Project description DEENESFRITPL Hilbert schemes of points on surfaces with singularities Hilbert schemes, which parametrise subschemes in algebraic varieties, have been extensively studied in algebraic geometry over the last 50 years. The EU-funded ModSingLDT project plans to study the enumerative invariants of one of the most interesting classes of Hilbert schemes, namely zero-dimensional subschemes of some basic classes of surface singularities. The project will also search for connections between the enumerative invariants and the Chern-Simons theory on the links of the singularities. To achieve its objectives, it will use representations of vertex (operator) algebras on the cohomologies or the derived categories of these moduli spaces as well as motivic measures with values in the Grothendieck rings of geometric dg categories. Show the project objective Hide the project objective Objective The aim of this project is to investigate enumerative invariants of the Hilbert schemes parametrizing zero-dimensional subschemes of some basic classes of surface singularities as well as of its higher rank analogues, and find connections between these enumerative invariants and the Chern-Simons theories on the links of the singularities. This question will open brand new relations between algebraic and topological invariants of these singularities. The main tool to approach the problem will be to develop representations of vertex algebras on the cohomologies or derived categories of these moduli spaces conjecturally giving rise to analogues of the Nekrasov parition function on the singularities. Then we will use recent new developements about a specific motivic measure with values in the Grothendieck ring of geometric dg categories to prove some simplification of the aimed correspondence. In the end we will raise these simplified results to the general level.This project will allow the researcher to broaden his area of expertise as well as to develop new directions in his research lines. He will complement his knowledge in low-dimensional topology at one of the most prestigious research institutes and under the guidance of one of the worldwide leaders in this field. Fields of science natural sciencesmathematicspure mathematicstopologyalgebraic topologynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Keywords Hilbert scheme of points normal surface singularities vertex algebras Nekrasov partition function Chern-Simons theory Programme(s) H2020-EU.4. - SPREADING EXCELLENCE AND WIDENING PARTICIPATION Main Programme Topic(s) WF-02-2019 - Widening Fellowships Call for proposal H2020-WF-2018-2020 See other projects for this call Sub call H2020-WF-02-2019 Funding Scheme MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF) Coordinator RENYI ALFRED MATEMATIKAI KUTATOINTEZET Net EU contribution € 151 850,88 Address Realtanoda street 13-15 1053 Budapest Hungary See on map Region Közép-Magyarország Budapest Budapest Activity type Other Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00
