My lecture on Jan 19, 2022 (tomorrow

[Siddhartha Gadgil]

I am giving the following lecture online at KREA, which may be of some interest. I have given variants of this before, but this one has a little bit of lean 4 programming at the end.

regards,

Siddhartha

Title: Lengths, Free groups and Computer proofs: A PolyMath adventure

Abstract:   Terence Tao posted on his blog a question of Apoorva Khare, asking whether the free group on two generators has a homogeneous, conjugacy invariant length function. 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 process of discovery of the proof. The unusual feature of the use of computers here was that a computer generated but human readable proof was read, understood, generalized and abstracted by mathematicians to obtain the key lemma in an interesting mathematical result - perhaps the first such instance.

Video link details:

Topic: KREA ONLINE EVENT

Time: Jan 19, 2022 03:15 PM India

Join Zoom Meeting

https://krea-edu-in.zoom.us/j/97676183894?pwd=ajBwZHJrR1Vnb2lvdEpJb1hYVHNhUT09

Meeting ID: 976 7618 3894

Passcode: 123456