This book provides the foundations for geometric applications of convex cones and presents
selected examples from a wide range of topics, including polytope theory, stochastic …

In this paper, we study various Rogers–Shephard-type inequalities for the lattice point
enumerator G n (⋅) on ℝ n. In particular, for any non-empty convex bounded sets K, L⊂ ℝ n …

We study sequential probability assignment in the Gaussian setting, where the goal is to
predict, or equivalently compress, a sequence of real-valued observations almost as well as …

Magnitude is a numerical invariant of compact metric spaces. Its theory is most mature for
spaces satisfying the classical condition of being of negative type, and the magnitude of …

We prove several estimates for the volume, the mean width, and the value of the Wills
functional of sections of convex bodies in John's position, as well as for their polar bodies …

Magnitude is a numerical invariant of compact metric spaces, originally inspired by category
theory and now known to be related to myriad other geometric quantities. Generalizing …

In this paper, we explore some properties of the dual Wills functional, which are part of the
dual Brunn–Minkowski theory. We give the upper and lower bounds for the dual Wills …

In order to guide the reader into these notes, it seems appropriate to recall a word from the
title:'Geometry'. This emphasizes our viewpoint, and it indicates that we will not deal with the …