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Speaker:

Boris Kunyavskii
Affiliation:

Bar-Ilan University/MPIM
Date:

Tue, 2018-04-24 11:00 - 12:00
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar We consider equations of the form w(x,y)=g where w

is a group word in two letters (= an element of the free

group on two generators), g is a fixed element of a fixed

group G, and solutions are sought among pairs of elements

of G. Our focus is on the case where G is a simple linear

algebraic group. In this talk we consider the case

G=SL(2,K) where K is a number field. We discuss approximation

properties of the corresponding algebraic K-variety.

For a broad class of words, we reduce the problem to a similar

problem for a certain surface, using the fibration method.

For the commutator word w=[x,y] we obtain conclusive results.

Several related open problems will also be discussed.

The talk is based on a joint work with T. Bandman.

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