Abstract: In this talk, we discuss about two-sided estimates on the density of (killed) Brownian motion with singular drift (signed measure drift). The existence and uniqueness of this process was established by Bass and Chen recently. The potential theory for this process, for example, two-sided estimates on the density, parabolic Harnack inequality, boundary Harnack inequality, Green function estimate and Harmonic measure will be discussed too.

This is a joint work with R. Song.