RMAST (786758)

  https://cordis.europa.eu/project/id/786758

  Horizon 2020 (2014-2020)

  Random Models in Arithmetic and Spectral Theory

  ERC Advanced Grant (ERC-2017-ADG)

  arithmetics

  2019-02-01 Start Date (YY-MM-DD)

  2024-01-31 End Date (YY-MM-DD)

  € 1,840,625 Total Cost

  Description

The proposal studies deterministic problems in the spectral theory of the Laplacian and in analytic number theory by using random models. I propose two projects in spectral theory on this theme, both with a strong arithmetic ingredient, the first about minimal gaps between the eigenvalues of the Laplacian, where I seek a fit with the corresponding quantities for the various conjectured universality classes (Poisson/GUE/GOE), and the second about curvature measures of nodal lines of eigenfunctions of the Laplacian, where I seek to determine the size of the curvature measures for the large eigenvalue limit. The third project originates in analytic number theory, on angular distribution of prime ideals in number fields, function field analogues and connections with Random Matrix Theory, where I raise new conjectures and problems on a very classical subject, and aim to resolve them at least in the function field setting.

  Complicit Organisations

1 Israeli organisation participates in RMAST.