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

Presented by: 
Frédéric Paulin Université Paris-Sud 11
Date: 
Tuesday 25th April 2017 -
10:00 to 11:00
Venue: 
INI Seminar Room 2
Abstract: 
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(2,K) on the moduli space PGL(2,K)/PGL(2,R) and the action of the lattice PGL(2,R) on the Bruhat-Tits tree of PGL(2,K). (Joint work with Uri Shapira)
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons