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SUMMARY:Basic Notions Seminar - Polymath 14: From word games to an analysi
 s-definition of abelian groups
DTSTART;VALUE=DATE-TIME:20260525T090000Z
DTEND;VALUE=DATE-TIME:20260525T103000Z
DTSTAMP;VALUE=DATE-TIME:20260603T061157Z
UID:indico-event-11351@ictp.it
DESCRIPTION:\n	Abstract:\n	 \n\n	Consider the following three properties 
 of a general group G:\n	 \n\n		\n			Algebra: G is abelian and torsion-fr
 ee.\n	\n	\n		\n			Analysis: G is a metric space that admits a "norm"\, na
 mely\, a translation-invariant metric d(.\,.) satisfying: d(1\,g^n) = |n| 
 d(1\,g) for all g in G and integers n.\n	\n	\n		\n			Geometry: G admits a
  length function with "saturated" subadditivity for equal arguments: l(g^2
 ) = 2 l(g) for all g in G.\n	\n\n	 \n\n	While these properties may a prio
 ri seem different\, in fact\, they turn out to be equivalent. The nontrivi
 al implication amounts to saying that there does not exist a non-abelian g
 roup with a “norm”.\n\n	 \n\n	We will discuss some of the proofs of t
 hese equivalences\, as well as the logistics of how the problem was solved
 \, via a PolyMath project that began on a blogpost of Terence Tao.\n\n	
  \n\n	(Joint - as D.H.J. PolyMath - with Tobias Fritz\, Siddhartha Gadgil
 \, Pace Nielsen\, Lior Silberman\, and Terence Tao.)\n	 \n\n	Register in 
 advance (Zoom):https://zoom.us/meeting/register/1hmMfblKTLmIeuFJBRVKhQ\n\n
 //indico.ictp.it/event/11351/
LOCATION:ICTP Leonardo Building - Euler Lecture Hall
URL://indico.ictp.it/event/11351/
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