Interactions between Symplectic and Holomorphic Convexity in 4 Dimensions (23w5123)


(University of Virginia)

(University of California, Davis)

(University of Alabama)


The Banff International Research Station will host the "Interactions between Symplectic and Holomorphic Convexity in 4 Dimensions" workshop in Banff from April 9 to April 14, 2023.

A shape is "convex" if for any two points in the shape, the line segment connecting them does not pass out of the shape. This fundamental notion is the beginning of a wide array of ideas in geometry and analysis, leading to much more general theories in which "line segment" is replaced by other more flexible objects, or where "convexity" is determined by properties only analogous to the classical ones. Such generalized ideas of convexity are particularly important in the mathematical fields of symplectic topology and complex geometry. While links between the symplectic and complex versions of complexity have been recognized for some time, recent years have begun to see the emergence of an even closer relationship in which techniques and tools from one field can shed light or inspire new directions in the other.

This workshop will include specialists in complex analysis, symplectic geometry, contact topology, and smooth manifold theory, with the goal of introducing researchers in these fields to the techniques, ideas, and open problems in the others, united by the theme of convexity in various forms. Students and emerging researchers will be grouped with established scholars to establish new professional connections and research directions, and groups will work together to begin to bring their various tools together toward the solution of major open problems in the field.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).