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CATEGORIES:The Archimedeans (CU Mathematical Society)
SUMMARY:Exceptional Symmetries - Beth Romano (DPMMS)
DTSTART;TZID=Europe/London:20180209T190000
DTEND;TZID=Europe/London:20180209T200000
UID:TALK97549AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/97549
DESCRIPTION:Lie groups lie at the intersection of geometry and
algebra\, making them useful for many diverse are
as of mathematics. As a representation theorist\,
I understand Lie groups by realizing them as symme
tries of vector spaces–as automorphisms that respe
ct some additional structure. In this talk I'll di
scuss the construction and symmetries of two non-c
ommutative algebras–the quaternions and the octoni
ons. The quaternions naturally give insights into
three- and four-dimensional geometry. The octonion
s are less easy to work with–they are not even ass
ociative. But we'll see that they are the key to u
nderstanding the "exceptional" Lie groups\, which
don't fall into any classical family.
LOCATION:MR2\, Centre for Mathematical Sciences
CONTACT:
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