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SUMMARY:Mahler Measure and Weber's Class Number Problem - Jack Lamplugh Un
 iversity of Cambridge
DTSTART:20131018T140000Z
DTEND:20131018T150000Z
UID:TALK48091@talks.cam.ac.uk
CONTACT:Julian Brough
DESCRIPTION:It has been an open problem for over 200 years as to whether t
 here are infinitely many number fields of class number 1. Over 100 years a
 go\, Weber studied the class numbers of the layers of cyclotomic Z_2 exten
 sion of the rationals and showed that the first 3 layers have class number
  one. Recently much progress has been made by Japanese mathematicians indi
 cating that perhaps all layers of all cyclotomic Z_p extensions for all pr
 imes p have class number 1. In my talk I will explain these results (and w
 hat the cyclotomic Z_p of the rationals is!) and talk about my work in ext
 ending this to non-cyclotomic Z_p extensions
LOCATION:CMS\, MR5
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