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Documents McMullen, Curtis T. 3 results

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Billiards and number theory - McMullen, Curtis T. (Author of the conference) | CIRM H

Multi angle

The dynamics of billiards in a regular polygon can be studied from a wide range of mathematical perspectives. In this talk we will discuss connections between periodic billiard paths and number theory, modular symbols, heights and Hilbert modular varieties. In particular we will describe a new form of arithmetic chaos that emerges from dynamics in the regular 12-gon.

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Curtis Tracy McMullen (born 21 May 1958) is Professor of Mathematics at Harvard University. He was awarded the Fields Medal in 1998 for his work in complex dynamics, hyperbolic geometry and Teichmüller theory. McMullen graduated as valedictorian in 1980 from Williams College and obtained his Ph.D. in 1985 from Harvard University, supervised by Dennis Sullivan. He held post-doctoral positions at the Massachusetts Institute of Technology, the Mathematical Sciences Research Institute, and the Institute for Advanced Study, after which he was on the faculty at Princeton University (1987–1990) and the University of California, Berkeley (1990–1997), before joining Harvard in 1997. He received the Salem Prize in 1991 and was elected to the National Academy of Sciences in 2007. In 2012 he became a fellow of the American Mathematical Society.[-]
Curtis Tracy McMullen (born 21 May 1958) is Professor of Mathematics at Harvard University. He was awarded the Fields Medal in 1998 for his work in complex dynamics, hyperbolic geometry and Teichmüller theory. McMullen graduated as valedictorian in 1980 from Williams College and obtained his Ph.D. in 1985 from Harvard University, supervised by Dennis Sullivan. He held post-doctoral positions at the Massachusetts Institute of Technology, the ...[+]

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Coupled rotations and snow falling on cedars - McMullen, Curtis T. (Author of the conference) | CIRM H

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We study cascades of bifurcations in a simple family of maps on the circle, and connect this behavior to the geometry of an absolute period leaf in genus $2$. The presentation includes pictures of an exotic foliation of the upper half plane, computed with the aid of the Möller-Zagier formula.

30F10 ; 30F30

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