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Eigenfunctions Seminar

Title: Homogeneous length functions on Groups: A polymath adventure
Speaker: Siddhartha Gadgil (and Apoorva Khare), IISc Mathematics
Date: 15 January 2018
Time: 4 – 5 pm
Venue: LH-1, Mathematics Department

Terence Tao posted on his blog a question of Apoorva Khare, asking whether the free group on two generators has a length function $l: F_2 \to\mathbb{R}$ (i.e., satisfying the triangle inequality) which is homogeneous, i.e., such that $l(g^n) = nl(g)$. A week later, the problem was solved by an active collaboration of several mathematicians (with a little help from a computer) through Tao’s blog. In fact a more general result was obtained, namely that any homogeneous length function on a group $G$ factors through its abelianization $G/[G, G]$.

I will discuss the proof of this result and also the process of discovery (in which I had a minor role).

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 17 May 2024