Tuesday, March 11th, 2014
2:00pm - 3:00pm, in McCormack 1-614

Mirjana Vuletic

UMass Boston

Asymptotics of Random Combinatorial Structures: Limit Shapes

Abstract: Pick a random domino tiling of a large region. Can you observe a pattern? It turns out that for some regions the pattern, called the limit shape, exists. An Aztec diamond is an example of such region, but square is not. In this talk, I will introduce various random models on combinatorial structures, e.g. tilings, graphs, plane partitions, and discuss their asymptotic behavior. The models and results that will be presented have emerged from various fields. I will briefly explain their relationship with statistical physics, quantum field theory, probability, combinatorics, representation theory, algebraic geometry, tropical geometry and number theory.