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SUMMARY:Bernold Fiedler (Institute of Mathematics\, Freie Universität Ber
 lin)
DTSTART:20200519T150000Z
DTEND:20200519T160000Z
DTSTAMP:20260404T122315Z
UID:LisbonWADE/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LisbonWADE/5
 /">Sturm meanders: global attractors\, Temperley-Lieb algebras\, and black
  holes</a>\nby Bernold Fiedler (Institute of Mathematics\, Freie Universit
 ät Berlin) as part of Lisbon webinar in analysis and differential equatio
 ns\n\n\nAbstract\nFusco and Rocha studied Neumann boundary value problems 
 for scalar ODEs of second order via a shooting approach. They introduced t
 he notion of what we now call Sturm permutations. These permutations relat
 e\, on the one hand\, to a special class of meandering curves as introduce
 d by Arnol’d in a singularity theory context. On the other hand\, they b
 ecame central in the study of global attractors of nonlinear parabolic par
 tial differential equations of Sturm type.\n\nWe discuss relations of Stur
 m meanders with further areas: the multiplicative and trace structure in T
 emperley-Lieb algebras\, discrete versions of Cartesian billiards\, and th
 e problem of constructing initial conditions for black hole dynamics which
  satisfy the Einstein constraints. We also risk a brief glimpse at the lon
 g and meandric history of meander patterns themselves.\n\nWe report on joi
 nt work with Pablo Castañeda\, Juliette Hell\, Carlos Rocha\, and Brian S
 mith. See also http://dynamics.mi.fu-berlin.de/\n\nFor further material we
  recommend the beautifully illustrated book “Meanders” by Anna Karnauh
 ova\, de Gruyter 2017.\n
LOCATION:https://researchseminars.org/talk/LisbonWADE/5/
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