I authored the book Several Complex Variables and the Geometry of Real Hypersurfaces; this book describes areas closely related to my research interests. In recent years I have become interested in positivity conditions for real-analytic real-valued functions of several complex variables. For example, David Catlin and I gave the following necessary and sufficient condition for a bihomogeneous polynomial $p$ of $n$ complex variables to be positive away from the origin. There is an integer $d$ so that $p$ is the quotient of squared norms of homogeneous holomorphic polynomial mappings, the numerator vanishes only at the origin, and the denominator is the d-th power of the Euclidean norm. We have extended this result to an isometric embedding theorem for holomorphic bundles. See Math Research Letters 6 (1999).In studying group invariant proper holomorphic mappings between balls in different dimensions I discovered a triangle of integers bearing a neat relationship to Pascal's triangle. Here are the first few rows! Can you figure out the rest?
1 1
1 3 1
1 5 5 1
1 7 14 7 1
1 9 27 30 9 1
1 11 44 77 55 11 1