ERC Consolidator Grant · 2017
Newton strata - geometry and representations
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…
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