Topology in Dimensions 3, 3.5 and 4

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This National Science Foundation award provides partial support for the Conference on Topology in Dimensions 3, 3.5 and 4, to be held at the University of California Berkeley from June 25 to 29, 2018. Topology studies the mathematical properties of "spaces," from the physical 3-dimensional space and 4-dimensional space-time in which we carry out our daily lives, to much more abstract spaces such as the space of all possible configurations of a robot or all possible solutions to an equation. This conference will bring together researchers working on the interplay between three and four dimensional topology to share state of the art knowledge, hear talks from a select group of internationally renowned experts, and develop new collaborations. This grant will support travel expenses for graduate students, early career researchers and speakers.There is a fundamental nexus of problems, including the smooth 4-dimensional Schonflies and Poincare conjectures and their connection to decompositions of 3-manifolds, which is deeply rooted in and has long motivated the work of Abby Thompson (working mostly in dimension 3), Marty Scharlemann (working in 3.5-dimensional topology), and Rob Kirby (working mostly in dimension 4). This conference uses the collective legacy of these researchers as an organizing theme with the goal of reinvigorating work on these foundational problems, reminding the community of the power of their tools, and showcasing recent topological advances in the spirit of their work. Speakers will share old and new ideas and participants will have sufficient time for discussion with each other and with the speakers and for the forging of new collaborations. We have specifically asked certain speakers to give historical talks to help maintain continuity with the past as our rapidly developing field moves into the future. These talks will be of especial benefit to students and younger researchers, and will also help in the process of archiving the mathematical past. The conference website is at https://sites.google.com/sjsu.edu/thompscharbyfest/This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.