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Results tagged with sg.symplectic-geometry
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user 5420
Hamiltonian systems, symplectic flows, classical integrable systems
26
votes
5
answers
11k
views
What does the word "symplectic" mean?
I know the definition of symplectic structure, symplectic group, and so on. But what does the word "symplectic" itself mean?
Meta question: I have many other mathematical words whose etymologies are …
- 6,133
21
votes
3
answers
2k
views
When is a coadjoint orbit an integrable system (in a weak sense explained below)?
Let $X$ be an affine holomorphic symplectic variety of dimension $2n$, with the associated Poisson bracket { , }. Let's say it's an integrable system when there are $n$ algebraically independent holom …
- 6,133
12
votes
1
answer
1k
views
What is the "symplectic duality" between holomorphic symplectic manifolds? Where can I read ...
I'm recently working on something called 3d mirror symmetry in QFT literature, which involves two hyperkähler manifolds.
There seems to be a corresponding(?) mathematical theory called symplectic dua …
- 6,133
7
votes
4
answers
2k
views
Why does Hom need an identity in the definition of the category?
I was studying the axioms of a category, and noted that one axiom says there is an element $1_X\in Hom(X,X)$ for any object $X$ which serves as the identity. Why is this axiom necessary? What happens …
- 6,133