Lie Groups, Differential Equations, and Geometry ― Advances and Surveys

This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.

Giovanni Falcone received his Ph.D. in Erlangen, Germany in 1998, and has been an Assistant Professor in Palermo, Italy since 1999. His work mainly focuses on Lie algebras, Lie groups and algebraic groups, and (in combinatorics) on block designs. He has been invited to give lectures at the University of Technology in Budapest (2017), at Nankai University in Tianjin (2016), and at the Nesin Mathematics Village in Izmir (2015). At the University of Palermo, he coordinated the project “Lie groups, Differential equations, and Geometry,” supported by the Marie Curie Action nr. 317721. This book is one of the outcomes of the project.