# Here There be Dragons in Sympletic Geometry

• I
• jedishrfu
In summary, sympletic geometry is a branch of mathematics that focuses on sympletic manifolds, which are geometric spaces with a special structure and coordinate system. It is used to study physical systems, and the phrase "Here There be Dragons" is often used to describe the presence of chaos and nonlinearity in these systems. Sympletic geometry is closely related to other branches of mathematics and has various real-world applications, such as in spacecraft design and data compression. Current research areas in sympletic geometry include integrable systems, sympletic topology, and sympletic field theory.
Yay!

Fascinating piece on the foundations of symplectic geometry. It reminds me a lot of foundational issues in other areas of science - physics, psychology and economics to name a few.

Despite all the purported intrinsic objectivity of what is deemed to be part of the subject matter of mathematics (whatever that may be), this just goes to show how much mathematics actually is like any other human endeavour.

jedishrfu

## 1. What is sympletic geometry?

Sympletic geometry is a branch of mathematics that studies sympletic manifolds, which are geometric spaces that have both a certain type of structure called a sympletic form and a coordinate system. This type of geometry is used to study physical systems, such as those found in classical mechanics and quantum mechanics.

## 2. What is the relevance of "Here There be Dragons" in sympletic geometry?

The phrase "Here There be Dragons" is often used in maps to indicate uncharted or dangerous territories. In sympletic geometry, it refers to the presence of chaos and nonlinearity in certain systems, which can be difficult to study and understand.

## 3. How is sympletic geometry related to other branches of mathematics?

Sympletic geometry is closely related to other branches of mathematics, such as differential geometry, topology, and algebraic geometry. It also has connections to physics, specifically in the study of dynamical systems and Hamiltonian mechanics.

## 4. What are some real-world applications of sympletic geometry?

Sympletic geometry has many practical applications, including in the design of spacecraft trajectories, the analysis of quantum systems, and the study of fluid dynamics. It also has applications in computer science, such as in the development of algorithms for data compression and image processing.

## 5. What are the current research areas in sympletic geometry?

Some current research areas in sympletic geometry include the study of integrable systems, sympletic topology, and sympletic field theory. Other topics of interest include sympletic reduction, sympletic groupoids, and mirror symmetry.

Replies
1
Views
288
Replies
8
Views
2K
Replies
1
Views
1K
Replies
40
Views
4K
Replies
3
Views
2K
Replies
1
Views
885
Replies
1
Views
1K
Replies
8
Views
948
Replies
6
Views
2K
Replies
1
Views
1K