Geometry, Lie Theory and Applications
The Abel Symposium 2019
Editors: Hervik, S., Kruglikov, B., Markina, I., The, D. (Eds.)
 Features contributions from world leading experts in differential geometry
 Contains survey and research papers on parabolic geometry, cone constructions, supergravity
 Includes applications to Einstein spaces, Ricci solitons, gravitational instantons, string theory
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 About this book

This book consists of contributions from the participants of the Abel Symposium 2019 held in Ålesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity.
The chapters are written by leading international researchers, and consist of both survey and research articles. The book gives the reader an insight into the current research in differential geometry and Lie theory, as well as applications of these topics, in particular to general relativity and string theory.  About the authors

Sigbjørn Hervik is a professor of mathematics at the Department of Mathematics and Physics at the University of Stavanger, Norway. His areas of research are general relativity, differential geometry, Lie theory, invariant theory and applications of these. In particular, he has been working on classification of pseudoRiemannian spaces using their polynomial curvature invariants, and significantly contributed to understanding when such invariants can be used to distinguish spaces. He is a coauthor of the book Einstein’s General Theory of Relativity, also published by Springer.
Boris Kruglikov is a professor in mathematics at the Department of Mathematics and Statistics at UiT the Arctic University of Norway, and professor II at the University of Stavanger, Norway. His research is on intersection of differential geometry, Lie theory and mathematical physics. This includes very general geometries like projective and conformal, almost complex and vector distributions, obtained by (possibly higher order) reductions and (possibly nonholonomic) constraints. The basic questions deal with symmetry algebras and Lie pseudogroups, integrability properties of differential equations and differential invariants of geometric structures.
Irina Markina is a professor of mathematics at the Department of Mathematics at the University of Bergen, Norway. Her areas of interest belong to differential geometry, real analysis, and partial differential equations. The focus of research is subRiemannian geometry and closely related theory of hypoelliptic and subelliptic partial differential equations, which play a role analogous to that of elliptic operators on Riemannian manifolds. She also published results in the fields of integrable systems, Lie groups and Lie algebras, as well as nonlinear potential theory and quasiconformal analysis.
Dennis The is an associate professor of mathematics at the Department of Mathematics and Statistics at UiT the Arctic University of Norway. His research interests lie at the intersection of differential geometry and representation theory, and are strongly influenced by ideas from Lie theory, Cartan geometry, and Tanaka theory. He focuses on equivalence and symmetry for numerous geometric structures, in particular those arising in the context of parabolic geometries (e.g. conformal, CR, vector distributions) and the geometry of differential equations.
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Bibliographic Information
 Bibliographic Information

 Book Title
 Geometry, Lie Theory and Applications
 Book Subtitle
 The Abel Symposium 2019
 Editors

 Sigbjørn Hervik
 Boris Kruglikov
 Irina Markina
 Dennis The
 Series Title
 Abel Symposia
 Series Volume
 16
 Copyright
 2021
 Publisher
 Springer International Publishing
 Copyright Holder
 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
 eBook ISBN
 9783030812966
 DOI
 10.1007/9783030812966
 Hardcover ISBN
 9783030812959
 Series ISSN
 21932808
 Edition Number
 1
 Number of Illustrations
 5 b/w illustrations
 Topics