### About

Much of my recent research activity is connected with complex-analytic aspects of projective duality. Specifically given a (suitably convex) real hypersurface S in complex projective space, the locus of affine complex hyperplanestangent to S form a dual hypersurface S* in the dual projective space. The interaction between (boundary values of) holomorphic functions on the two hypersurfacesis regulated by an explicit singular integral operator, the *Leray transform*. The norm of this operator is significant for the function theory;in several situations it has been established that the norm (or at the least theessential norm) is tightly connected with the projective geometry of S. (With postdoc Luke Edholm, I am pursuing a program to establish a general conjecture along these lines.) Along more purely geometric lines, along with Dusty Grundmeier, I have shown that that the boundary of any bounded strongly pseudoconvex complete circular domain in ℂ2 must contain points that are exceptionally tangent to a projective image of the unit sphere.