Objective
"Our main goal is to apply the powerful analytical tools that are now emerging from areas of more ""applicable"" parts of mathematics such as ergodic theory, random walks, harmonic analysis and additive combinatorics to some longstanding open problems in more theoretical parts of mathematics such as group theory and number theory. The recent work of Green and Tao about arithmetic progressions of prime numbers, or Margulis' celebrated solution of the Oppenheim Conjecture about integer values of quadratic forms are examples of the growing interpenetration of such seemingly unrelated fields. We have in mind an explicit set of problems: a uniform Tits alternative, the equidistribution of dense subgroups, the Andre-Oort conjecture, the spectral gap conjecture, the Lehmer problem. All these questions involve group theory in various forms (discrete subgroups of Lie groups, representation theory and spectral theory, locally symmetric spaces and Shimura varieties, dynamics on homogeneous spaces of arithmetic origin, Cayley graphs of large finite groups, etc) and have also a number theoretic flavor. Their striking common feature is that each of them enjoys some intimate relationship, whether by the foreseen methods to tackle it or by its consequences, with ergodic theory on the one hand and harmonic analysis and combinatorics on the other. We believe that the new methods being currently developed in those fields will bring crucial insights to the problems at hand. This proposed research builds on previous results obtained by the author and addresses some of the most challenging open problems in the field."
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 applied mathematics dynamical systems
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
- natural sciences mathematics pure mathematics arithmetics prime numbers
- natural sciences mathematics pure mathematics algebra algebraic geometry
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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.
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-2007-StG
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
91405 ORSAY CEDEX
France
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.