Objective
I will introduce new techniques to address two big open questions in the theory of derived/triangulated categories and their many applications in algebraic geometry.
The first one concerns the theory of Bridgeland stability conditions, which provides a notion of stability for complexes in the derived category. The problem of showing that the space parametrizing stability conditions is non-empty is one of the most difficult and challenging ones. Once we know that such stability conditions exist, it remains to prove that the corresponding moduli spaces of stable objects have an interesting geometry (e.g. they are projective varieties). This is a deep and intricate problem.
On the more foundational side, the most successful approach to avoid the many problematic aspects of the theory of triangulated categories consisted in considering higher categorical enhancements of triangulated categories. On the one side, a big open question concerns the uniqueness and canonicity of these enhancements. On the other side, this approach does not give a solution to the problem of describing all exact functors, leaving this as a completely open question. We need a completely new and comprehensive approach to these fundamental questions.
I intend to address these two sets of problems in the following innovative long-term projects:
1. Develop a theory of stability conditions for semiorthogonal decompositions and its applications to moduli problems. The main applications concern cubic fourfolds, Calabi-Yau threefolds and Calabi-Yau categories.
2. Apply these new results to the study of moduli spaces of rational normal curves on cubic fourfolds and their deep relations to hyperkaehler geometry.
3. Investigate the uniqueness of dg enhancements for the category of perfect complexes and, most prominently, of admissible subcategories of derived categories.
4. Develop a new theory for an effective description of exact functors in order to prove some related conjectures.
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.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
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.
ERC-COG - Consolidator Grant
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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) ERC-2017-COG
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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.
20122 Milano
Italy
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.