Book Review: Combinatorial integral geometry with applications to mathematical stereology

Combinatorial Geometry with Algorithmic Applications

Institute for Mathematical Physics Intermediate Inversion Formulas in Integral Geometry Intermediate Inversion Formulas in Integral Geometry

We solve the following \intermediate" problem of integral geometry: to reconstruct integrals of a function over p-dimensional planes in R n starting from its integrals over k-planes, where p < k. Some generalizations are also presented.

Book Review: Mathematical Linguistics by Kornai, András

For readers of traditional textbooks such as that of Partee, ter Meulen, and Wall (1990), the term 'mathematical linguistics' denotes a rather narrowly circumscribed set of issues including automata theory, set theory, and lambda calculus, with maybe a little formal language theory thrown in. Kornai's contribution is refreshingly different in that he treats, in this relatively compact volume, p...

Quasicrystals and geometry: a Book Review

Penrose tilings (Fig. 1) are beautiful. They also suggest significant new mathematics, so it is about time someone wrote a book about them which is readable (in fact, eminently readable) by mathematicians. The book, Quasicrystals and geometry, by Marjorie Senechal, has an even broader goal: to present certain developments in crystallography from the past decade. The developments were generated ...

An Integral Formula in Kahler Geometry with Applications

We establish an integral formula on a smooth, precompact domain in a Kahler manifold. We apply this formula to study holomorphic extension of CR functions. Using this formula we prove an isoperimetric inequality in terms of a positive lower bound for the Hermitian curvature of the boundary. Combining with a Minkowski type formula on the complex hyperbolic space we prove that any closed, embedde...