NEW TIME! Basic Notions Seminar - Polymath 14: From word games to an analysis-definition of abelian groups

[ICTP Math Section]

*Basic Notions Seminar *

*Date and Venue*: Monday 25 May at *11:00* - ICTP Leonardo Building 
Euler Lecture Hall

*Speaker: *Apoorva Khare (Indian Institute of Science)

*Title:* Polymath 14: From word games to an analysis-definition of 
abelian groups

*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(1,g^n) = |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(g^2) = 2 l(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 some of the proofs of these equivalences, as well as the 
logistics of how the problem was solved, via a PolyMath project that 
began on a blogpost 
<https://terrytao.wordpress.com/2017/12/16/bi-invariant-metrics-of-linear-growth-on-the-free-group/> 
of Terence Tao.

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


Register in advance (Zoom): 
https://zoom.us/meeting/register/1hmMfblKTLmIeuFJBRVKhQ

All are welcome to join.

https://indico.ictp.it/event/11351/ <https://indico.ictp.it/event/11333/>

-- 
Micol Stock
Secretariat of the ICTP Math Section

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