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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.

Kollokvier 2010

Titel Datum
Torsten Ekedahl: The Sato-Tate conjecture 2010‑11‑03
Jesper Grodal: Finite loop spaces 2010‑11‑10
Amol Sasane: An analogue of Serre’s Conjecture and Control Theory 2010‑10‑13
Reiner Werner: Quantum correlations - how to prove a negative from finitely many observations 2010‑09‑29
Warwick Tucker: Validated Numerics - a short introduction to rigorous computations 2010‑09‑22
Idun Reiten: Cluster categories and cluster algebras 2010‑09‑01
Stefano Demichelis: Use and misuse of mathematics in economic theory 2010‑05‑26
Gregory G. Smith: Old and new perspectives on Hilbert functions 2010‑04‑14
Tony Geramita: Sums of Squares: Evolution of an Idea. 2010‑03‑31
Jens Hoppe: Non-commutative curvature and classical geometry 2010‑03‑24
Margaret Beck: Understanding metastability using invariant manifolds 2010‑03‑03
Jan-Erik Björk: Glimpses from work by Carleman 2010‑02‑10