Objective
Sofic groups, defined by Gromov and Weiss, are those finitely generated groups with a Cayley graph that can be approximated by finite graphs. The following is a major open problem: Are all groups sofic? A main goal of this proposal is to resolve this in the negative, namely prove the existence of non-sofic groups. The reason why sofic groups received so much attention in the last couple of decades is that various fundamental problems which are open for general groups can be proved in this class. If all groups are indeed sofic, then all of these conjectures would be resolved. On the other hand, if one seeks to refute these conjectures, then they are missing a starting point, as the refutation must use a non-sofic group.
Groups can be generalized in various ways, and the notion of soficity generalizes with them. As every group is a quotient of a free group, the collection of normal subgroups of free groups is a mirror image of the class of groups. Invariant Random Subgroups (IRSs), probability distributions on subgroups of the free group that are invariant under conjugation, are a natural generalization of normal subgroups and thus generalize groups. Such IRSs can be cosofic, and a normal subgroup is cosofic if and only if the quotient of the free group by it is sofic. Similar to Gromov and Weiss, Aldous and Lyons asked whether every IRS is cosofic, which became a major open problem in probability theory. Together with Bowen, Lubotzky and Vidick we recently used cutting edge results from quantum information theory to resolve this problem and construct non-cosofic IRSs. Quite surprisingly, our approach uses the fact that some complexity class contains undecidable languages. In addition to finding non-sofic groups, this proposal aims to resolve other open problems in group theory and in particular the well known generation gap problem for the relation module of finite groups, by using state of the art tools from complexity theory and quantum information theory.
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 physical sciences quantum physics
- natural sciences mathematics applied mathematics statistics and probability
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
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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)
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Topic(s)
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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
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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
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2026-STG
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69978 Tel Aviv
Israel
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