Objective
The study of Gromov-Witten (GW), Donaldson-Thomas, and stable pair invariants of Calabi-Yau 3-folds X forms an active area of research for geometers and physicists. These invariants play a central role in string theory and have relations with many branches of mathematics including number theory and representation theory.
I am interested in questions of enumerative geometry on algebraic surfaces S. Invariants of the total space X of the canonical bundle over S can be used to answer classical enumerative questions on S. Two recent developments in stable pair theory are: (1) A better understanding of stable pairs on X not contained in the zero-section S. (2) Refinements of stable pair invariants.
The first theme of my project is the study of stable pairs on X not contained in S in relation to enumerative questions. For Fano surfaces, GW invariants with sufficiently many point insertions are enumerative. By the GW/stable pairs correspondence these are equal to certain stable pair invariants of X. When the curve class is not sufficiently ample, the stable pair count may include stable pairs on X not contained in S. I propose to compute such contributions in order to obtain curve counts on S outside the ample regime.
The second theme of my project is the study of refined stable pair invariants. I intend to relate the refined topological vertex appearing in the physics literature to refined invariants in the mathematics literature.
Since stable pair invariants are often easiest to calculate of all the invariants of Calabi-Yau 3-folds, I expect this leads to new curve counting formulae and new calculations of refined invariants.
Utrecht University, housing one of the leading schools in geometry in Europe, and Prof. Faber, one of the world's leading experts on moduli of curves, provide the perfect location and supervisor for this project. The diverse expertise of the members of the Mathematics (and Physics) Department at UU allow me to explore links with other areas.
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 mathematical analysis functional equations
- natural sciences physical sciences theoretical physics string theory
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
- natural sciences mathematics pure mathematics algebra algebraic geometry
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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-EF-ST - Standard EF
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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-2014
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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.
3584 CS Utrecht
Netherlands
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.