Flow equivalence of shift spaces (and their C*-algebras)
Shift spaces are zero-dimensional dynamical systems (a compact space
and a homeomorphism) of a particular simple form related to formal
language theory and computer science. They are, in many interesting
cases, finitely presented.
Flow equivalence is a coarse
relation which may be described both in terms of symbolics/language
theory and in terms of actions of R. The ultimate goal of this lecture
series is to cover what is known about classification of finitely
presented shift spaces up to this relation. We intend to achieve this
over 7-10 lectures every other Tuesday starting January 18, 2011.
Lecture 1 18.01.11 10-12, Aud 2
In the first lecture I will try to give a general overview with many examples and few proofs.
Lecture 2 01.02.11 13-15, Aud 8
Toke Meier Carlsen
We proved the Parry-Sullivan theorem.
Lecture 3 15.02.11 10-12, BIO 4024
Two classes of shift spaces have been classified up to flow equivalence by appealing and readily comparable invariants: The irreducible shifts of finite type, and the Sturmian shifts. I will carefully describe these two classes of shifts and the invariants - and less carefully sketch the proofs that the invariants are in fact complete.
Lecture 4 01.03.11 10-12, Aud 10
I continue the investigation of the flow classification of shifts of finite type and the Sturmian shifts. I intend to give full details of the Franks theorem that the Bowen-Franks invariant is complete, as it paves the way for the equivariant and reducible cases which are of great importance to us. I will also sketch of to compute and compare the invariants for Sturmian shifts.
Lecture 5 15.03.11 10-12, BIO 4024
Toke Meier Carlsen
We now turn to the systematic develoment of sofic shifts, describing their canonical covers. In particular, we shall see how these in a certain sense are flow invariants.
Lecture 6 29.03.11 10-12, Aud 5
Lecture 7 12.04.11 10-12, Aud 8
In this final lecture I go over the proof of the extension theorem by Boyle, Carlsen and myself, give applications and speculate about what the future may hold.
Last modified: Sun Aug 19 23:15:39 CEST 2012