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
Location: SLMath: Eisenbud 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
18C10  Theories (e.g., algebraic theories), structure, and semantics [See also 03G30]
17B35  Universal enveloping (super)algebras [See also 16S30]
Vogtmann
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
Vogtmann
H.264 Video 
6Vogtmann.mp4

Download 
Please report video problems to itsupport@slmath.org.
See more of our Streaming videos on our main VMath Videos page.