Objective
In the past 25 years, networks, such as social, economic and communication networks, have
become society’s backbone and arteries. Remarkable insight into network structure has been
derived using random graphs, and into network functionality using random processes living on
them. This double randomness gives rise to deep and fascinating mathematical problems at the
core of modern probability theory.
My focus in this proposal is on solving challenges around tipping points, or phase transitions,
of random processes on random graphs. These challenges have so far resisted efforts, yet their
solution is now feasible due to recent breakthroughs, including my own. My proposal embarks on
the ambitious and timely endeavour to develop a novel transformative theory to determine the
behaviour close to the phase transitions of paradigmatic processes on random graphs, with a focus
on percolation and spin systems. The holy grail is to give a tangible and effective criterion when
the random graph disorder is relevant or irrelevant for the process on it, i.e. when the behaviour is
mean field. Throughout my proposal, percolative properties, describing how connectivity depends
on model parameters, are a leitmotif.
My innovative approach is to use dynamics of and on random graphs. Dynamics arise in three
intertwined ways. (1) Key graph properties can be distilled by exploring the graph. (2) Phase
transitions and their universality classes are key to understanding random processes on graphs.
(3) Dynamic graphs change over time in a way that may depend on the process on them, a setting
so-far hardly studied in mathematics. Despite the fact that these three forms of dynamics each
have attracted ample attention, my approach leverages their effective combination, a key example
being percolation on preferential attachment models.
I am a leader worldwide in the mathematics of networks, and uniquely positioned to tackle the
above challenges, whose solution will provide a major breakthrough.
Fields of science (EuroSciVoc)
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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)
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.
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-2025-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.
5612 AE Eindhoven
Netherlands
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.