Summer School on Surgery and the Classification of Manifolds

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This award provides partial support towards the travel of US-based early-career mathematicians to the "Summer School on Surgery and the Classification of Manifolds" held at the University of Calgary, Alberta, Canada, on July 18-22, 2016. This international event is sponsored by the Pacific Institute of Mathematical Sciences (PIMS) Collaborative Research Group (CRG) in Applied, Algebraic, and Geometric Topology. Manifolds are geometric objects that locally resemble flat space. For example, the surface of a doughnut is a two-dimensional manifold called a torus. The technique of surgery, which involves cutting and pasting pieces of manifolds, allows a transition from questions in geometry to quantifiable and easier questions in algebra. The technique of surgery is a central area of mathematics, but it is quite difficult to learn because it draws on many other areas. This summer school is an educational outreach program designed to make the techniques of surgery and manifold topology accessible to a wide range of graduate students and junior mathematicians. The program includes lectures by experts, mini-lectures by participants on background topics, and exercise sessions mentored by experts. Graduate students, junior faculty, women, minorities, and persons with disabilities are especially encouraged to participate and to apply for support.Classification of manifolds is a central area of geometric topology and intersects with many other fields, including analysis, geometry, algebra, and group theory. This summer school aims to stimulate education and research in classification of manifolds and related areas of mathematics. Participants will have diverse mathematical backgrounds, with knowledge in geometric topology, algebraic topology, geometric group theory, differential geometry, and geometric functional analysis. Depending on interest, participants will have different take-aways from the summer school. A geometric topologist may learn about handle analysis and the specifics of the topology of manifolds. An algebraic topologist might learn about how classifying spaces, generalized (co)homology theories, and algebraic K-theory are used in practice. A geometer might learn about metrics of positive scalar curvature and tools for the topological classification of manifolds with geometric structure. A geometric group theorist might learn about applications of (co)homology of groups and large scale geometry. A geometric functional analyst would learn about a world parallel to that of C*-algebras and noncommutative geometry. The website of the summer school is http://www.pims.math.ca/scientific-event/160718-ssscm