The project
Homotopical group theory: the mathematics of symmetry and deformation.
Winner
Dr Jesper Grodal
University of Copenhagen
Department of Mathematics, Institute for Mathematical Sciences
Copenhagen DK-2100
Denmark
http://www.math.ku.dk
Jesper Grodal is a 33 year old Danish pure mathematician. After completing his MS in Mathematics at the University of Copenhagen, Grodal went on to MIT to undertake his PhD. His thesis, ‘Higher limits via subgroup complexes’ was widely acclaimed and went on to be published in the Annals of Mathematics – a measure of the very high esteem he is held in by his peers. The EURYI award would allow Grodal to come back to Copenhagen, where they have recently made other related and strong appointments. With the appointments from this award he will find himself a leader in a young fresh and worldclass group in Algebraic Topology.
Dr Grodal said: "The project is a very challenging and exciting one that should continue the process of bringing together algebra and topology at a very high level. I’m very grateful for being given this tremendous opportunity."
Provisional Award
€ 1,249,352
Project Description
Symmetry is one of the most fundamental notions in nature: in physics it gives rise to conservation laws, in chemistry it determines the structure of molecules, and in evolutionary biology, as well as other aspects of life, it often underlies the notion of “beauty”. The abstract study of symmetry at least goes back to the ancient Greek’s fascination with the Platonic solids, and has in modern day evolved into the mathematical discipline of group theory. The symmetries of a geometric object, or topological space, are however not stable under deformation, or homotopy*: whereas a perfectly round sphere has all rotational and reflectional symmetries, deforming the sphere slightly destroys these symmetries.
This project aims to reconcile this, combining the mathematical disciplines of group theory and homotopy theory in a novel way, to study symmetry deformation-invariantly. We seek to answer the following broad question: given a geometric object X, what kind of ‘instrinsic’, deformation invariant symmetries does it possess?
*Homotopy: A continuous change of a geometric object, roughly obtained by bending, stretching, or squeezing.
