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A mathematical approach to the liquid-glass transition: kinetically constrained models, cellular automata and mixed order phase transitions

Objective

This proposal focuses on the mathematics of three cross-disciplinary, very active and deeply interlaced research themes: interacting particle systems with kinetic constraints, bootstrap percolation cellular automata and mixed order phase transitions. These topics belong to the fertile area of mathematics at the intersection of probability and mathematical statistical mechanics. They are also extremely important in physics. Indeed they are intimately connected to the fundamental problem of understanding the liquid-glass transition, one of the longstanding open questions in condensed matter physics.
The funding of this project will allow the PI to lead a highly qualified team with complementary expertise. Such a diversity will allow a novel, interdisciplinary and potentially groundbreaking approach. Even if research on each one of the above topics has been lately quite lively, very few exchanges and little cross-fertilization occurred among them. One of our main goals is to overcome the barriers among the three different research communities and to explore the interfaces of these yet unconnected fields. We will open two novel and challenging chapters in the mathematics of interacting particle systems and cellular automata: interacting particle glassy systems and bootstrap percolation models with mixed order critical and discontinuous transitions. In order to achieve our groundbreaking goals we will have to go well beyond the present mathematical knowledge. We believe that the novel concepts and the unconventional approaches that we will develop will have a deep impact also in other areas including combinatorics, theory of randomized algorithms and complex systems.
The scientific background and expertise of the PI, with original and groundbreaking contributions in each of the above topics and with a broad and clearcut vision of the mathematics of the proposed research as well as of the fundamental physical questions,make the PI the ideal leader of this project.

Fields of science (EuroSciVoc)

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Keywords

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Programme(s)

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Topic(s)

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Funding Scheme

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ERC-STG - Starting Grant

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Call for proposal

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(opens in new window) ERC-2015-STG

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Host institution

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Net EU contribution

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.

€ 883 250,00
Address
RUE MICHEL ANGE 3
75794 Paris
France

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Region
Ile-de-France Ile-de-France Hauts-de-Seine
Activity type
Research Organisations
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Total cost

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.

€ 883 250,00

Beneficiaries (1)

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