Abstract: Convexity has played an important role in the development of several complex variables (SCV). Complex analysts have their own version of convex sets and convex functions, which form the basis of many classical results in SCV. At the same time, new analogies between SCV and convex analysis are still being discovered. In this talk, we will look at some results from convex analysis that establish asymptotic estimates for the gap between a convex domain and approximating polyhedra of increasing complexity. We will motivate the rationale behind developing an analogous theory on the complex side, and work with simple examples to illustrate the main components of this relatively new exploration. This talk will be accessible to graduate students.
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