The volume consists of a set of surveys on geometry in the broad sense. The goal is to present a certain number of research topics in a non-technical and appealing manner.
The topics surveyed include spherical geometry, the geometry of finite-dimensional normed spaces, metric geometry (BishopGromov type inequalities in Gromov-hyperbolic spaces), convexity theory and inequalities involving volumes and mixed volumes of convex bodies, 4-dimensional topology, Teichmüller spaces and mapping class groups actions, translation surfaces and their dynamics, and complex higher-dimensional geometry.
Several chapters are based on lectures given by their authors to middle-advanced level students and young researchers.
The whole book is intended to be an introduction to current research trends in geometry.
1 Athanase Papadopoulos, Introduction.- 2 Marek Lassak, Spherical
geometry - A survey on width and thickness of convex bodies.- 3 Vitor
Balestro and Horst Martini, Minkowski geometry - some concepts and recent
developments.- 4 Javier Alonso at al., Orthogonality types in normed linear
spaces.- 5 Ivan Izmestiev, Mixed volumes and inequalities.- 6 Gérard Besson
and Gilles Courtois, Compactness and finiteness results for Gromov-Hyperbolic
spaces.- 7 Valentin Poénaru, All 4-dimensional smooth Schoenflies balls are
geometrically simply-connected - A fast survey of the proof.- 8 Valentin
Poénaru, Classical differential topology and non-commutative geometry.- 9
Daniel Massart, A short introduction to translation surfaces, Veech surfaces
and Teichmüller dynamics.- 10 Ken'ichi Ohshika, Teichmüller spaces and the
rigidity of mapping class action.- 11 Indranil Biswas and Sorin Dumitrescu,
Holomorphic G-structures and foliated Cartan geometries on compact complex
manifolds.
Athanase Papadopoulos (born 1957) is Directeur de Recherche at the French Centre National de la Recherche Scientifique. His main fields of interest are geometry and topology, the history and philosophy of mathematics, and mathematics and music. He has held visiting positions at the Institute for Advanced Study, Princeton (198485 and 199394), USC (19981999), CUNY (Ada Peluso Professor, 2014), Brown University (Distinguished visiting professor, 2017), Tsinghua University, Beijing (2018), Lamé Chair of the State University of Saint Petersburg (2019), and has had several month visits to the Max-Plank Institute for mathematics (Bonn), the Erwin Schrödinger Institute (Vienna), the Graduate Center of CUNY (New York), the Tata Institute (Bombay), Galatasaray University (Istanbul), the University of Florence (Italy), Fudan University (Shanghai), Gakushuin University (Tokyo) and Presidency University (Calcutta). He is the author of more than 200 published articles and 35 monographsand edited books.
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