Martin Schlichenmaier Books

This book gives an introduction to modern geometry. Starting from an elementary level the author develops deep geometrical concepts, playing an important role today in contemporary theoretical physics. He presents various techniques and viewpoints, thereby showing the relations between the alternative approaches. At the end of each chapter suggestions for further reading are given to allow the reader to study the touched topics in greater detail. This second edition of the book contains two additional more advanced geometric techniques - the modern language and modern view of Algebraic Geometry, and Mirror Symmetry. The book grew out of lecture courses. The presentation style is therefore similar to a lecture.

The book explores the generalization of certain classes of infinite dimensional Lie algebras, initially introduced by Krichever and Novikov, to accommodate applications in various fields such as Conformal Field Theory and integrable systems. It delves into the geometric origins of these algebras, emphasizing their manageability and relevance to moduli space problems and deformation theory. The work highlights the importance of extending the Virasoro algebra to higher genus Riemann surfaces, providing a comprehensive framework for these advanced mathematical concepts.