Curtis T. McMullen
Harvard University
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Primary Section: 11, Mathematics Membership Type:
Member
(elected 2007)
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Research Interests
My research focuses on the interaction between complex analysis, geometry, dynamics and low-dimensional topology. A central idea is that the tension between the flexibility of 2-dimensional objects and the rigidity of higher-dimensional objects is mediated by fixed-point phenomena on moduli spaces. This theme has ramifications ranging from the theory of renormalization (self-organizing critical structures) to the geometrization of 3-manifolds (curved tilings associated to knots). Recently connections with algebra and number theory have also emerged, leading to new examples of polygons with optimal billiard dynamics, new constructions of surfaces with many symmetries, and new calculations in string theory.
