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Jesper Grodal: Finite loop spaces

Jesper Grodal, University of Copenhagen

Time: Wed 2010-11-10 16.00 - 17.00

Location: Room 3721, Department of Mathematics, KTH, Lindstedtsvägen 25, 7th floor

Hilbert's 5th problem, in its most basic form, asks if every compact topological group, which admits the structure of a smooth manifold, is a Lie group. In this form, it was answered affirmatively by von Neumann in 1929. If one takes a homotopical interpretation of the word "admits", the question is more subtle, and one is led to the notion of a finite loop space. These turn out not quite to be Lie groups, but nevertheless posses a rich enough structure to admit a classification. My talk will outline this story, which starts with a 1941 paper of Hopf: "Uber die Topologie der Gruppen-Mannigfaltigkeiten und ihre Verallgemeinerungen" and ends close to the present.

Colloquia 2010

Title Date
Torsten Ekedahl: The Sato-Tate conjecture Nov 03, 2010
Jesper Grodal: Finite loop spaces Nov 10, 2010
Amol Sasane: An analogue of Serre’s Conjecture and Control Theory Oct 13, 2010
Reiner Werner: Quantum correlations - how to prove a negative from finitely many observations Sep 29, 2010
Warwick Tucker: Validated Numerics - a short introduction to rigorous computations Sep 22, 2010
Idun Reiten: Cluster categories and cluster algebras Sep 01, 2010
Stefano Demichelis: Use and misuse of mathematics in economic theory May 26, 2010
Gregory G. Smith: Old and new perspectives on Hilbert functions Apr 14, 2010
Tony Geramita: Sums of Squares: Evolution of an Idea. Mar 31, 2010
Jens Hoppe: Non-commutative curvature and classical geometry Mar 24, 2010
Margaret Beck: Understanding metastability using invariant manifolds Mar 03, 2010
Jan-Erik Björk: Glimpses from work by Carleman Feb 10, 2010