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DTSTART:20070311T020000
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DTSTAMP:20260924T144849Z
DTSTART;TZID=America/New_York:20261002T110000
DTEND;TZID=America/New_York:20261002T120000
URL;TYPE=URI:https://www.wpi.edu/news/calendar/events/mathematical-sciences
 -department-colloquium-francisco-ponce-carrion-wpi
SUMMARY:Mathematical Sciences Department Colloquium: Francisco Ponce Carrio
 n\, WPI
DESCRIPTION:Title: Real solutions to polynomial systems and Newton Homotopi
 es.\n\n\nAbstract: Given a system of n polynomials in n variables\, a comm
 on problem in numerical algebraic geometry is to find all its real solutio
 ns without having to compute all its complex solutions. A first approach t
 o this issue could be to use Newton’s method. However\, the fractal natu
 re of the boundaries of the basins of attraction for Newton’s method can
  cause numerical instability when using a random initial guess. In this ta
 lk\, we will give an overview of Newton Homotopy: a generalization of Newt
 on’s method that fits within the framework of homotopy continuation meth
 ods. We will then discuss new geometric results describing the boundaries 
 of the basins of attraction in Newton Homotopies for small generic systems
 . This is based on joint work with Jennifer Buettner\, Jonathan Hauenstein
 \, Caroline Hills\, Hoon Hong\, and Emma Schmidt.
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