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Homogeneous length functions on Groups: A polymath adventure

Speaker: Siddhartha Gadgil, Indian Institute of Science

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Abstract: 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→R (i.e., a function satisfying the triangle in-equality) which is homogeneous, i.e., such that l(gn)=nl(g)l(gn)=nl(g). A week later, the problem was solved by an active collaboration of several mathematicians (with a little help from a comput-er) 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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