Colloquium

Interface problems for partial differential equations are initial boundary value problems for which the solution of an equation in one domain prescribes boundary conditions for the equations in adjacent domains. These types of problems occur widely in applications including heat transfer, quantum mechanics, and mathematical biology. These problems, though linear, are often not solvable analytically using classical approaches. In this talk I present an introduction to the Unified Transform Method as well as an extension appropriate for solving interface problems.