Title: Tilings, Symbolic Dynamical Systems, and Undecidability
Abstract: The area of
symbolic dynamical systems was developed as a tool to understand
geodesic flows on manifolds of negative curvature. It evolved
into an area with applications to computer science, information theory,
as well as statistical mechanics. Research in the past two decades has
uncovered a deep connection between the basic objects of study in
symbolic dynamics and theoretical computer science. In this talk
we will give an introduction to the field and describe some of these
connections. We will also describe some recent research (joint
with M. Schraudner and I. Ugarcovici) involving the
existence of strongly aperiodic tilings for the Heisenberg group.
Bio: Ayşe Şahin received her BA
in mathematics from Mount Holyoke College in ’88 and her MA (’92) and
PhD (’94) in mathematics from the University of Maryland, College
Park. She was an Assistant Professor at North Dakota State
University in Fargo, ND from 1994-2000 and an Associate Professor from
2000-2001. She moved to DePaul University in Chicago, IL in 2000
where she was promoted to full professor in 2010. She joined the
faculty at Wright state in July, 2015 as the Chair of Mathematics and
Statistics. Şahin’s research area is in ergodic theory and dynamical
systems. Her focus is on actions of amenable groups. She
has published in the areas of orbit equivalence of group actions,
tilings of groups, and special representations of group actions.
She has organized numerous conferences and has presented her research
in conferences across the United States and internationally. Şahin also
has interests in curriculum development and teacher training. She
has designed special mathematics courses for science majors and also
future and practicing teachers. She has designed and organized
professional development programs for teachers in the Common Core State
Standards in mathematics. She is interested in inquiry based
learning methods in the college classroom and has co-authored an
inquiry based advanced undergraduate level text on dynamical
systems. Most recently at Wright State University she has been
the project lead in the design and implementation of co-remediation for
entry level mathematics courses.