Anosov representations of word hyperbolic groups into higher-rank semisimple Lie groups
are representations with finite kernel and discrete image that have strong analogies with …

This is the second edition of a book which appeared in 2005. The new edition is an
expanded and revised version. The book is about metric spaces of nonpositive curvature in …

We study a notion of convex cocompactness for discrete subgroups of the projective general
linear group acting (not necessarily irreducibly) on real projective space, and give various …

Clustering categorical distributions in the probability simplex is a fundamental task met in
many applications dealing with normalized histograms. Traditionally, differential-geometric …

We construct and study a natural homeomorphism between the moduli space of polynomial
cubic differentials of degree d on the complex plane and the space of projective equivalence …

We investigate representations of Coxeter groups into GL. n; R/as geometric reflection
groups which are convex cocompact in the projective space PR n/. We characterize which …

This is a survey article concerning applications of Hilbert's metric in the analysis and
dynamics of linear and nonlinear mappings on cones. It will appear as a chapter in the" …

A key technique of machine learning and computer vision is to embed discrete weighted
graphs into continuous spaces for further downstream analysis. Embedding discrete …

For any rank-one convex projective manifold with a compact convex core, we prove that
there exists a unique probability measure of maximal entropy on the set of unit tangent …

We investigate the horofunction boundary of the Hilbert geometry defined on an arbitrary
finite-dimensional bounded convex domain D. We determine its set of Busemann points …