Project description
Advanced mathematical models to describe real world networks
The concepts of randomness and expansion are pervasive throughout mathematics. The EU-funded CARPE project will build on the success of various exciting new methods based on random process and expansion theories to address challenging problems that concern networks and are inspired by real life phenomena. For example, although there are physical models that can sufficiently describe phase transitions or the spread of information or diseases throughout a network, they cannot be justified mathematically. Researchers will combine various tools to further elucidate the mathematical theories that apply to any possible network. These include a classic statistical physics tool called cluster expansion method as well as global hypercontractivity – a structural refinement of the classical hypercontractivity theorem.
Objective
The concepts of Randomness and Expansion are pervasive throughout Mathematics and its applications to many areas of Science and Engineering. The mathematical study of Expansion can be traced back to the ancient Greeks and of Probability to the analysis (e.g. by Fermat and Pascal) of games of chance. In the modern era, both concepts are influential in many areas of Mathematics (this proposal will emphasise Combinatorics and Probability, and also touch on Analysis, Geometry, Topology, Number Theory and Theoretical Computer Science). Within Science and Engineering, topics related to the mathematical problems covered in this proposal include Approximation Algorithms (Counting and Sampling), Statistical Physics (Magnetism, Lattice Gases, Polymer Models), Mathematical Biology (Epidemiology), Control Theory and Fluid Flow.
My recent and ongoing research has generated several exciting new ideas and methods. The most recent of these, the Cluster Expansion Method (work with Matthew Jenssen), is a far-reaching program to apply a classical tool from Statistical Physics to developing methods for describing the typical structure of models such as random homomorphisms from a discrete torus. Another exciting recent technique, Global Hypercontractivity (work with Noam Lifshitz, Eoin Long and Dor Minzer), is a structural refinement of the classical hypercontractivity theorem; we will generalise many of its applications to Mathematics and Computer Science and give several new applications, e.g. in Extremal Combinatorics (via the Junta Method). I will also develop new Absorption techniques to answer constructive mathematical questions that seem beyond the reach of Randomised Algebraic Construction (a method I developed to solve Steiner's 1852 question on the Existence of Designs).
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.
- medical and health sciences health sciences public health epidemiology
- natural sciences mathematics pure mathematics topology
- natural sciences chemical sciences polymer sciences
- 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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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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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-ADG - Advanced Grant
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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-2019-ADG
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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.
OX1 2JD Oxford
United Kingdom
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.