AG Algebra, Geometrie und Computeralgebra

David Stewart, Newcastle: Gröbner bases, smooth centralisers and the Lefschetz principle


Referent: David Stewart, Newcastle

Zeit: Donnerstag, 17.01.2019, 17:15 h

Ort:Raum 48-436

Abstract:

(Joint with Ben Martin and Lewis Topley).

In a paper in the now defunct LMS Journal of Computation I used GAP to compute the Lie-theoretic centralisers in the exceptional groups of elements in their minimal modules in all characteristics, establishing when the centralisers in the groups were smooth. Non-smoothness was only found in very small characteristics, even where there are infinitely many orbits. This led to a question on when all centralisers of elements in a Z-defined representation would be smooth if the characteristic were large enough.

With my co-authors we managed to prove this using the Lefschetz principle from model theory applied to Gröbner bases, which gave rise to what we call "d-bounded Hopf quadruples". I'll explain some of this.

 

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