Skip to content. | Skip to navigation

Personal tools

Theme for TIFR Centre For Applicable Mathematics, Bangalore


You are here: Home / Events / PolyMath14: Groups with norms

PolyMath14: Groups with norms

Prof. Apoorva Khare IISc
Prof. Apoorva Khare IISc
When Mar 12, 2019
from 03:00 PM to 04:00 PM
Where LH006
Add event to calendar vCal

Abstract: Consider the following three properties of a general group G:
(1) Algebra: G is abelian and torsion-free.

(2) Analysis: G is a metric space that admits a ”norm”, namely, a translation- invariant metric d(.,.) satisfying: d(l,gn= |n|d(1,g) for all g in G and integers n.

(3) Geometry: G admits a length function with ”saturated” subadditivity for equal arguments: l(g2) = 2l(g) for all g in G.

While these properties may a priori seem different, in fact they turn out to be equivalent. The nontrivial implication amounts to saying that there does not exist a non-abelian group with a ”norm”.

We will discuss motivations from analysis, probability, and geometry; then the proof of the above equivalences; and finally, the logistics of how the problem was solved, via a PolyMath project that began on a blogpost of Terence Tao.

(Joint - as D.H.J. PolyMath - with Tobias Fritz, Siddhartha Gadgil, Pace Nielsen, Lior Silberman, and Terence Tao.)


Filed under: