Richard Kenyon

Abstract:   This is joint work with Andrei Okounkov. We discuss a probability model of random "stepped surfaces" which are monotone piecewise linear surfaces composed from unit squares of the cubic lattice. For fixed boundary conditions and lattice spacing tending to zero these random surfaces converge to non-random smooth surfaces which can be defined by a variational principle: they minimize a certain surface tension functional. An exact solution of the variational problem can be given in terms of holomorphic functions, much like the Weierstrass formula for minimal surfaces. One interesting feature of the solutions is that they are only piecewise analytic: they develop facets.

Here are some directions to Northeastern University. Lake Hall and Nightingale Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street. The two halls are connected, with no well-defined boundary in between. In particular, 509 Lake Hall is on the same corridor as 544 Nightingale Hall.

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