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SUMMARY:On a Problem posed by Steve Smale - Felipe Cucker (City University
  of Hong Kong)
DTSTART:20110511T140000Z
DTEND:20110511T150000Z
UID:TALK30276@talks.cam.ac.uk
CONTACT:Dr Shadrin
DESCRIPTION:At the request of the International Mathematical Union\, in 19
 99\, Steve Smale proposed a list of 18 problems for the mathematicians of 
 the 21st century. The 17th of these problems asks for the existence of a d
 eterministic algorithm computing an approximate solution of a system of $n
 $ complex polynomials in $n$ unknowns in time polynomial\, on the average\
 , in the size $N$ of the input system. The talk gives fundamental advances
  in this problem including the smoothed analysis\nof a randomized algorith
 m and a deterministic algorithm working in\nnear-polynomial (i.e.\, $N^{O(
 \\log\\log N)}$) average time.
LOCATION:CMS\, MR14
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