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.