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SUMMARY:Exceptional Symmetries - Beth Romano (DPMMS)
DTSTART:20180209T190000Z
DTEND:20180209T200000Z
UID:TALK97549@talks.cam.ac.uk
CONTACT:47767
DESCRIPTION:Lie groups lie at the intersection of geometry and algebra\, m
 aking them useful for many diverse areas of mathematics. As a representati
 on theorist\, I understand Lie groups by realizing them as symmetries of v
 ector spaces–as automorphisms that respect some additional structure. In
  this talk I'll discuss the construction and symmetries of two non-commuta
 tive algebras–the quaternions and the octonions. The quaternions natural
 ly give insights into three- and four-dimensional geometry. The octonions 
 are less easy to work with–they are not even associative. But we'll see 
 that they are the key to understanding the "exceptional" Lie groups\, whic
 h don't fall into any classical family.
LOCATION:MR2\, Centre for Mathematical Sciences
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