[Turkmath:6143] FGC-HRI-IPM number theory seminars[Olga Lukina, Leiden][June 14, 5pm]

[Özlem Ejder]

Dear all,

Olga Lukina (Leiden University, Netherlands) is our speaker in the
FGC-HRI-IPM Number Theory Seminar this upcoming week.

*Date and Time:* Wednesday June 14, 17:00 Istanbul time

*Title: *Weyl groups in Cantor dynamics

*Abstract:* Arboreal representations of absolute Galois groups of number
fields are given by profinite groups of automorphisms of regular rooted
trees, with the geometry of the tree determined by a polynomial which
defines such a representation. Thus arboreal representations give rise to
dynamical systems on a Cantor set, and allow to apply the methods of
topological dynamics to study problems in number theory. In this talk we
consider the conjecture of Boston and Jones, which states that the images
of Frobenius elements under arboreal representations have a certain cycle
structure. To study this conjecture, we borrow from the Lie group theory
the concepts of maximal tori and Weyl groups, and introduce maximal tori
and Weyl groups in the profinite setting. We then use this new technique to
give a partial answer to the conjecture by Boston and Jones in the case
when an arboreal representations is defined by a post-critically finite
quadratic polynomial over a number field. Based on a joint work with Maria
Isabel Cortez.

*Zoom Meeting ID: *856 1386 0958
*Passcode: *513992

Sevgiler,
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