Objective
Our goal is to construct generalisations of the Hitchin and Wess--Zumino--Witten (WZW) and Knizhnik--Zamolodchikov (KZ) connections, both in geometric and deformation quantisation, and of their associated monodromy representations.
The Hitchin connection achieved the quantisation of compact Chern--Simons theory and resulted in the construction of a topological quantum field theory. A different projectively flat connection provides a viable mathematical definition of correlation functions in the WZW model for conformal field theory. The resulting projectively flat vector bundles are isomorphic, and their monodromies have far-reaching applications in low-dimensional topology/geometry (quantum invariants of knots/3-manifolds) and representation theory (of mapping class/quantum/braid groups).
Our guiding viewpoint is that the connections of Hitchin/WZW can be derived from the quantisation of moduli spaces of connections on Riemann surfaces. We will extend this further, focusing on meromorphic connections with high-order poles (i.e. wild singularities), generalising the above bundles and their applications.
The motivation for this project is twofold.
First, there is now a complete understanding of the Poisson/symplectic nature of isomonodromic deformations of wild singularitites, which are naturally amenable to quantisation. The quantum theory is much less developed than the classical one, and this naturally motivates us to close the gap using the latter as a guide.
Second, recent work related the genus-zero WZW connection---that is, the KZ connection---to a new version of the Hitchin connection, and this was then used for the quantisation of moduli spaces of parabolic bundles. We want to pursue extensions of this identification; in particular, we will use the new flat connections constructed on the deformation quantisation side as candidates for `wild' Hitchin connections, in the geometric quantisation of wild character varieties: a complete novelty.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences physical sciences quantum physics quantum field theory
- natural sciences mathematics pure mathematics topology algebraic topology
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics applied mathematics mathematical physics conformal field theory
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-GF - HORIZON TMA MSCA Postdoctoral Fellowships - Global Fellowships
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Call for proposal
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(opens in new window) HORIZON-MSCA-2022-PF-01
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
34090 Montpellier
France
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