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Created January 23, 2018 03:45
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sample-seminar.md
speaker title date time venue
Siddhartha Gadgil and Apoorva Khare (IISc Mathematics)
Eigenfunctions Seminar: Homogeneous length functions on Groups: A polymath adventure
15 January, 2018
4 pm
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).

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