Explore a cutting-edge lecture on the six-vertex model in the rare corners regime presented by Vadim Gorin from the University of California, Berkeley. Delve into the latest findings on limit shapes for the height function in this celebrated model, focusing on a degeneration that leads to a low density of corners of paths. Discover new features such as hyperbolic PDEs, discontinuities in densities, and connections to random permutations. Gain insights into joint projects with A. Borodin and R. Kenyon, I. Prause, as part of IPAM's Vertex Models: Algebraic and Probabilistic Aspects of Universality Workshop. Enhance your understanding of this complex topic through this 51-minute presentation recorded on May 21, 2024, at the Institute for Pure & Applied Mathematics (IPAM) at UCLA.