Project description
Research into random planar maps could solve key problems in statistical physics
Planar maps are a booming research field at the intersection between probability theory, geometry, combinatorics, complex analysis and statistical physics. They are embeddings of topological maps into the plane, subdividing it into vertices, edges and faces. As discrete random surfaces, they could converge on limit surfaces. The EU-funded UniversalMap project aims to demonstrate that embeddings of certain random planar maps converge to Liouville quantum gravity – a class of natural random surface models, which has its roots in conformal field theory. Combining expertise from different fields, the project also plans to prove the universality principles of embedded random planar maps. Project research could offer tailored solutions to central problems in statistical physics, such as providing distance measurements of an n-step self-avoiding walk.
Objective
The PI proposes to study a variety of open problems involving random planar maps and trees. This is a booming field at the intersection of probability, geometry, statistical physics, combinatorics and complex analysis. It has grown tremendously in the last two decades, in depth and breadth, and has seen breakthroughs on long-standing classical problems.
The PI's first goal is to study the universality of embedded random planar maps and prove their convergence to what is known as Liouville quantum gravity, a class of random surfaces predicted by physicists to be the universal limit to such discrete random surfaces. Various map embedding mechanisms will be studied such as harmonic embedding, square-tiling, circle packing and others. The second goal is to solve problems concerning stochastic processes (such as random walks, percolation and the Ising model) on embedded random planar maps. This will shed light on the behavior of the same stochastic processes on regular lattices (such as the square or triangular grids) due to the non-rigorous Knizhnik-Polyakov-Zamolodchikov correspondence, a conjectural formula from the physics literature relating the behavior of critical statistical physics models on random lattices to their behavior on regular lattices. We will gain progress on these inspiring yet non-rigorous predictions by developing various probabilistic, geometric and complex analytic tools aimed to show that instabilities in the embeddings cancel out due to the randomness of the planar maps.
This project has the potential to lead to the solution of the most central problems in two-dimensional statistical physics, such as estimating the typical displacement of the self-avoiding walk, proving conformal invariance for critical percolation on the square lattice and many others.
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
You need to log in or register to use this function
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.
-
H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
See all projects funded under this programme
Topic(s)
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.
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.
ERC-COG - Consolidator Grant
See all projects funded under this funding scheme
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-2020-COG
See all projects funded under this callHost institution
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.
69978 Tel Aviv
Israel
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.