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CATEGORIES:The Archimedeans (CU Mathematical Society)
SUMMARY:Associativity in topology - Sarah Whitehouse (Shef
field)
DTSTART;TZID=Europe/London:20180126T190000
DTEND;TZID=Europe/London:20180126T200000
UID:TALK87681AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/87681
DESCRIPTION:Familiar operations in arithmetic\, such as additi
on and multiplication of numbers\, are associative
. This means that the answers we obtain don't depe
nd on the order in which we carry out the operatio
ns. For example\, (2+3)+4 = 2+(3+4)\, and so we do
not normally bother writing the brackets.\n\nMy w
ork involves the interaction of algebraic conditio
ns like associativity with topology\, the study of
shapes up to continuous deformations. In topologi
cal settings\, it turns out that a weaker version
of associativity is more natural. This leads to ve
ry rich and interesting structures which have beco
me important in many different areas of mathematic
s\, including algebra\, geometry and mathematical
physics. Similar topological games can be played w
ith other familiar algebraic conditions.\n\nAlong
the way\, I'll talk about a famous sequence of num
bers known as the Catalan numbers. They play a key
role\, because the Catalan numbers count how many
different bracketings there are.\n
LOCATION:MR2\, Centre for Mathematical Sciences
CONTACT:
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