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DESCRIPTION:Infinite dimensional dynamical systems and the Navier-Stokes eq
 uations: a rigorous computational approach.\n\nNonlinear dynamics shape th
 e world around us. It shapes biology\, from the electrophysiological prope
 rties of neurons\, via the spiralling waves in contracting heart muscles\,
  to gene regulatory networks. It shapes physics\, from the swirling motion
 s in fluid flows\, via the creation of complex patterns in materials\, to 
 the harmonious motions of celestial bodies. It shapes chemistry\, from the
  rich reaction kinetics phenomena\, via the chemical basis of morphogenesi
 s at the origin of patterns on animals\, to the complicated biochemistry i
 n the living cell. Mathematically these beautiful and highly complex pheno
 mena are described by nonlinear dynamical systems in the form of ODEs\, PD
 Es and DDEs. Unfortunately\, the presence of nonlinearities in the models 
 often obstructs the mathematicians and the scientists from obtaining analy
 tic formulas for the solutions. In particular\, the difficulties are even 
 greater for PDEs and DDEs\, which are naturally defined on infinite dimens
 ional function spaces. As a consequence of these challenges and with the r
 ecent availability of powerful computers and sophisticated software\, nume
 rical simulations are quickly becoming the primary tool used by scientists
  to study the complicated dynamics arising in the models. However\, while 
 the pace of progress increases\, sometimes we need to take a step back and
  pose the question\, just how reliable are our computations?\n	\n	In this ta
 lk\, we introduce and present the recent field of rigorous computing in dy
 namical systems which emerged to address this fundamental scientific issue
  in the context of nonlinear dynamics. More specifically\, we will ask the
  following questions and partially answer some of them. Can we mathematica
 lly demonstrate the reliability of the solutions computed using the forced
  Navier-Stokes equations? Can we rigorously control the errors made when c
 omputing the solutions of Cauchy problems of parabolic PDEs? If so\, can w
 e show that the 3D Navier-Stokes equations do not develop singularities as
  time evolves for a large class of initial conditions? Can we develop rigo
 rous computations to understand properties of materials? Can we use rigoro
 us numerics as a tool for reliable predictions and computations in astrody
 namics?\n\n\n\n
DTSTART:20161208T200000Z
DTEND:20161208T210000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Jean-Philippe Lessard\, Université Laval
URL:https://www.mcgill.ca/mathstat/channels/event/jean-philippe-lessard-uni
 versite-laval-264605
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