About the Authors

Joseph M. Landsberg

Professor of Mathematics

Texas A\&M University

College Station, TX, USA

jml[ta]math[td]tamu[td]edu

www.math.tamu.edu/~jml

Professor of Mathematics

Texas A\&M University

College Station, TX, USA

jml[ta]math[td]tamu[td]edu

www.math.tamu.edu/~jml

**Joseph M. Landsberg**works on questions at the interface of algebraic geometry, differential geometry and representation theory. His current research is focused on geometric problems originating in complexity theory. Landsberg obtained his Ph.D. in 1990 from Duke University under the direction of Robert Bryant on minimal submanifolds and a generalization of calibrations. He has directed six Ph.D. theses, is the author of

*Tensors: Geometry and Applications*, is a co-author of

*Cartan for Beginners*, and has published over fifty research articles. Fall 2014 he co-organized

*Algorithms and Complexity in Algebraic Geometry*at the Simons Institute for the Theory of Computing, UC Berkeley, where he was also the Chancellor's Professor and gave a course on geometry and complexity theory whose class notes will hopefully soon be a book.

Giorgio Ottaviani

Professore Ordinario di Geometria

Università di Firenze

Firenze, Italy

ottaviani[ta]math[td]unifi[td]it

web.math.unifi.it/users/ottaviani/

Professore Ordinario di Geometria

Università di Firenze

Firenze, Italy

ottaviani[ta]math[td]unifi[td]it

web.math.unifi.it/users/ottaviani/

**Giorgio Ottaviani**is a Professor of Geometry at the University of Florence, Italy. He received his Ph.D. in mathematics in 1987 at the University of Florence, under the guidance of Vincenzo Ancona, discussing the thesis “Vector bundles on Grassmannians and Quadrics.” His M.Sc. advisor was Francesco Gherardelli. He moved to the University of Rome Tor Vergata as an assistant researcher and then to the University of L'Aquila as a professor. Ottaviani was awarded the Foundation Severi Prize in 1989. His first works discussed instanton vector bundles, homogeneous vector bundles, small codimension projective subvarieties, and enjoying the help of computational tools. In the past eight years, Ottaviani has become interested in the field of tensors and their applications, focusing on tensor rank.