Tiling problems

Wednesday, November 12, 2014 - 11:00am - 11:25am
Greta Panova (University of Pennsylvania)
We will discuss some probabilistic aspects of random lozenge tilings, the statistical mechanics generalization of the usual plane partitions from algebraic combinatorics. We will show how to study their limiting behavior (as the grid size goes to 0) using symmetric functions. Results include the fact that the positions of the horizontal lozenges near a flat vertical boundary have the same distribution as the eigenvalues of matrices from the Gaussian Unitary Ensemble; and the existence of a limit shape for symmetric plane partitions.
Wednesday, November 12, 2014 - 10:30am - 10:55am
Jed Yang (University of Minnesota, Twin Cities)
Knutson, Tao, and Woodward introduced puzzle pieces
consisting of two triangles and a rhombus (with edge labels).
They proved that tilings by these puzzle pieces (allowing rotations)
of triangular regions (with edge labels)
are counted by Littlewood--Richardson coefficients.
These numbers appear naturally in many contexts,
intersection of Schubert varieties,
multiplication of Schur functions,
and tensor products of irreducible representations of general linear groups.
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