000243017 001__ 243017
000243017 005__ 20230212174144.0
000243017 0247_ $$2CORDIS$$aG:(EU-Grant)891437$$d891437
000243017 0247_ $$2CORDIS$$aG:(EU-Call)H2020-MSCA-IF-2019$$dH2020-MSCA-IF-2019
000243017 0247_ $$2originalID$$acorda__h2020::891437
000243017 035__ $$aG:(EU-Grant)891437
000243017 150__ $$aModuli Spaces associated with Singularities$$y2021-01-01 - 2022-12-31
000243017 372__ $$aH2020-MSCA-IF-2019$$s2021-01-01$$t2022-12-31
000243017 450__ $$aModSingLDT$$wd$$y2021-01-01 - 2022-12-31
000243017 5101_ $$0I:(DE-588b)5098525-5$$2CORDIS$$aEuropean Union
000243017 680__ $$aThe 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.
000243017 909CO $$ooai:juser.fz-juelich.de:899457$$pauthority$$pauthority:GRANT
000243017 909CO $$ooai:juser.fz-juelich.de:899457
000243017 980__ $$aG
000243017 980__ $$aCORDIS
000243017 980__ $$aAUTHORITY