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SUMMARY:The weight of groups and complexity of surface maps - Lvzhou Chen\
 , Purdue
DTSTART:20240509T124500Z
DTEND:20240509T134500Z
UID:TALK213688@talks.cam.ac.uk
CONTACT:Francesco Fournier-Facio
DESCRIPTION:The weight of a group is the minimal number of elements that n
 ormally generate the group. The (unsolved) Wiegold problem asks if there a
 re finitely generated perfect groups with weight greater than one. It is c
 onjectured that taking free products typically increases the weight\, but 
 there are limited tools for proving lower bounds of weights. I will explai
 n how sharp lower bounds of a suitable complexity notion of surface maps (
 relative to the boundary) can be used to show some free products have weig
 ht greater than one. This relates the problem to the analogous spectral ga
 p properties of stable commutator length (scl). I will sketch a method of 
 Calegari proving spectral gaps of scl in hyperbolic manifold groups and ex
 plain how it can be adapted in the new setting.
LOCATION:MR11
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