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Mathematics Colloquium: Steve Hurder (University of Illinois at Chicago)

Event Type
Department of Mathematics
245 Altgeld Hall
Oct 17, 2013   4:00 pm  

Steve Hurder (University of Illinois at Chicago) will present "Foliations - Thurston Zebras to Cantor Geometries."  Abstract: It was forty years ago that William Thurston electrified the theory of foliations with his celebrated constructions of foliations, and raised the hope of classifying these geometric structures on manifolds. This was followed by an intense period of development over the next ten years of the theory of characteristic classes for foliations. The study of foliations since then has taken many twists and turns, finding applications in dynamical systems and ergodic theory, and incorporating many new ideas in the quest for a viable classification scheme. In this talk, I will survey three aspects of these developments: the role of algebra in the works of Kamber and Tondeur in the 1970's on secondary class theory; the rise of dynamical and ergodic theory methods in the 1980's and 1990's; and the current development of topological methods and the techniques of Cantor actions to gain a new understanding of the structure of foliations.

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