Brian Street

I am interested in singular integrals as they relate to linear partial differential equations. For instance, if P is a partial differential operator, there is sometimes an inverse operator T with PT=I, where I denotes the identity. Much of my research revolves around studying operators like T. More precisely, under what conditions on P can we obtain a good picture of what T looks like.

The classical case is when P is an elliptic operator, and there the theory of pseudodifferential operators fully addresses the above question. Outside of the elliptic situation, the question becomes much more delicate, and much work has been done in various situations to understand these operators. My research focuses on situations where T can be described in terms of some geometries associated to P, which are often different from usual Riemannian geometries. Often, the so-called sub-Riemannian geometries comes into play, along with other, related, geometries.

Princeton University
Assistant Professor
Research Interests: 
Singular Integrals, Several Complex Variables, Linear PDE
Brian Street
street at math dot wisc dot edu