Marcus Schaefer - Böcker

Crossing Numbers of Graphs is the first book devoted to the crossing number, an increasingly popular object of study with surprising connections. The field has matured into a large body of work, which includes identifiable core results and techniques. The book presents a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science. The first part of the text deals with traditional crossing number, crossing number values, crossing lemma, related parameters, computational complexity, and algorithms. The second part includes the rich history of alternative crossing numbers, the rectilinear crossing number, the pair crossing number, and the independent odd crossing number.It also includes applications of the crossing number outside topological graph theory.Aimed at graduate students and professionals in both mathematics and computer scienceThe first book of its kind devoted to the topicAuthored by a noted authority in crossing numbers

Crossing Numbers of Graphs is the first book devoted to the crossing number, an increasingly popular object of study with surprising connections. The field has matured into a large body of work, which includes identifiable core results and techniques. The book presents a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science. The first part of the text deals with traditional crossing number, crossing number values, crossing lemma, related parameters, computational complexity, and algorithms. The second part includes the rich history of alternative crossing numbers, the rectilinear crossing number, the pair crossing number, and the independent odd crossing number.It also includes applications of the crossing number outside topological graph theory.Aimed at graduate students and professionals in both mathematics and computer scienceThe first book of its kind devoted to the topicAuthored by a noted authority in crossing numbers

"In a time oversaturated with images and quickconsumption, Marcus Schaefer’s photographic work standsas a quiet rebellion. It defies easy categorization, resistssuperficial clarity, and insists on depth, ambiguity, andsensation. Spanning more than a decade, this body of work,collected in Marcus Schaefer — Photographic Works2013–2025, is not merely a retrospective, but a portalinto a unique aesthetic universe: one where the knownis made strange, and the invisible is drawn delicately intoview. From abstract portraits and conceptual still lifesto spectral nudes, object studies, and previously unseenstreet and travel images, Schaefer’s photographs speakin visual riddles. They are less concerned with the outerappearance of things than with the inward resonancethey provoke. This retrospective captures the evolutionof that vision across twelve years — a period duringwhich Schaefer’s vocabulary has grown more refined,his experiments more confident, and his voice more assured.Marcus Schaefer is a Paris-based multi-disciplinaryartist working in photography, sculpture and painting.The artist puts the color black at the heart of his work,using it as a central component to his visual messaging.His first book Mapping Subconciousness was publishedwith Patrick Remy Studio in 2024."