Project description
Stability conditions in representation theory under study
The overall aim of the EU-funded STABRT project is to establish new connections between representation theory and algebraic geometry. In particular, it plans to increase understanding of stability conditions over module categories using the tau-tilting theory. The topics that will be addressed include how tau-tilting theory relates to the finitistic dimension conjecture and how the wall and chamber structure of two algebras encode the homological relation between them. The focus will also be on wall-crossing phenomena beyond the realm of cluster algebras and on establishing the relation between certain homological properties of finite-dimensional algebras with the homological properties of their associated toric varieties.
Objective
The overall aim of this project is to establish a new connection between representation theory and algebraic geometry. In recent years, great progress has been done in the understanding of stability conditions over module categories, notably in the description of the wall and chamber structure of finite-dimensional algebras via tau-tilting theory. During this fellowship I will undertake research that will lead to a deeper understanding of these stability conditions and I will apply these tools to the Homological Mirror Symmetry Program and the study of toric varieties.
It is known that most of the information of wall-crossing phenomena of cluster algebras is encoded in the so-called cluster scattering diagram, recently introduced by Gross-Hacking-Keel-Kontsevich. In a seminal paper, Bridgeland showed that these scattering diagrams are intimately related with the wall and chamber structure of certain jacobian algebras. The wall and chamber structure of an algebra has a rich combinatorial structure. In particular, it has the structure of what is known as a fan in toric geometry. Each fan determines uniquely a toric variety.
In this project, I will study tau-tilting theory and stability conditions in four different ways. From the more representation theoretic to the more geometric, these are the following: I will attack problems on tau-tilting theory related with the finitistic dimension conjecture; I will show how the wall and chamber structure of two algebras encode the homological relation between them; I will use the knowledge about wall and chamber structures for finite-dimensional algebra to study wall-crossing phenomena beyond the realm of cluster algebras; I will establish the relation between certain homological properties of finite-dimensional algebras with the homological properties of their associated toric varieties.
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 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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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-2019
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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.
75006 Paris
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.