|
|
|
|
|
|
|
|
Shapes of crystalline surfaces
This is joint work with Andrei Okounkov. We study a simple model of crystalline surfaces. Microscopically, these are random discrete surfaces, arising in the so-called dimer model, or domino tiling model. The law of large numbers implies that at large scales the surfaces take on definite shapes, which are smooth surfaces satisfying a certain PDE, similar in certain respects to the minimal surface equation. We show how this equation can be solved via complex analytic functions, and investigate the behavior of solutions, in particular the formation of facets. This is the first model of facet formation which can be analytically solved.
Thursday, August 26, 2004, 245 Altgeld Hall, 4 p.m.
Mathematics Colloquia homepage