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Eric Rains (CalTech) Lozenge tilings and elliptic biorthogonal functions One of the many combinatorial models in which fluctuations are controlled by random-matrix-related distributions is that of uniform random lozenge tilings of hexagons (or, equivalently, uniform random plane partitions in a box). These exhibit an "arctic circle" phenomenon--an inscribed ellipse outside of which the tiling can be reliably predicted--and the fluctuations in said ellipse are controlled by the TracyWidom distribution. The analysis of the uniform case rests on the fact that the tiling model can be viewed as a determinantal process with kernel expressed via Hahn polynomials. I'll discuss a recent generalization of this (joint with Borodin and Gorin), in which a suitable weighting of the probabilities by elliptic functions gives a process related to elliptic biorthogonal functions and degenerations thereof (e.g., q-Racah polynomials).