Henrik Shahgholian - Free Boundaries on Lattice, and Their Scaling Limits

Explore the fascinating world of free boundaries on lattices and their scaling limits in this lecture by Henrik Shahgholian. Delve into classical potential theory, examining the mean value property for harmonic functions over spherical shells or balls. Investigate similar properties for harmonic functions on the lattice sZ^2 and discover how interesting new objects may emerge as the lattice size approaches zero. Learn about the potential creation of facets in free boundary problems and gain insights from recent collaborative works with Hayk Aleksanyan. Presented as part of the Hausdorff Trimester Program on Evolution of Interfaces, this hour-long talk offers a deep dive into advanced mathematical concepts at the intersection of potential theory and lattice structures.