Research Directions in Symplectic and Contact Geometry and Topology

This book highlights recent research advances in symplectic and contact geometry and topology, with a focus on low-dimensional topology. It includes original results and survey articles, showcasing collaborative research by female and nonbinary mathematicians at different career levels. The projects began at WiSCon 2019, leading to new connections and directions in the field.

Format: Paperback / softback
Length: 329 pages
Publication date: 04 February 2023
Publisher: Springer Nature Switzerland AG

This comprehensive book delves into the latest research breakthroughs in the fields of symplectic and contact geometry, topology, and related areas in low-dimensional topology. Over the past few decades, this field has witnessed remarkable and exhilarating growth, and this volume serves as an accessible entry point into numerous active research problems within this domain. The authors of the papers in this volume have crafted their work with a broad audience in mind, aiming to reach a diverse range of mathematicians across different levels of expertise. In addition to imparting knowledge about emerging research areas, this book will ignite the curiosity of researchers, encouraging them to delve deeper into the field and ask thought-provoking questions that will further advance its development.

The volume encompasses a diverse range of contributions, featuring both original research results and comprehensive survey articles. These projects originated at the Research Collaboration Conference for Women in Symplectic and Contact Geometry and Topology (WiSCon), held at ICERM, Brown University, in July 2019. Each group of authors consisted of female and nonbinary mathematicians from various career stages and with diverse areas of specialization. By fostering inclusivity and diversity, these collaborations paved the way for new connections between mathematicians from different continents and fostered the development of fresh partnerships and directions that are prominently showcased in this work.

The chapters in this book are organized into four sections, each addressing a specific aspect of the field. The first section focuses on symplectic and contact geometry, exploring topics such as symplectic structures, Hamiltonian dynamics, and geometric quantization. The second section delves into topology, covering areas such as knot theory, 3-manifolds, and hyperbolic geometry. The third section explores applications of symplectic and contact geometry to other fields, including mathematical physics, string theory, and computer science. The final section presents survey articles that provide an overview of the state-of-the-art research in the field, highlighting key developments, open problems, and future directions.

Throughout the book, the authors employ a clear and concise writing style, making the content accessible to a wide range of readers. Each chapter includes detailed explanations, examples, and exercises to aid in understanding and applying the concepts presented. Additionally, the book features a comprehensive bibliography that provides further resources for those interested in exploring the field in greater depth.

In conclusion, this book is a valuable resource for mathematicians, researchers, and students interested in symplectic and contact geometry, topology, and related areas. It offers a comprehensive overview of the latest research developments, fosters interdisciplinary connections, and inspires further exploration into the field. The collaborative nature of the research featured in this volume showcases the power of diversity and inclusivity in driving scientific progress.

Weight: 534g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030809812
Edition number: 1st ed. 2021