Interval exchange permutations
Anton Zorich
IMJ-PRG, Paris
https://webusers.imj-prg.fr/~anton.zorich/
Date(s) : 30/09/2022 iCal
11h00 - 12h00
Twenty years ago Vladimir Arnold posed a question on asymptotic statistics of cycle decomposition of special permutations of large number of elements; such permutations can be seen as random integral exchange transformations with a fixed permutation. It was proved by I. Pak and A. Redlich in 2008 that a random interval exchange permutation (A,B,C) -> (C,B,A) is transitive with asymptotic probability $6/pi^2$. However, there was no further progress in Arnold’s problem ever since.
I will present a solution of Arnold’s problem for an arbitrary permutation based, as usual, on combination of combinatorics, geometry, and dynamics of the moduli space of Abelian differentials. En route I will suggest some further conjectures. I will try to make the talk accessible to a general audience. The talk would be in English or in French depending on preferences of the audience.
(joint work with V. Delecroix, E. Goujard, and P. Zograf)
Emplacement
Saint-Charles - FRUMAM (2ème étage)
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