Project description
Large genus asymptotic geometry and dynamics of moduli spaces
Characterising and controlling dynamical processes occurring on surfaces is essential to numerous areas of physics and engineering. A simple example is electron transport at surfaces. Leveraging the geometry and dynamics of the moduli spaces has supported models of such systems and become one of the most active areas of modern mathematics research. The ERC-funded UniGeoDyM project aims to study large genus asymptotic geometry and dynamics of moduli spaces and of related objects from probabilistic and asymptotic perspectives. Outcomes could reveal universality phenomena in geometry and dynamics of moduli spaces with important applications in mathematics and dynamics.
Objective
Geometry and dynamics in the moduli spaces proved to be extremely efficient in the study of surface foliations, billiards in polygons and in mathematical models of statistical and solid state physics like Ehrenfest billiards or Novikov's problem on electron transport. Ideas of study of surface dynamics through geometry of moduli spaces originate in works of Thurston, Masur and Veech. The area is flourishing ever since. Contributions of Avila, Eskin, McMullen, Mirzakhani, Kontsevich, Okounkov, Yoccoz, to mention only Fields Medal and Breakthrough Prize winners, made geometry and dynamics in the moduli spaces one of the most active areas of modern mathematics. Moduli spaces of Riemann surfaces and related moduli spaces of Abelian differentials are parametrized by a genus g of the surface. Considering all associated hyperbolic (respectively flat) metrics at once, one observes more and more sophisticated diversity of geometric properties when genus grows. However, most of metrics, on the contrary, progressively share certain similarity. Here the notion of most of has explicit quantitative meaning, for example, in terms of the Weil-Petersson measure. Global characteristics of the moduli spaces, like Weil-Petersson and Masur-Veech volumes, Siegel-Veech constants, intersection numbers of -classes were traditionally studied through algebra-geometric tools, where all formulae are exact, but difficult to manipulate in large genus. Most of these quantities admit simple uniform large genus approximate asymptotic formulae. The project aims to study large genus asymptotic geometry and dynamics of moduli spaces and of related objects from probabilistic and asymptotic perspectives. This will provide important applications to enumerative geometry, combinatorics and dynamics, including count of meanders in all genera, solution of Arnolds problem on statistics of random interval exchange permutations, asymptotics of Lyapunov exponents and of diffusion rates of Ehrenfest billiards.
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 mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
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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)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
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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
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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-ERC - HORIZON ERC Grants
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2023-ADG
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75006 PARIS
France
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