Objective
The main subject of the proposed research is the theory of Frobenius manifolds, which unifies different areas of mathematics such as the theory of singularities, quantum cohomologies of algebraic varieties, and Hurwitz spaces. From the point of view of physics, some Frobenius structures describe the moduli space of topological conformal field theories. They also appear in other areas of active current research - from random matrices to interface dynamics.
The first goal of this project is to construct, starting with an arbitrary Frobenius manifold, an associated Frobenius manifold whose dimension is twice as large as the dimension of the given manifold. Such a construction was found in the previous work of the applicant for Frobenius structures on Hurwitz spaces (spaces of meromorphic functions on a Riemann surface). A generalization of the construction to an arbitrary Frobenius manifold would be of great interest due appearance of Frobenius structures in aforementioned topics. The second goal is to find new Frobenius structures on Hurwitz spaces which in the simplest case correspond to Hitchin's two-parametric solution to the Painlev\'e-6 equation.
This problem has already been partially addressed in the work of the applicant: new Frobenius structures related to a one-parameter subfamily of Hitchin's solutions were found. However, the problem of introducing two parameters into the simplest Hurwitz Frobenius structures remains an intriguing open question. Finally, we plan to investigate the meaning of new Frobenius structures from the point of view of applications. In particular, we shall explore a recently established relationship between Frobenius structures on Hurwitz spaces and random matrix theory. We plan to use the obtained Frobenius structures to find new random matrix models.
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.
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Keywords
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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.
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.
Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP6-2004-MOBILITY-7
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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.
IIF - Marie Curie actions-Incoming International Fellowships
Coordinator
Germany
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.