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Counting representations of Fuchsian groups over finite fields (live stream)

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Michael Larsen
Indiana University Bloomington
Fri, 26/07/2024 - 09:30 - 10:30
MPIM Lecture Hall

Recent progress on character bounds for groups of Lie type makes it feasible in many cases to find the asymptotic growth, for fixed q and n tending to infinity, of the number of n-dimensional representations of a Fuchsian group G over the field with q elements.  Applications include determining the dimensions of complex representation varieties of Fuchsian groups in high degree and proving the existence of strongly Zariski-dense Fuchsian subgroups, in the sense of Breuillard-Green-Guralnick-Tao, of classical groups of high rank.

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