This volume contains refereed papers related to the lectures and talks given at a conference held in Siena (Italy) in June 2004. Also included are research papers that grew out of discussions among the participants and their collaborators. All the papers are research papers, but some of them also contain expository sections which aim to update the state of the art on the classical subject of special projective varieties and their applications and new trends like phylogenetic algebraic geometry.

The topic of secant varieties and the classification of defective varieties is central and ubiquitous in this volume. Besides the intrinsic interest of the subject, it turns out that it is also relevant in other fields of mathematics like expressions of polynomials as sums of powers, polynomial interpolation, rank tensor computations, Bayesian networks, algebraic statistics and number theory.

Autorentext

Ciro Ciliberto is Professor in Geometria Superiore at the University of Roma 'Tor Vergata', Italy. **

Antony V. Geramita is Professor at the Department of Mathematics and Statistics, Queen's University, Kingston, Canada, and Professore Ordinario at the Dipartimento di Matematica, University of Genova, Italy. **

Brian Harbourne is Professor at the Department of Mathematics, University of Nebraska, Lincoln, USA.

Rosa Maria Miró-Roig is Professor at the Faculty of Mathematics, University of Barcelona, Spain. **

Kristian Ranestad is Professor at the Mathematical Institute, University of Oslo, Norway.