TQFT

The geometry of topological quantum field theories

 Coordinatore ALBERT-LUDWIGS-UNIVERSITAET FREIBURG 

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

Mappa


 Word cloud

Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.

power    forms    theory    strands    terp    frobenius    structures    construction    geometry    picture    tqft    spaces    quantisation    geometric    functions    manifolds    qft    complete    structure    generalised   

 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.'

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