Algebra Seminar

Tobias Fritz, Max Planck Institute for Mathematics in the Sciences / Perimeter Institute

"Homogeneous length functions on groups: a Polymath adventure"

A length function on a group is a measure of the size of a group element that is non-degenerate, symmetric, and subadditive. These properties are analogous to those of a norm on a vector space, except in that homogeneity is not required. So on which groups does there exist a length function that is also homogeneous? I will prove that these groups are precisely the torsion-free abelian groups, and state a more precise quantitative theorem. These are the results of the Polymath14 project initiated and moderated by T. Tao (arXiv:1801.03908).

MC 5403