Virginia Topology Conference 2018

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This award provides partial support for the 2018 Virginia Topology Conference, which will be held December 12-14, 2018, on the campus of the University of Virginia. The conference will bring together a collection of mathematicians from all career stages. Scientifically, the conference will provide a timely forum for interaction between groups of researchers in four-dimensional topology who approach similar research questions using different sets of tools, and stimulate learning, mathematical development, and collaboration between these groups. To promote professional development, the conference includes speaking slots set aside for graduate students, which will be scheduled so as to maximize attendance by senior mathematicians or others who may have travel constraints, thereby ensuring the broadest exposure for the junior speakers. Conference activities will be scheduled so as to maximize opportunities for interactions between researchers at different career stages and situations. The organizers will also make every effort to encourage participation by women and members of underrepresented groups. Gauge theory has played a dominant role in the study of smooth four-dimensional manifolds for nearly thirty-five years, but there are many questions in four-manifold topology that have not been resolved by gauge-theoretic methods. In the last few years certain constructive techniques have emerged for the study of problems in smooth four-dimensional topology, in the form of trisections; the theory of trisections is attracting considerable interest among topologists and contains the potential to uncover new structure or properties of four-manifolds in a manner similar to the handle calculus due to Akbulut and Kirby in the 1970s. The central goal of this conference is to bring together researchers on various sides of the potential connection between gauge theory and trisections, with the hope of stimulating further progress on central problems in the field: these include the relationship between trisections and gauge-theoretic invariants of four-manifolds and surfaces they contain, the generalized Property R conjecture for links, and the Andrews-Curtis conjecture. The list of speakers includes experts in gauge theory, three- and four-manifold topology, and Heegaard Floer invariants, as well as pioneers in the development and application of trisection theory. The conference web site can be found at http://www.faculty.virginia.edu/tmark/VTC2018/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.