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DTSTAMP:20190318T141114Z
LAST-MODIFIED:20180413T135605Z
DTSTART:20180420T160000Z
DTEND:20180420T170000Z
UID:event1884@bu.edu
URL:http://physics.bu.edu/events/show/1884
SUMMARY:"Laplacian Growth"
DESCRIPTION:Featuring Mark Mineev-Weinstein\, Natal\nHosted by: Anatoli Pol
kovnikov\n\nPart of the Condensed Matter Theory Seminar Series.\n\nNumerous
unstable non-equilibrium physical processes produce a multitude of rich co
mplex patterns\, both compact and (more often) fractal. Shapes of patterns
in a long time limit include fingers in porous media\, dendritic trees in
crystallization\, fractals in bacterial colonies and malignant tissues\, ri
ver networks\, and other bio- and geo- systems. The patterns are often univ
ersal and reproducible. Geometry and dynamics of these forms present great
challenges\, because mathematical treatment of nonlinear\, non-equilibrium\
, dissipative\, and unstable dynamical systems is\, as a rule\, very diffic
ult\, if possible at all. While many impressive experimental and computati
onal results were accumulated\, powerful analytic methods for these systems
were very limited until recently. Remarkably\, many of these growth proces
ses were reduced (after some idealization) to a mathematical formulation\,
which owns rich\, powerful and beautiful integrable structure\, and reveals
deep connections with other exact disciplines\, lying far from non-equilib
rium growth. In physics the examples include quantum gravity\, quantum Hall
effect\, and phase transitions. In classical mathematics\, this structure
was found to be deeply interconnected with such fields as the inverse poten
tial problem\, classical moments\, orthogonal polynomials\, complex analysi
s\, and algebraic geometry. In modern mathematical physics we established t
ight relations of nonlinear growth to integrable hierarchies and deformatio
ns\, normal random matrices\, stochastic growth\, and conformal theory. Thi
s mathematical structure made possible to see many outstanding problems in
a new light and solve several long-standing challenges in pattern formation
and in mathematical physics.\n\nDuring the talk I will provide brief histo
ry with key experiments and paradigms in the field\, make short surveys of
mathematics mentioned above\, expose the integrable structure hidden behind
the interface dynamics\, and will present major results up to date in this
rapidly growing field.
LOCATION:SCI 352\, 590 Commonwealth Avenue\, 02215
STATUS:CONFIRMED
CLASS:PUBLIC
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