University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > On diagonal group actions, trees and continued fractions in positive characteristic

On diagonal group actions, trees and continued fractions in positive characteristic

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NPC - Non-positive curvature group actions and cohomology

If R, k and K are the polynomial ring, fraction field and Laurent series field in one variable over a finite field, we prove that the continued fraction expansions of Hecke sequences of quadratic irrationals in K over k behave in sharp contrast with the zero characteristic case. This uses the ergodic properties of the action of the diagonal subgroup of PGL on the moduli space PGL / PGL and the action of the lattice PGL on the Bruhat-Tits tree of PGL . (Joint work with Uri Shapira)

This talk is part of the Isaac Newton Institute Seminar Series series.

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