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SUMMARY:Associativity in topology - Sarah Whitehouse (Sheffield)
DTSTART:20180126T190000Z
DTEND:20180126T200000Z
UID:TALK87681@talks.cam.ac.uk
CONTACT:47767
DESCRIPTION:Familiar operations in arithmetic\, such as addition and multi
 plication of numbers\, are associative. This means that the answers we obt
 ain don't depend on the order in which we carry out the operations. For ex
 ample\, (2+3)+4 = 2+(3+4)\, and so we do not normally bother writing the b
 rackets.\n\nMy work involves the interaction of algebraic conditions like 
 associativity with topology\, the study of shapes up to continuous deforma
 tions. In topological settings\, it turns out that a weaker version of ass
 ociativity is more natural. This leads to very rich and interesting struct
 ures which have become important in many different areas of mathematics\, 
 including algebra\, geometry and mathematical physics. Similar topological
  games can be played with other familiar algebraic conditions.\n\nAlong th
 e way\, I'll talk about a famous sequence of numbers 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
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