School of Mathematics & Physics, University of Lincoln
On Wednesday the 30th of January 2019 Dr David Stewart (Newcastle University) visited the Charlotte Scott Centre for Algebra in Lincoln and gave a talk “Gröbner bases, smooth centralisers and the Lefschetz principle”.
Abstract: “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. (This is joint work with Ben Martin and Lewis Topley.)”