Project description
Answering persistent open questions regarding Artin groups via cube complex theories
Artin groups are a class of infinite groups defined by simple algebraic expressions. They are primarily used in geometric group theory, topology and low-dimensional geometry to study the symmetry of spaces and the braiding of paths. Their braid relations are also crucial in the study of integrable systems and quantum groups. Despite being extensively studied since their introduction about six decades ago, many basic questions remain unanswered. With the support of the Marie Skłodowska-Curie Actions programme, the CubeArt project aims to tackle some of those questions after laying the foundations with the study of Artin groups as quotients of cubulated groups using cubical small-cancellation theory.
Objective
Artin groups occupy an important place in modern mathematics, sitting at the intersection of algebra, geometry, and topology. They generalise free groups, free abelian groups, and braid groups - already central objects with deep connections to knot theory, low-dimensional topology, and mathematical physics - while extending this richness across a vast family of groups associated with Coxeter systems. Despite their introduction in the 1960s, and the extensive body of work that has arisen from their study, many of the most basic questions about Artin groups remain unresolved.
The goal of this proposal is to study Artin groups as quotients of cubulated groups by developing and exploiting the tools of cubical small-cancellation theory, with the aim of tackling central open questions, such as the K(pi,1) conjecture and residual finiteness, and foundational algorithmic challenges, such as the word and conjugacy problems.
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 topology knot theory
- natural sciences mathematics pure mathematics algebra
- natural sciences mathematics pure mathematics topology algebraic topology
- natural sciences mathematics pure mathematics 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.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
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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
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.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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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) HORIZON-MSCA-2025-PF
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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.
48940 Leioa
Spain
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.