Project description
A new look in the mirror: vibrating strings and curve counting
String theory postulates that the universe is made of quantum particles that are one-dimensional vibrating strings rather than points. It is a way of unifying quantum mechanics and gravity, extending Einstein’s general theory of relativity, which describes gravitational effects as arising from curvature in the fabric of spacetime, to shorter distances and higher energy scales. Mirror symmetry is an important aspect of string theory, intricately related to curve counting, where a complex curve represents the worldsheet of a string propagating through spacetime. With the support of the Marie Skłodowska-Curie Actions programme, the NCMS project is developing a new mathematical approach to mirror symmetry and other curve counting theories.
Objective
A Marie Sklodowska-Curie IF at ETH-Zurich will lead to major developments of the PI's current research.
The PI's research focuses on better understanding the mathematical implications of the physical dualities that arise in the study of string theory. Mirror symmetry, which is a kind of duality in string theory, equates two physical theories called the A-model and B-model. Mirror symmetry predicts that the A-model (resp. the B-model) of a space/variety is equivalent to the B-model (resp. the A-model) of its
mirror space/variety. In mathematics, the A-model corresponds to Gromov--Witten (GW) theory, which is one of the first modern curve counting theories in enumerative geometry. To a physicist, a complex curve represents the worldsheet of a string propagating through space-time.
In 2018, the PI initiated a new research program which provides a novel approach of using orbifold techniques to count curves in algebraic varieties with tangency conditions along co-dimension one sub-varieties (divisors). This novel approach defines a generalization of relative GW theory which plays a central role in mirror symmetry. Several major advances have been achieved in the past two years and a new research direction has been created.
This proposal focuses on this new research program and its applications to curve counting theories and mirror symmetry. We expect to build a firm foundation for our new theory and expand this program along various directions. The proposal is divided into three main projects. The first project focuses on structural properties of the new GW theory and its relation with punctured GW theory. The second project explores applications of the new theory to several aspects of mirror symmetry including Gross--Siebert program, the Strominger--Yau--Zaslow (SYZ) conjecture and the Doran--Harder--Thompson (DHT) conjecture. The third application focuses on its connections with other curve counting theories.
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.
This project's classification has been validated by the project's team.
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.
This project's classification has been validated by the project's team.
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-2020
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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.
8092 Zuerich
Switzerland
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.