Tel Aviv University, Colloquium
Hello everyone,
The next colloquium talk will be held on:
Monday, 17/12/2012, 12:15, Schreiber 006, Tel Aviv University.
Speaker: Lionel Levine (Cornell University)
Title: Scaling Limit of the Abelian Sandpile
The abstract is given below. Tea and coffee at 12:00, same room.
Hope to see you there. For information about future colloquia, see
Abstract: Let n particles starting at the origin in Z^2 spread out by a
deterministic rule: At each time step, each site with 4 or more
particles sends one particle to each of its neighbors (North, South,
East and West). The resulting final configuration has a complex
fractal structure that remains mysterious.  In a breakthrough work in
2011, Pegden and Smart proved existence of its scaling limit as n goes
to infinity.  Their insight was to ask which functions on R^2 can be
expressed as limits of superharmonic functions from (1/n) Z^2 to
(1/n^2) Z.  I will discuss joint work with Pegden and Smart on the
case of quadratic functions, where this question has a surprising and
beautiful answer: the maximal such quadratics are classified by the
circles in a certain Appolonian circle packing of R^2.
Technion Math Net-2 (TECHMATH2)
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