Objective
"In recent years there has been spectacular progress in studying growth in groups. A central result in this new area, obtained by Pyber-Szabo' (with a similar result proved by Breuillard-Green-Tao), shows that powers of generating subsets of finite simple groups of ""bounded dimension"" grow fast. Extending this Product Theorem Szabo' and the PI also proved a weaker version of a conjecture of Helfgott-Lindenstrauss. The Product Theorem has deep consequences in the study of groups, number theory and random walks. A central open question of the area is to remove the dependence on dimension in our Product Theorem. The PI formulated a new Conjecture, as a step forward. The way to further progress is via combining techniques from asymptotic group theory and probability theory. It is from this perspective that the current GROGandGIN proposal addresses issues concerning random walks. We examine how recent probabilistic arguments for random walks in the symmetric group may be transferred to matrix groups. While the first results in the subject of growth concern matrix groups we see an evolving theory of growth in permutation groups. This relies on earlier work of Babai and the PI which aims at finding proofs which do not use the Classification of Finite Simple Groups (CFSG). Similarly, Babai's famous Quasipolynomial Graph Isomorphism Algorithm builds on ideas from CFSG-free proofs due to him. The PI has recently removed CFSG from the analysis of Babai's algorithm. Our method goes ""halfway"" towards removing CFSG from proofs of growth results for permutation groups, currently a major open problem. The GROGandGIN initiative plans to improve various other parts of Babai's paper, working with several people who look at it from different angles, with an eye towards obtaining a Polynomial Graph Isomorphism algorithm. The GROGandGIN team will also study growth in Lie groups since the theory of random walks in Lie groups has been revitalised using analogues of our Product Theorem."
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciences mathematics pure mathematics arithmetics
- natural sciences mathematics applied mathematics statistics and probability
- natural sciences mathematics pure mathematics algebra algebraic geometry
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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-2016-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.
1053 Budapest
Hungary
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.