[Binghamton Geometry/Topology Seminar] November 18

[Lucas Sabalka]

                  BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

Date:  Thursday, November 18, 2010
Time:  2:50-3:50pm
Place:  Library North 2205 followed by coffee/tea in the Anderson
         Reading Room.

Speaker:  Dave McCune (Nebraska)
Title:  Semigroups arising from asynchronous automata

Abstract:  Groups and semigroups generated by synchronous automata have been
well-studied, particularly since the early 1980’s.  An interesting
generalization of these semigroups is the class of semigroups generated by
asynchronous automata.  In this talk we will discuss semigroups generated by
asynchronous automata, primarily restricting to a new class of semigroups
generated by a subclass of asynchronous automata which includes synchronous
automata.  We call this new class of semigroups “expanding automaton
semigroups.”  We show that the class of semigroups generated by synchronous
automata is strictly contained in the class of expanding automaton
semigroups, and that the class of expanding automaton semigroups is strictly
contained in the class of semigroups generated by asynchronous automata.  As
with groups and semigroups generated by synchronous automata, expanding
automaton semigroups act on regular rooted trees.  We show that
undecidability arises in the dynamics of these actions, and use this to show
that undecidability arises when trying to understand the fixed point sets of
asynchronous automaton semigroups.
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