Project description
Study explores the connection between geometry and model theory
How many symmetries can model theory recognise? To answer this question, the EU-funded Hilbert5th vs models project will use advanced techniques from the model theory to the class of locally compact groups arising from the solution of Hilbert’s fifth problem. After providing a general (first-order) model-theoretical description of the locally compact groups, researchers will study the relationship between model theory and locally compact groups. In the next stage, researchers will deploy techniques from the so-called geometric stability theory in a class of locally compact groups, for example, in locally compact groups that are projective limits of Lie groups and do not consist of small subgroups.
Objective
The main goal of the project is to apply advanced techniques from the model theory (a branch of mathematical logic) to the class of locally compact groups arising from the solution of Hilbert's 5th problem (so at the end, to the class of Lie groups), to answer the following question: how much geometry can model theory recognize? There does not exist a general (first-order) model-theoretic description of the locally compact groups, thus our first goal will be to develop such a description. Then, we will study how notions from these two corners of mathematics, i.e. model theory and locally compact groups, correspond to each other. For example, we will try to enrich the classification of locally compact and Lie groups by translating the dividing lines from the model-theoretic stability hierarchy. In the next stage, machinery from the so called geometric (neo)stability theory will be deployed in a tame class of locally compact groups, for example in the class of locally compact groups being projective limits of Lie groups and not having small subgroups (so in the groups from the solution of Hilbert's 5th problem). In this spirit, one could consider the definable homogeneous space coming from the Group Configuration Theorem, which is a part of the aforementioned machinery, and try to relate it to the unsolved Hilbert-Smith conjecture - this will be one of our milestones.
In short, we aim to find connections between model-theoretic theorems of geometric nature and classical theorems on the Lie groups, so theorems which depend on the geometry of Lie groups. After understanding these connections, we want to transport techniques from the model theory into the locally compact and Lie groups and vice versa.
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 discrete mathematics mathematical logic
- natural sciences mathematics pure mathematics geometry
- 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.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
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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.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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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) HORIZON-MSCA-2021-PF-01
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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.