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Vadim Gorin: Six-vertex model in the rare corners regime

Time: Thu 2024-09-19 11.00 - 12.00

Location: Zoom

Video link: Meeting ID: 921 756 1880

Participating: Vadim Gorin, University of California, Berkeley

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Abstract:

The limit shapes for the height function in the celebrated six-vertex model are still unknown in general situations. However, we recently found ways to compute them in a degeneration, which leads to a low density of corners of paths (or, equivalently, of c-type vertices; or, equivalently, of horizontal/vertical molecules of water). I will report on the progress in this direction emphasizing various new features (as compared to, say, dimers): appearance of hyperbolic PDEs; discontinuities in densities; connections to random permutations.