Workshops in Geometric Topology

University Of Wisconsin-Milwaukee, Milwaukee WI

Investigators

Abstract

This grant is to fund the 32nd annual Workshop in Geometric Topology, to be hosted at Texas Christian University in Fort Worth, Texas, June 25-27, 2015, as well as the 33rd and 34th workshops in 2016 and 2017, to be hosted by Colorado College and Brigham Young University. Such mathematics workshops provide an opportunity for mathematicians working in a certain subfield, in this case geometric topology, to meet, interact, and share their research through both official lecture presentations and informal discussions. Grant funds will be utilized primarily to support the travel and attendance costs of conference participants, particularly graduate students, young Ph.D.s, and other researchers without their own sources of funding. The field of geometric topology, broadly speaking, is the study of spatial configuration, both in the physical universe and of abstract "spaces" that can model real-life phenomena. For example, a topologist might study how a physical string or protein strand is knotted in the real three-dimensional world, or he or she might study the abstract space of positions that a machine could inhabit, allowing for an arbitrary number of parameters that describe the positions of various components. Research in this field can vary from the highly abstract to more concrete applications supported by those abstract underpinnings. Modern applications of topology occur in such diverse areas as robot motion planning, data analysis, image processing, sensor networks, and mathematical biology. A primary goal of these Workshops in Geometric Topology is to provide mathematicians in geometric topology (and, more recently, the closely related field of geometric group theory) who have active research programs, but limited support, an opportunity to discuss their work with others in the field. Another important goal is to expand the interests of the participants by having a nationally-recognized expert discuss an important area of current interest. A third goal is to provide a serious but informal research atmosphere in which graduate students can meet and learn from others in the field. At each workshop, participants will have the opportunity to attend three lectures given by a principal speakers chosen for his or her top-tier research credentials and superb expository abilities. The principal speaker at the 32nd annual Workshop will be the internationally-renowned Wolfgang Lück of the University of Bonn and the Hausdorff Research Institute for Mathematics; he will provide introductory talks about L2-Betti numbers and the Farrell-Jones Conjecture and then a talk about applications to 3-manifolds. The other workshop participants will be invited to share their own work by giving short talks in a congenial environment, and important time will be provided for informal discussion and interaction among participants and with the principal speaker. Overall, the workshops will provide opportunities for geometric topologists to interact and share ideas, leading to possible research collaborations. The workshops will be advertised nationally. Graduate students and members of underrepresented groups will be given top priority for funding and will be particularly encouraged to attend and to speak. The website for the 32nd annual workshop can be found at http://faculty.tcu.edu/gfriedman/GTW2015/