Project description
New methods for constructing infinite monster groups
Groups are abstract algebraic structures that mathematically encode the notion of symmetry. They are ubiquitous in all areas of mathematics and also have important implications for theoretical physics and computer science. The theory of infinite monster groups is an important part of group theory, offering examples of infinite groups with exceptional geometric, analytic and algebraic properties. Funded by the Marie Skłodowska-Curie Actions programme, the SPECMON project plans to develop new methods for constructing infinite monster groups. These methods will be used to study key open questions such as Diximier's problem on unitarisable groups, Kaplansky's zero-divisor conjecture and the Baum–Connes conjecture.
Objective
Groups are abstract algebraic structures that mathematically encode the notion of symmetry. Groups are ubiquitous in all areas of mathematics and have applications, for example, to theoretical physics and computer science. Group theory tries to understand particular classes as well as global properties of groups. The theory of infinite monster groups is a crucial part of the theory. It provides examples of infinite groups with exceptional geometric, analytic, and algebraic properties, thus clarifying boundaries of classes of groups and often resolving outstanding open questions.
This project aims to develop further methods for constructing and studying infinite monster groups, providing new techniques for producing such groups as well as a deeper understanding of the spectrum of phenomena encountered in the existing theory. The monsters within the scope of this project arise from methods of geometric group theory, which studies finitely generated infinite groups through their actions on geometric structures. The planned work will benefit greatly from the excellent synergies between the ER's geometric viewpoint and Prof. Thom's more analytic viewpoint on infinite groups, a combination which has produced outstanding results in the past.
The methods and results developed in this project will lead to significant advances in outstanding open questions. Particular topics addressed by the project are, for example: Diximier's problem on unitarizability of groups (open since 1950), the Kaplansky zero-divisor conjecture (1956), the Baum-Connes conjecture (1982), and the open questions of residual finiteness of hyperbolic groups and of quasi-isometry invariance of acylindrical hyperbolicity. Furthermore, the project will lead to new models of random groups, in particular infinitely presented ones and periodic ones.
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 computer and information sciences
- natural sciences mathematics
- natural sciences physical sciences theoretical physics
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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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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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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.
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)
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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) H2020-MSCA-IF-2018
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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.
01069 DRESDEN
Germany
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.