Traditionally, Lorentzian geometry has been used as a necessary tool to understand general relativity, as well as to explore new genuine geometric behaviors, far from classical Riemannian techniques.
The volume conjecture states that a certain limit of the colored Jones polynomial of a knot in the three-dimensional sphere would give the volume of the knot complement.
The work consists of two introductory courses, developing different points of view on the study of the asymptotic behaviour of the geodesic flow, namely: the probabilistic approach via martingales and mixing (by Stephane Le Borgne); the semi-classical approach, by operator theory and resonances (by Frederic Faure and Masato Tsujii).
A Fields medalist recounts his lifelong effort to uncover the geometric shape-the Calabi-Yau manifold-that may store the hidden dimensions of our universe.
This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field.
This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein's spacetime in one accessible, self-contained volume.
Essential mathematical insights into one of the most important and challenging open problems in general relativity-the stability of black holesOne of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations.
An important new perspective on AFFINE AND PROJECTIVEGEOMETRY This innovative book treats math majors and math education studentsto a fresh look at affine and projective geometry from algebraic,synthetic, and lattice theoretic points of view.
This textbook is a comprehensive and yet accessible introduction to non-Euclidean Laguerre geometry, for which there exists no previous systematic presentation in the literature.
The first part of this monograph is devoted to a characterization of hypergeometric-like functions, that is, twists of hypergeometric functions in n-variables.
In 1920, Pierre Fatou expressed the conjecture that--except for special cases--all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration.
Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985.
This unique book overturns our ideas about non-Euclidean geometry and the fine-structure constant, and attempts to solve long-standing mathematical problems.
The package of Gromov's pseudo-holomorphic curves is a major tool in global symplectic geometry and its applications, including mirror symmetry and Hamiltonian dynamics.
Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics.
A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.
Cet ouvrage contient les correspondances actives et passives de Jules Hoüel avec Joseph-Marie De Tilly, Gaston Darboux et Victor-Amédée Le Besgue ainsi qu’une introduction qui se focalise sur la découverte de l’impossibilité de démontrer le postulat des parallèles d’Euclide et l’apparition des premiers exemples de fonctions continues non dérivables.
Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory.
This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements.
This book presents the proceedings of the 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds, which was held at the Kyungpook National University from June 21 to 25, 2016.
This undergraduate textbook provides a comprehensive treatment of Euclidean and transformational geometries, supplemented by substantial discussions of topics from various non-Euclidean and less commonly taught geometries, making it ideal for both mathematics majors and pre-service teachers.
A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.
This book presents the proceedings of the 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds, which was held at the Kyungpook National University from June 21 to 25, 2016.