Author: Jayadev S. Athreya
Publisher: American Mathematical Society
ISBN: 147047655X
Category : Mathematics
Languages : en
Pages : 195
Book Description
This textbook offers an accessible introduction to translation surfaces. Building on modest prerequisites, the authors focus on the fundamentals behind big ideas in the field: ergodic properties of translation flows, counting problems for saddle connections, and associated renormalization techniques. Proofs that go beyond the introductory nature of the book are deftly omitted, allowing readers to develop essential tools and motivation before delving into the literature. Beginning with the fundamental example of the flat torus, the book goes on to establish the three equivalent definitions of translation surface. An introduction to the moduli space of translation surfaces follows, leading into a study of the dynamics and ergodic theory associated to a translation surface. Counting problems and group actions come to the fore in the latter chapters, giving a broad overview of progress in the 40 years since the ergodicity of the Teichmüller geodesic flow was proven. Exercises are included throughout, inviting readers to actively explore and extend the theory along the way. Translation Surfaces invites readers into this exciting area, providing an accessible entry point from the perspectives of dynamics, ergodicity, and measure theory. Suitable for a one- or two-semester graduate course, it assumes a background in complex analysis, measure theory, and manifolds, while some familiarity with Riemann surfaces and ergodic theory would be beneficial.
Translation Surfaces
Author: Jayadev S. Athreya
Publisher: American Mathematical Society
ISBN: 147047655X
Category : Mathematics
Languages : en
Pages : 195
Book Description
This textbook offers an accessible introduction to translation surfaces. Building on modest prerequisites, the authors focus on the fundamentals behind big ideas in the field: ergodic properties of translation flows, counting problems for saddle connections, and associated renormalization techniques. Proofs that go beyond the introductory nature of the book are deftly omitted, allowing readers to develop essential tools and motivation before delving into the literature. Beginning with the fundamental example of the flat torus, the book goes on to establish the three equivalent definitions of translation surface. An introduction to the moduli space of translation surfaces follows, leading into a study of the dynamics and ergodic theory associated to a translation surface. Counting problems and group actions come to the fore in the latter chapters, giving a broad overview of progress in the 40 years since the ergodicity of the Teichmüller geodesic flow was proven. Exercises are included throughout, inviting readers to actively explore and extend the theory along the way. Translation Surfaces invites readers into this exciting area, providing an accessible entry point from the perspectives of dynamics, ergodicity, and measure theory. Suitable for a one- or two-semester graduate course, it assumes a background in complex analysis, measure theory, and manifolds, while some familiarity with Riemann surfaces and ergodic theory would be beneficial.
Publisher: American Mathematical Society
ISBN: 147047655X
Category : Mathematics
Languages : en
Pages : 195
Book Description
This textbook offers an accessible introduction to translation surfaces. Building on modest prerequisites, the authors focus on the fundamentals behind big ideas in the field: ergodic properties of translation flows, counting problems for saddle connections, and associated renormalization techniques. Proofs that go beyond the introductory nature of the book are deftly omitted, allowing readers to develop essential tools and motivation before delving into the literature. Beginning with the fundamental example of the flat torus, the book goes on to establish the three equivalent definitions of translation surface. An introduction to the moduli space of translation surfaces follows, leading into a study of the dynamics and ergodic theory associated to a translation surface. Counting problems and group actions come to the fore in the latter chapters, giving a broad overview of progress in the 40 years since the ergodicity of the Teichmüller geodesic flow was proven. Exercises are included throughout, inviting readers to actively explore and extend the theory along the way. Translation Surfaces invites readers into this exciting area, providing an accessible entry point from the perspectives of dynamics, ergodicity, and measure theory. Suitable for a one- or two-semester graduate course, it assumes a background in complex analysis, measure theory, and manifolds, while some familiarity with Riemann surfaces and ergodic theory would be beneficial.
Geometry and topology of wild translation surfaces
Author: Randecker, Anja
Publisher: KIT Scientific Publishing
ISBN: 3731504561
Category : Mathematics
Languages : en
Pages : 162
Book Description
A translation surface is a two-dimensional manifold, equipped with a translation structure. It can be obtained by considering Euclidean polygons and identifying their edges via translations. The vertices of the polygons form singularities if the translation structure can not be extended to them. We study translation surfaces with wild singularities, regarding the topology (genus and space of ends), the geometry (behavior of the singularities), and how the topology and the geometry are related.
Publisher: KIT Scientific Publishing
ISBN: 3731504561
Category : Mathematics
Languages : en
Pages : 162
Book Description
A translation surface is a two-dimensional manifold, equipped with a translation structure. It can be obtained by considering Euclidean polygons and identifying their edges via translations. The vertices of the polygons form singularities if the translation structure can not be extended to them. We study translation surfaces with wild singularities, regarding the topology (genus and space of ends), the geometry (behavior of the singularities), and how the topology and the geometry are related.
Veech Groups and Translation Coverings
Author: Finster, Myriam
Publisher: KIT Scientific Publishing
ISBN: 3731501805
Category : Mathematics
Languages : en
Pages : 154
Book Description
A translation surface is obtained by taking plane polygons and gluing their edges by translations. We ask which subgroups of the Veech group of a primitive translation surface can be realised via a translation covering. For many primitive surfaces we prove that partition stabilising congruence subgroups are the Veech group of a covering surface. We also address the coverings via their monodromy groups and present examples of cyclic coverings in short orbits, i.e. with large Veech groups.
Publisher: KIT Scientific Publishing
ISBN: 3731501805
Category : Mathematics
Languages : en
Pages : 154
Book Description
A translation surface is obtained by taking plane polygons and gluing their edges by translations. We ask which subgroups of the Veech group of a primitive translation surface can be realised via a translation covering. For many primitive surfaces we prove that partition stabilising congruence subgroups are the Veech group of a covering surface. We also address the coverings via their monodromy groups and present examples of cyclic coverings in short orbits, i.e. with large Veech groups.
Mostly Surfaces
Author: Richard Evan Schwartz
Publisher: American Mathematical Soc.
ISBN: 0821853686
Category : Mathematics
Languages : en
Pages : 330
Book Description
The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.
Publisher: American Mathematical Soc.
ISBN: 0821853686
Category : Mathematics
Languages : en
Pages : 330
Book Description
The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.
Transactions of the American Mathematical Society
Author: American Mathematical Society
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 538
Book Description
Monthly journal devoted entirely to research in pure and applied mathematics, and, in general, includes longer papers than those in the Proceedings of the American Mathematical Society.
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 538
Book Description
Monthly journal devoted entirely to research in pure and applied mathematics, and, in general, includes longer papers than those in the Proceedings of the American Mathematical Society.
Bulletin of the American Mathematical Society
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 900
Book Description
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 900
Book Description
Bulletin (new Series) of the American Mathematical Society
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 616
Book Description
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 616
Book Description
American Journal of Mathematics
Author:
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 432
Book Description
The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics.
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 432
Book Description
The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics.
Annals of Mathematics
Author:
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 410
Book Description
Founded in 1884, Annals of Mathematics publishes research papers in pure mathematics.
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 410
Book Description
Founded in 1884, Annals of Mathematics publishes research papers in pure mathematics.
Revue Semestrielle Des Publications Mathématiques
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 362
Book Description
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 362
Book Description