Objective
Hilbert's solution to Waring problem in Number Theory shows that every positive integer is a sum of g(n) nth powers. Surprising non-commutative analogues of this phenomenon were discovered recently in Group Theory, where powers are replaced by general words. Moreover, the study of group words occurs naturally in important contexts, such as the Burnside problems, Serre's problem on profinite groups, and finite simple group theory. We propose a systematic study of word maps on groups, their images and kernels, as well as related Waring type problems. These include a celebrated conjecture of Thompson, problems regarding covering numbers and mixing times of random walks, as well as probabilistic identities in finite and profinite groups. This is a highly challenging project in which we intend to utilize a wide spectrum of tools, including Representation Theory, Algebraic Geometry, Number Theory, computational group theory, as well as probabilistic methods and Lie methods. Moreover, we aim to establish new results on representations and character bounds, which would be very useful in various additional contexts. Apart from their intrinsic interest, the problems and conjectures we propose have exciting applications to other fields, and the project is likely to shed new light not just in group theory but also in combinatorics, probability and geometry.
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 arithmetics
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
- 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.
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.
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.
ERC-2009-AdG
See other projects for this call
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.
Host institution
91904 JERUSALEM
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.