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Outer space, symplectic derivations of free Lie algebras and modular forms

Hot Topics: Galois Theory of Periods and Applications March 27, 2017 - March 31, 2017

March 28, 2017 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Karen Vogtmann (University of Warwick)
Location: MSRI: Simons Auditorium
  • Galois theory

  • Galois orbits

  • Periods

  • operads

  • free Lie algebras

  • Lie algebras

  • universal mapping properties

  • modular forms

  • Lie operad

  • outer automorphisms

  • symplectic automorphisms

  • simplicial trees

  • group cohomology

  • Lie algebra cohomology

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



In this talk I will describe the connection, discovered by Kontsevich, between symplectic derivations of a free Lie algebra and the “symmetric space” for the group Out(F_n) of outer automorphisms of a free group. The latter is known as Outer space, and can be described as a space of free actions of F_n on metric simplicial trees. The fact that the quotients of such actions are finite graphs leads to a combinatorial understanding of this space which can be used to gain cohomological information about both the group Out(F_n) and the Lie algebra of symplectic derivations. One surprising outcome is a way of constructing cohomology classes from classical modular forms, as described in joint work with Conant and Kassabov. No prior knowledge of Outer space or Kontsevich’s theorem will be assumed

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Video/Audio Files


H.264 Video 6-Vogtmann.mp4 583 MB video/mp4 rtsp://videos.msri.org/data/000/028/102/original/6-Vogtmann.mp4 Download
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