ERC Consolidator Grant "Newton strata"

  • Proposal 770936: NewtonStrat
  • Consolidator Grant (CoG), PE1, ERC-2017-CoG
  • granted for 6/2018 - 5/2023
  • PI: Eva Viehmann

Description

The Langlands programme is a far-reaching web of conjectural or proven correspondences joining the fields of representation theory and of number theory. It is one of the centerpieces of arithmetic geometry, and has in the past decades produced many spectacular breakthroughs, for example the proof of Fermat’s Last Theorem by Taylor and Wiles. The most successful approach to prove instances of Langlands’ conjectures is via algebraic geometry, by studying suitable moduli spaces such as Shimura varieties. Their cohomology carries actions both of a linear algebraic group (such as GLn) and a Galois group associated with the number field one is studying. A central tool in the study of the arithmetic properties of these moduli spaces is the Newton stratification, a natural decomposition based on the moduli description of the space.

The aim of this project is a novel approach to the local Langlands programme via a comprehensive investigation of various types of Newton strata in moduli spaces and the exploitation of their mutual relations. This involves several recent developments such as representation-theoretic methods and results to describe their geometry and cohomology and an investigation of the adic version of the Newton stratification recently introduced by Scholze and Caraiani.

 

Open positions

There are open PhD and postdoc-positions within the project. Successful candidates for a PhD position have (or will soon obtain) a master degree with a strong background in algebraic or arithmetic geometry. Candidates for a postdoc position are recent (or near future) PhDs in a related area of arithmetic geometry and interested in the topics of the project. Applications should be sent to Eva Viehmann. Applications are considered until the positions are filled.

 

Members

Prof. Dr. Eva Viehmann

Dr. Paul Hamacher

Dr. Shinan Liu

Giorgi Vardosanidze