Random lozenge tilings and Hurwitz numbers

Series: 
Job Candidate Talk
Thursday, January 8, 2015 - 11:00
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
MIT
Organizer: 
This talk will be about random lozenge tilings of a class of planar domains which I like to call "sawtooth domains." The basic question is: what does a uniformly random lozenge tiling of a large sawtooth domain look like? At the first order of randomness, a remarkable form of the law of large numbers emerges: the height function of the tiling converges to a deterministic "limit shape." My talk is about the next order of randomness, where one wants to analyze the fluctuations of tiles around their eventual positions in the limit shape. Quite remarkably, this analytic problem can be solved in an essentially combinatorial way, using a desymmetrized version of the double Hurwitz numbers from enumerative algebraic geometry.