We define united KK-theory for real C*-algebras A and B such that A is separable and B is σ-unital, extending united K-theory in the sense that KKCRT (R, B) = KCRT (B). United KK-theory contains real, complex, and self-conjugate KK-theory; but unlike unaugmented real KK-theory, it admits a universal coefficient theorem. For all separable A and B in which the complexification of B is in the boot...

We introduce real log canonical threshold and real jumping numbers for real algebraic functions. A real jumping number is a root of the b-function up to a sign if its difference with the minimal one is less than 1. The real log canonical threshold, which is the minimal real jumping number, coincides up to a sign with the maximal pole of the distribution defined by the complex power of the absol...

A Grauert tube, or adapted complex structure, gives a canonical complexification of a real analytic Riemannian manifold defined on a neighborhood of the zero section of the (co-)tangent bundle. Such a tube is called entire if it is defined on the whole tangent bundle of the real analytic Riemannian manifold M, g. Very few examples of such entire tubes are known, but a general statement has prov...