: Katrin Cognome: Wendland Email: send email Telefono: 497612000000	DE (FREIBURG)	hostInstitution	0.00

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 Obiettivo del progetto (Objective)

'The predictive power of quantum field theory (QFT) is a perpetual driving force in geometry. Examples include the invention of Frobenius manifolds, mixed twistor structures, primitive forms, and harmonic bundles, up to the discovery of the McKay correspondence, mirror symmetry, and Gromov-Witten invariants. Still seemingly disparate, in fact these all are related to topological (T) QFT and thereby to the work by Cecotti, Vafa et al of more than 20 years ago. The broad aim of the proposed research is to pull the strands together which have evolved from TQFT, by implementing insights from mathematics and physics. The goal is a unified, conclusive picture of the geometry of TQFTs. Solving the fundamental questions on the underlying common structure will open new horizons for all disciplines built on TQFT. Hertling’s “TERP” structures, formally unifying the geometric ingredients, will be key. The work plan is textured into four independent strands which gain full power from their intricate interrelations. (1) To implement TQFT, a construction by Hitchin will be generalised to perform geometric quantisation for spaces with TERP structure. Quasi-classical limits and conformal blocks will be studied as well as TERP structures in the Barannikov-Kontsevich construction of Frobenius manifolds. (2) Relating to singularity theory, a complete picture is aspired, including matrix factorisation and allowing singularities of functions on complete intersections. A main new ingredient are QFT results by Martinec and Moore. (3) Incorporating D-branes, spaces of stability conditions in triangulated categories will be equipped with TERP structures. To use geometric quantisation is a novel approach which should solve the expected convergence issues. (4) For Borcherds automorphic forms and GKM algebras their as yet cryptic relation to “generalised indices” shall be demystified: In a geometric quantisation of TERP structures, generalised theta functions should appear naturally.'