Nipissing University will offer a Workshop on Recent Advances in Topological and Measure-Theoretic Methods in Dynamical Systems in order to bring researchers and students in these areas together for a five-day series of talks and seminars. The workshop will be jointly supported by the US National Science Foundation and the Fields Institute of Canada, and will be held at Nipissing?s campus in North Bay, Ontario, Canada, May 17-22, 2010. The scientific focus of the workshop will be on recent developments in topological and measure-theoretic methods in dynamical systems. Senior researchers will share fundamental research techniques, and recent results, in the areas of focus with attendees, including graduate students, post-doctoral students, and researchers that have recently received the PhD. James Yorke (U. of Maryland), Mariusz Urbanski (North Texas State U.), Michael Yampolsky (U. of Toronto), and Vladimir Pestov (U. of Ottawa) art among the principal speakers. Topics include topological and measure-theoretic properties of attractors, basin boundaries, and Julia sets of rational and entire maps, minimal maps on manifolds, and dynamics of infinite-dimensional groups.
The mathematics research fields of dynamical systems, topology, and measure theory have long had significant areas of overlap, and a continuing tradition of researchers working across these fields, and borrowing tools from each other. Over the last 25 years, there have been many developments that have increased the interaction among topology, dynamical systems, and measure theory. NSF support will be used to enable at least 10 US-based students and recent PhDs to attend the workshop. The workshop will provide the opportunity for recently trained professional mathematicians and students to prepare for research in areas in which current developments are moving rapidly at the intersection point of topology, measure theory, and dynamical systems. Major speakers with international reputations have been selected who are active in these research areas.
This project is jointly funded by the Topology Program and the Analysis Program.
Nipissing University, North Bay, Ontario, the Fields Institute, and the National Science Foundation supported a "Workshop on Recent Advances in Topological and Measure-Theoretic Methods in Dynamical Systems" in order to bring senior and junior researchers and students in these areas together for a five-day series of workshops. The workshop was held at Nipissing University campus in North Bay in May, 2010, and again in May 2011. The National Science Foundation supported attendance at the workshops by 18 US-based graduate students, post-docs, and recent PhDs. The Broad Impact of this proposal was to provide the opportunity for recently trained professional mathematicians to prepare for research in areas in which current developments are moving rapidly, the intersection point of topology, measure theory, and dynamics. Major speakers with international reputations were selected, including James Yorke (U. Maryland), Mariusz Urbanski (U. North Texas), Jan van Mill (Free University, Amsterdam) who are active in these research areas. . In addition to the students and post-docs 33 senior researchers attended the workshops. Ample time was provided in the workshop schedule for both formal talks and informal interactions among the junior and senior participants. Altogether there were a total of 36 hour-long talks in the two workshops. In addition, one feature popular with the students and post-docs was a question and answer session each afternoon in which the days’ speaker answered questions in an open and informal atmosphere. The links formed are likely to have continuing impact on the research direction of both junior and senior participants. The Intellectual Merit of the workshops are that they focused on areas of overlap of research thrusts which have a traditional background of working together, but in which it is somewhat difficult for a student to acquire the research background needed to work in overlapping fields. Topological and measure-theoretic methods in dynamics are two such areas that were the focus of the workshops. There is a record of success in these areas, but many opportunities yet remain.
