Powerful ideas from top nonfiction
Try Blinkist to get the key ideas from 7,500+ bestselling nonfiction titles and podcasts. Listen or read in just 15 minutes.
Get started
Blink 3 of 8 - The 5 AM Club
by Robin Sharma
Lectures on Symplectic Geometry summary
Ana Cannas da Silva
Brief summary
Lectures on Symplectic Geometry by Ana Cannas da Silva provides a comprehensive introduction to the fundamental concepts and techniques of symplectic geometry. It covers a wide range of topics, from basic symplectic structures to Hamiltonian dynamics and symplectic topology.
Topics
Table of Contents
Lectures on Symplectic Geometry
Summary of key ideas
Understanding the Basics of Symplectic Geometry
In Lectures on Symplectic Geometry by Ana Cannas da Silva, we embark on a journey through the fascinating field of symplectic geometry. The book begins with an introduction to the basic concepts, starting with a discussion on the symplectic form, the fundamental object in this area of study. This form is a non-degenerate, closed 2-form, which encodes the geometric and dynamic information of a symplectic manifold.
Furthermore, the author explains the symplectic vector space, which is equipped with a non-degenerate, skew-symmetric bilinear form. She then moves on to symplectic linear algebra, focusing on linear symplectic transformations and their properties. These early chapters lay a solid foundation for understanding the symplectic geometry that follows.
Exploring Symplectic Manifolds
Continuing in her exploration of symplectic geometry, Cannas da Silva introduces the concept of symplectic manifolds. These are smooth manifolds equipped with a closed, non-degenerate 2-form. The author discusses the properties of these manifolds, including symplectic diffeomorphisms and their role in preserving the symplectic structure.
She then delves into the study of Hamiltonian vector fields, which are vector fields associated with a symplectic form. These fields play a crucial role in the Hamiltonian dynamics, a classical mechanics formalism that relies on the symplectic structure to describe the evolution of physical systems. The discussion on Hamiltonian dynamics provides a bridge between symplectic geometry and physics.
Understanding Symplectic Reduction and Applications
In the subsequent sections of Lectures on Symplectic Geometry, Cannas da Silva explores the concept of symplectic reduction. This process allows us to study the dynamics of a system on a symplectic manifold with a group action, by projecting it onto a lower-dimensional symplectic manifold. The author explains the Marsden-Weinstein-Meyer theory, a key result in symplectic reduction, and its applications in various fields, including mechanics and control theory.
Moreover, the book discusses the symplectic cut, a tool used to understand the topology of the reduced space. It also covers symplectic toric manifolds, which are symplectic manifolds equipped with an effective torus action, and their applications in symplectic geometry and beyond. The author provides detailed explanations and examples to illustrate these advanced concepts.
Concluding Remarks and Further Readings
In the concluding sections, Cannas da Silva discusses symplectic capacities and their role in understanding the symplectic geometry of higher dimensions. She also touches upon the symplectic aspects of contact geometry, a related area of study.
Throughout the book, the author maintains a clear and engaging writing style, making the complex subject of symplectic geometry accessible to both beginners and experts. She provides numerous examples and exercises to reinforce the understanding of the material. In the end, Lectures on Symplectic Geometry serves as an excellent introductory text for anyone interested in this intriguing branch of mathematics. The book also provides a comprehensive bibliography, guiding readers towards further exploration of the topic.
How do we create content on this page?
More knowledge in less time
Read or listen
Get the key ideas from nonfiction bestsellers in minutes, not hours.
Find your next read
Get book lists curated by experts and personalized recommendations.
Shortcasts New
We’ve teamed up with podcast creators to bring you key insights from podcasts.
What is Lectures on Symplectic Geometry about?
Lectures on Symplectic Geometry by Ana Cannas da Silva provides a comprehensive introduction to the fascinating field of symplectic geometry. Through clear explanations and insightful examples, the book covers key concepts such as symplectic manifolds, Hamiltonian dynamics, and symplectomorphisms. It is a valuable resource for anyone interested in delving into this elegant branch of mathematics.
Lectures on Symplectic Geometry Review
Lectures on Symplectic Geometry provides a comprehensive exploration of the fundamental concepts and applications of symplectic geometry, making it a valuable resource for those interested in the subject. Here's why this book stands out:
- With its clear explanations and insightful examples, it simplifies complex ideas, making symplectic geometry accessible to readers at all levels of expertise.
- The book offers practical insights into real-world problems in mathematics and physics, showcasing the relevance of symplectic geometry in various fields.
- Its engaging approach keeps readers intrigued and invested, proving that a deep dive into symplectic geometry doesn't have to be dry or impenetrable.
Who should read Lectures on Symplectic Geometry?
Graduate students and researchers in mathematics or physics with an interest in symplectic geometry
Individuals looking to deepen their understanding of geometric structures and their applications
Readers who enjoy challenging and thought-provoking academic texts
Categories with Lectures on Symplectic Geometry
Book summaries like Lectures on Symplectic Geometry
People ❤️ Blinkist
Sven O.
It's highly addictive to get core insights on personally relevant topics without repetition or triviality. Added to that the apps ability to suggest kindred interests opens up a foundation of knowledge.
Thi Viet Quynh N.
Great app. Good selection of book summaries you can read or listen to while commuting. Instead of scrolling through your social media news feed, this is a much better way to spend your spare time in my opinion.
Jonathan A.
Life changing. The concept of being able to grasp a book's main point in such a short time truly opens multiple opportunities to grow every area of your life at a faster rate.
Renee D.
Great app. Addicting. Perfect for wait times, morning coffee, evening before bed. Extremely well written, thorough, easy to use.
People also liked these summaries
4.7 Stars
Average ratings on iOS and Google Play
36 Million
Downloads on all platforms
10+ years
Experience igniting personal growth
Lectures on Symplectic Geometry FAQs
What is the main message of Lectures on Symplectic Geometry?
The main message of Lectures on Symplectic Geometry is understanding the fundamental concepts of symplectic geometry.
How long does it take to read Lectures on Symplectic Geometry?
To read Lectures on Symplectic Geometry, it takes time. For a quicker grasp, consider the Blinkist summary.
Is Lectures on Symplectic Geometry a good book? Is it worth reading?
Lectures on Symplectic Geometry is valuable for exploring symplectic geometry without excess technicalities.
Who is the author of Lectures on Symplectic Geometry?
The author of Lectures on Symplectic Geometry is Ana Cannas da Silva.
What to read after Lectures on Symplectic Geometry?
If you're wondering what to read next after Lectures on Symplectic Geometry, here are some recommendations we suggest:
- Where Good Ideas Come From by Steven Johnson
- Incognito by David Eagleman
- God Is Not Great by Christopher Hitchens
- A Brief History of Time by Stephen Hawking
- The Selfish Gene by Richard Dawkins
- Simply Complexity by Neil F. Johnson
- Antifragile by Nassim Nicholas Taleb
- Physics of the Future by Michio Kaku
- The Black Swan by Nassim Nicholas Taleb
- Musicophilia by Oliver Sacks