Objective
The proposal describes two main projects. Both of them concern cohomology of moduli spaces of Riemann surfaces, but the aims are rather different.
The first is a natural continuation of my work on tautological rings, which I intend to work on with Qizheng Yin and Mehdi Tavakol. In this project, we will introduce a new perspective on tautological rings, which is that the tautological cohomology of moduli spaces of pointed Riemann surfaces can be described in terms of tautological cohomology of the moduli space M_g, but with twisted coefficients. In the cases we have been able to compute so far, the tautological cohomology with twisted coefficients is always much simpler to understand, even though it “contains the same information”. In particular we hope to be able to find a systematic way of analyzing the consequences of the recent conjecture that Pixton’s relations are all relations between tautological classes; until now, most concrete consequences of Pixton’s conjecture have been found via extensive computer calculations, which are feasible only when the genus and number of markings is small.
The second project has a somewhat different flavor, involving operads and periods of moduli spaces, and builds upon recent work of myself with Johan Alm, who I will continue to collaborate with. This work is strongly informed by Brown’s breakthrough results relating mixed motives over Spec(Z) and multiple zeta values to the periods of moduli spaces of genus zero Riemann surfaces. In brief, Brown introduced a partial compactification of the moduli space M_{0,n} of n-pointed genus zero Riemann surfaces; we have shown that the spaces M_{0,n} and these partial compactifications are connected by a form of dihedral Koszul duality. It seems likely that this Koszul duality should have further ramifications in the study of multiple zeta values and periods of these spaces; optimistically, this could lead to new irrationality results for multiple zeta values.
Fields of science (EuroSciVoc)
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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.
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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.1.1. - 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-STG - Starting 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-STG
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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.
10691 Stockholm
Sweden
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.