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SUMMARY:Fixed-energy harmonic functions - Richard Kenyon (Brown)
DTSTART:20151110T163000Z
DTEND:20151110T173000Z
UID:TALK60694@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:This is joint work with Aaron Abrams.\nWe study the map from c
 onductances to edge energies for harmonic functions\non graphs with Dirich
 let boundary conditions.\nWe prove that for any compatible acyclic orienta
 tion and choice of energies there is a unique\nchoice of conductances such
  that the associated harmonic function realizes those orientations and ene
 rgies.\n\nFor rational energies and boundary data\nthe Galois group of $\\
 Q^{tr}$ (the totally real algebraic numbers) over $\\Q$ permutes the\nenha
 rmonic functions\, acting on the set of compatible acyclic orientations.\n
 \nConnections with square ice and SLE_{12} (based on work with Angel\, Mil
 ler\, Sheffield\, Wilson)\nwill be briefly discussed.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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