Nipissing University, North Bay, Ontario will offer a Workshop on Recent Advances in General Topology, Dimension Theory, Continuum Theory, and Dynamical Systems in order to bring senior and junior researchers and students in these areas together for a five-day series of talks and seminars. The workshop will be held at Nipissing University campus in North Bay, May 17-22, 2012. It will be jointly supported by the National Science Foundation and the Fields Institute of Canada. The scientific focus of the workshop will be on recent advances in topology, including dimension theory and continuum theory, and dynamical systems. Senior researchers will share fundamental research techniques and recent results with attendees, including post-doctoral, graduate and advanced undergraduate students, and junior researchers who received the PhD within the last 6 years. Among other topics, recent results on the topology of buried points in Julia sets, the solution of Lelek's problem on the span of continua, and extending isotopies of plane continua, all of which have application in both topology and dynamical systems, will be discussed.
Dynamical systems uses tools from many areas of mathematics, and motivates these same areas by raising questions, both fundamental and applied. In the workshop, students and junior researchers, whose focus on the way to a PhD has necessarily often been narrow, will be exposed to research techniques and results that draw from multiple sources. The areas of topology, dimension theory, and dynamical systems traditionally have experienced overlapping research interests, but it is somewhat daunting for students to acquire the background needed to work in the overlap. NSF support will enable at least 10 US-based students and junior researchers to attend the workshop and expand their research horizons. Major speakers with international reputations are being selected who are active in these research areas. The format of the workshop is designed to maximize the opportunities for interaction among the participants beyond the lectures. Time is provided in the workshop schedule for both formal talks and informal interactions among the junior and senior participants, including every afternoon an informal question and answer session for the students and junior researchers with the day's speakers. The links formed are likely to have continuing impact on the research direction of both junior and senior participants.
url: www.nipissingu.ca/topology
took place at Nipissing University, North Bay, Ontario, May 14-18, 2012. There were 13 one-hour lectures; some of these lectures were video streamed. The videos continue to be accessible on the Nipissing University website (nipissingu.ca/topology). In addition to the Fields Institute funding, the National Science Foundation provided funding for US-based graduate students, recent PhDs and faculty to participate in the workshop. The participants came from Canada, USA, Holland and Mexico. The workshop provided the opportunity for recently trained professional mathematicians and students to prepare for research in areas in which General Topology, Dimension Theory, Continuum Theory and Dynamical Systems intersect and play an important role in other areas such as Analysis, Dynamical Systems. Major speakers with international reputations, who are active in these research areas, devoted a significant amount of their time to working with students. A total 8 US based graduate students and recent PhDs and 5 senior mathematicians were supported. In addition 8 more US based students were supported at the related Summer Topology Conference at the same location which took place in July 2013. The workshop featured two series of lectures by Jan van Mill, VU-Amsterdam, and Piotr Minc, Auburn U. Jan van Mill's two lectures were titled Various Aspects of Countable Dense Homogeneity. van Mill's lecture gave a survey of results concerning spaces with the countable dense homogeneity property. Piotr Minc's three lectures were focused on the inverse limits of (topological) graphs with simplicial bonding maps. Minc has been working on developing combinatorial techniques to study continua which can be constructed using graphs, in particular trees, and simplicial maps. The remaining lectures covered a variety of topics. Sergey Antonyan of UNAM gave a talk on Gromov-Hausdorff Hyperspaces. Lex Oversteegen of U. Alabama-Birmingham lectured on laminations of the unit disk, a technique used to study the dynamics of complex polynomials on their Julia sets from a combinatorial/topological viewpoint. Logan Hoehn lectured on shortest paths in planar domains and E. D. Tymchatyn ( U. of Saskatchewan) gave a talk on a classical problem concerned with the existence of non-separating subcontinua of a plane continuum. V. Martinez ( UNAM) gave a presentation on examples of continua which can be obtained using generalized inverse limits of [0,1]. In addition, two graduate students who are finishing their Ph.D. theses presented their work. Francis Kibedi from York U. presented his work "Saturated Linear Orders and Martin's Axiom". Ross Ptacek from U. of Alabama-Birmingham presented his work on laminations of cubic polynomials.
