Talk by Mike Cranston (University of California, Irvine)

Date and Time: February 27, 10:00 AM in AP&M 6402

Title: Self-adjoint extensions, point potentials, and pinned polymers

Abstract: In this talk we discuss closed self adjoint extensions of the Laplacian and fractional Laplacian on L^2 of Euclidean space minus the origin. In many cases there is a one parameter family of these operators that behave like the original operator plus a potential at the origin. Using these operators, we can construct polymer measures which exhibit interesting phase transitions from an extended state to a bound state where the pinning at the origin due to the potential takes over. The talk is based on joint works with Koralov, Molchanov, Squartini and Vainberg.