Convex and Complex

Perspectives on Positivity in Geometry

Robert J. Berman, Yanir A. Rubinstein

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English

American Mathematical Society
31 March 2025

Geometry; Topology

Series: Contemporary Mathematics

This volume presents a collection of research articles arising from the conference on """"Convex and Complex: Perspectives on Positivity in Geometry,"""" held in Cetraro, Italy, from October 31-November 4, 2022. The conference celebrated the 70th birthday of Bo Berndtsson and the vitality of current research across complex and convex geometry, as well as interactions between the two areas, all united by the overarching concept of positivity. Positivity plays a central role in complex and convex geometry. It arises from a range of complementary perspectives, as illustrated by the breadth of the papers appearing in this volume, including existence Kahler-Einstein edge metrics, Santalo-type inequalities, curvature of direct images of bundles, extension theorems for holomorphic functions, optimal transport and Hessian manifolds, interpolation and Brunn-Minkowski theory, and non-Archimedean geometry. The format of the workshop was innovative compared to standard conferences in mathematics, with focused 30-minute talks, aimed at stimulating lively discussions and a """"flipped classroom"""" where the audience becomes more engaged and the speaker is not expected to transmit more information than listeners can possibly absorb. Lengthy breaks between talks and a relatively small number of talks allowed for useful time blocks for collaboration.

This volume reflects the spirit of the conference, showcasing the vitality of current research in these areas as well as the profound impact of Bo Berndtsson's contributions to the field.

Edited by: Robert J. Berman, Yanir A. Rubinstein
Imprint: American Mathematical Society
Country of Publication: United States
Volume: 810
Dimensions: Height: 254mm, Width: 178mm,
ISBN: 9781470473389
ISBN 10: 1470473380
Series: Contemporary Mathematics
Pages: 308
Publication Date: 31 March 2025
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Robert J. Berman, Chalmers University of Technology and University of Gothenburg, Sweden. Yanir A. Rubinstein, University of Maryland, College Park, MD.