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SUMMARY:Solving equations with topology - Dr. Oscar Randall-Williams
DTSTART:20160429T180000Z
DTEND:20160429T190000Z
UID:TALK65895@talks.cam.ac.uk
CONTACT:Dexter Chua
DESCRIPTION:Topology is often useful in showing that equations have soluti
 ons without necessarily finding out what the solutions are. The first exam
 ple of this is the intermediate value theorem: a continuous function f: R 
 → R which takes both positive and negative values must take the value 0\
 ; the topological input is that R is connected. The second of these is the
  fundamental theorem of algebra: a polynomial function p: C → C of posit
 ive degree must take the value 0\; the topological input is the calculatio
 n of the fundamental group of the circle.\n\nI will explain these as well 
 as the less-well known example of solving equations in groups: given a "po
 lynomial" such as w(x)=g_1 x^2 g_2 x^(-4) g_3 x^3 with g_1\, g_2\, g_3 in 
 a group G and x a formal symbol\, is there a bigger group H ≥ G and a h 
 ϵ H such that w(h)=e ϵ H?
LOCATION:MR2\, Centre for Mathematical Sciences
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