Recorded 21 May 2024. Vadim Gorin of the University of California, Berkeley, presents "Six-vertex model in the rare corners regime" at IPAM's Vertex Models: Algebraic and Probabilistic Aspects of Universality Workshop. 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. Based on joint projects with A.Borodin and with R.Kenyon, I.Prause. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iv-vertex-models-algebraic-and-probabilistic-aspects-of-universality/