Zoom link:  https://princeton.zoom.us/j/99136657600

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(The colloquium password will be distributed to Princeton University and IAS members. We ask that you do not share this password. If you would like to be included in the colloquium and are not a member of either institution, please email the organizer Casey Kelleher (caseyk@princeton.edu) with an email requesting to participate which introduces yourself, your current affiliation and stage in your career.)

The statistical behavior of random tilings of large domains has been an intense topic of mathematical research for decades, partly since they highlight a central phenomenon in physics: local behaviors of highly correlated systems can be very sensitive to boundary conditions. Indeed, a salient feature of random tiling models is that the local densities of tiles can differ considerably in different regions of the domain, depending on the shape of the domain. Thus, a question of interest, originally mentioned by Kasteleyn in 1961, is how the shape of the domain affects the local behavior of a random tiling. In this talk, we outline recent work that provides an answer (originally predicted by Cohn-Kenyon-Propp in 2001) to this question for random lozenge tilings of essentially arbitrary domains. The proofs are based on a combination of results from exactly solvable systems with more analytic and probabilistic arguments.