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SUMMARY:The Hele-Shaw flow and the moduli of holomorphic discs - Julius Ro
 ss\, Cambridge
DTSTART:20130130T160000Z
DTEND:20130130T170000Z
UID:TALK42100@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:The Hele-Shaw Flow is a model for describing the propagation o
 f\nfluid in a cell consisting of two parallel plates separated by a small\
 ngap.   This model has been intensely studied for over a century\, and is 
 a\nparadigm for understanding more complicated systems such as the flow of
 \nwater in porous media\, melting of ice and models of tumor growth.\n\nIn
  this talk I will discuss how this flow fits into the more general\nframew
 ork of "inverse potential theory" through the idea of complex\nmoments.   
 I will then discuss joint work with David Witt Nystrom that\nconnects to t
 he moduli space of holomorphic discs with boundary in a\ntotally real mani
 fold.  Using this we prove a number of short time\nexistence/uniqueness re
 sults for the flow\, including the case of the Hele\nShaw flow with varyin
 g permeability starting from a smooth Jordan domain\,\nand for the Hele Sh
 aw flow starting from a single point.
LOCATION:MR13
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