[Colloquium] FW: Guest Speaker

[Ponda Barnes]

Reminder!!
 
Guest Speaker Announcement
 
Presented by: Toyota Technological Institute at Chicago
 
Speaker: Michael Shub
Speaker's home page: http://www.math.utoronto.ca/shub
 
Date: Tuesday, May 22, 2007
Time: 3:00pm
Location: TTI-C Conference room
 
Title: Smale's 17th Problem: Recent progress
 
Abstract:
 
 
In a series of papers written in the first half of the 1990's Steve Smale
and I studied the complexity of solving systems of n polynomial equations in
n complex variables.  We studied path following techniques. A system with
known solution is connected by a path to the system we want to solve and the
solution is "continued"  
along the path.  The path we chose was the straight line connecting the
systems.  We proved that "on average" systems can be solved with polynomial
cost but we did not prove the existence of a uniform algorithm.  The
question of the existence of a uniform algorithm is Smale's 17th problem.
Recently, Beltran and Pardo have made significant progress on this problem.
Moreover, Jointly with Beltran I have linked the complexity to the length of
the (problem, solution) path in the condition number Riemannian structure.
Surprisingly short paths exist!  So the study of the geodesics of this
Riemannian structure presents interesting challenges.
 
 
 
If you have any questions or would like to meet the speaker, please contact
Ponda Barnes at pondabarnes at tti-c.org
For future TTI-c talks and events, please visit
http://ttic.uchicago.edu/cal/month.php
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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