2017 Pingree Park Dynamical Systems School

University Of Denver, Denver CO

Investigators

Abstract

The Pingree Park Dynamical Systems School will take place at the Pingree Park Campus of Colorado State University, CO on the dates July 16-21, 2017. A group of 36 research mathematicians will be brought together to discuss problems in dynamical systems, focused mainly on problems related to symbolic dynamics. There will be three extended mini-courses on exciting new research presented by three well-known experts in this field. In addition, sixteen other 30 minute talks will be presented by conference participants. Participants will include graduate students, postdocs as well as more senior researchers. The organizer will conduct a one hour "problem session" in which participants pose open problems in the area to stimulate discussion throughout the conference. The goal of the meeting is to bring together researchers working in different, but closely related, fields to disseminate results and initiate new lines of inquiry. As with the successful 2014 Pingree conference, the meeting participants will include a heavy proportion of young researchers who, through the mini-courses, can both learn foundational material and be brought up to speed on new developments. The Pingree Park Campus provides an ideal environment for interaction and thoughtful investigation, fostering research and development in this broad area of research. The main topic of this meeting will be group actions on zero-dimensional spaces, but related fields in dynamics will also be represented. The conference will revolve around three mini-courses, given by experts on the main topics of the meeting. Much recent activity on symbolic dynamics of general group actions centers on some unexpected connections to computability theory and algorithmic complexity. Emmanuel Jeandel is a world-renowned researcher in this area and his mini-course should provide a useful introduction, and describe current fertile directions for research. For Z-actions, symbolic dynamics is a standard tool for modeling more general systems, but similar techniques for more general group actions are still not well-understood. Anthony Quas and Ayse Sahin have done significant work of this sort, including a multidimensional version of Rokhlin's Lemma and hypotheses guaranteeing existence of Markov partitions for multidimensional systems. At least one of their minicourses will pertain to some of this work, and that the other may relate to some of their other excellent work, such as Sahin's work on actions of the Heisenberg group or Quas's work on relative maximal entropy.