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Ib Madsen: Moduli Spaces and Topology

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Time: Wed 2014-06-11 15.15 - 16.15

Lecturer: Ib Madsen, University of Copenhagen

Place: Lecture hall Oskar Klein, Alba Nova


14:15-15:00 Precolloquium for PhD and master students by Olof Bergvall, SU (Room Oskar Klein, Albanova)

15:15-16:15 Colloquium lecture by Ib Madsen (Room Oskar Klein, Albanova)

16:15-17:00 SMC social get together with refreshments


I will discuss the relationship between the classical moduli space of Riemann surfaces and the configuration space of surfaces smoothly embedded in high dimensional euclidian space. The homological structure of the latter space can be completely determined when the genus of the embedded surfaces tend to infinity. The configuration space may also be defined for manifolds of dimension larger than two. A recent theorem of Galatius and Randal-Williams identifies the homology of the configuration space of certain 2d-dimensional manifolds embedded in high dimensional euclidian space, the so called generalized surfaces. The above results concerning homology of moduli spaces do not give any information about the homotopy groups, mainly because the spaces are not simply connected. But for manifolds of dimension at least five,there is an alternative approach to the moduli spaces. I will end the lecture with a brief description of joint work with Alexander Berglund concerning the homotopical and homological structure of the homotopy automorphism group of the generalized surfaces in terms of derivations of free Lie algebras and outer automorphisms of free groups. This represents the first step in the alternative approach.

The lecture will be as non technical as I can master.

Title Date
Michael Rathjen: Is Cantor’s continuum problem still open? Oct 15, 2014
Irene Fonseca: Variational Methods in Materials and Image Processing Sep 03, 2014
Ib Madsen: Moduli Spaces and Topology Jun 11, 2014
Mikko Salo: Can one hear the shape of a space? Mar 27, 2014
Svante Janson: Random Graphs Jan 29, 2014
Mireille Bousquet-Mélou: Self-avoiding walks May 07, 2014