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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:The Hele-Shaw flow and the moduli of holomorphic d
iscs - Julius Ross\, Cambridge
DTSTART;TZID=Europe/London:20130130T160000
DTEND;TZID=Europe/London:20130130T170000
UID:TALK42100AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/42100
DESCRIPTION:The Hele-Shaw Flow is a model for describing the p
ropagation of\nfluid in a cell consisting of two p
arallel plates separated by a small\ngap. This m
odel has been intensely studied for over a century
\, and is a\nparadigm for understanding more compl
icated systems such as the flow of\nwater in porou
s media\, melting of ice and models of tumor growt
h.\n\nIn this talk I will discuss how this flow fi
ts into the more general\nframework of "inverse po
tential theory" through the idea of complex\nmomen
ts. I will then discuss joint work with David Wi
tt Nystrom that\nconnects to the moduli space of h
olomorphic discs with boundary in a\ntotally real
manifold. Using this we prove a number of short t
ime\nexistence/uniqueness results for the flow\, i
ncluding the case of the Hele\nShaw flow with vary
ing permeability starting from a smooth Jordan dom
ain\,\nand for the Hele Shaw flow starting from a
single point.
LOCATION:MR13
CONTACT:Ivan Smith
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