2,012 reputation
818
bio website homepages.ulb.ac.be/~samulisi
location Nantes, France
age
visits member for 3 years, 8 months
seen Oct 23 at 15:14

Postdoc working in symplectic/contact topology. I'm currently at the Université de Nantes.


Sep
24
awarded  Autobiographer
May
17
answered When is symplectic pullback bundle trivial
May
16
awarded  Revival
Apr
18
awarded  Enlightened
Apr
18
awarded  Nice Answer
Apr
6
comment Symplectic submanifolds in $\mathbb{R}^{4}$
@studiosus: your example isn't relevant to my claim because the punctured surface isn't a manifold with boundary. However, I think you are right that the actions on the boundary are relevant. I'll adjust my answer accordingly. Thank you.
Apr
5
comment Symplectic submanifolds in $\mathbb{R}^{4}$
@studiosus: Thank you for the corrected reference. In this case, since the surfaces are compact with boundary, I think it's possible to make some minor modifications to Moser so that it works. In particular, I believe you can modify Moser's proof by hand to make the flow of the vector field he constructs be defined up to time 1. Since that's the piece where compactness is necessary, I think everything else should carry through.
Apr
3
comment Symplectic submanifolds in $\mathbb{R}^{4}$
you didn't mention that you had cross-posted this to MO! Next time, be sure to mention it when you do, so we don't waste time duplicating effort.
Apr
3
answered Symplectic submanifolds in $\mathbb{R}^{4}$
Apr
2
comment please tell me what does $C^{0}(M)$ means in quasi states on symplectic manifold $M$
It means the space of continuous functions on $M$.
Mar
16
awarded  Yearling
Mar
15
comment Top current research topics in Complex Algebraic and Differential Geometry
I really think that this type of question is best discussed with an expert in the areas that interest you. In particular, I don't think you want lots of opinions from people on the internet.
Mar
15
answered vector bundles and their cross-sections
Mar
15
comment Is $f(x)+\sum_{p,i=1,…,m}\lambda_{p,i}x_{p,i}(x)$ globally defined?
Where is this question coming from? This seems pretty unmotivated.
Mar
15
answered What does it mean by saying that $u^n, J^n$ “$C^{\infty}$ converges” to u, J?
Feb
17
comment Derivative of a function involving inverse of a matrix-lifting a diffeomorphism to a symplectomorphism
I haven't given this enough thought for this to count as an answer... in particular, I'm ignoring the specific details of your construction of $f$. The general fact is that a diffeomorphism $f \colon X \to X$ induces a symplectic diffeomorphism of $T^*X \to T^*X$, and $T^*X$ has a canonical symplectic structure. If all is right in the world, you have merely restated this fact in a special case.
Feb
17
answered Second Hirzebruch surface as Delzant space associated to trapezoid
Feb
16
comment On the definition/notation for pseudoholomorphic curves
Now, consider $u \colon D \to M$. Look at some point $z \in D$, and let $p = u(z) \in M$. Then, we take a coordinate chart around $p$ as in my previous comment. We can then think of $u \colon D \to \mathbb{R}^{2n}$. The differential $du \colon T_z D \to T_{u(z)} \mathbb{R}^{2n}$. Now, $J$ is an endomorphism of $T_{u(z)}\mathbb{R}^{2n}$, and this matrix is then $J( u(z ))$. Does this make sense?
Feb
16
comment On the definition/notation for pseudoholomorphic curves
A key point: $M$ is not a complex manifold. This means that the coordinate chart we choose is just a real coordinate chart. Thus, we should think of $z = (x_1, y_1, x_2, y_2, \dots, x_n, y_n)$. At each point in this coordinate chart, the tangent space is spanned by $\partial_{x_i}, \partial_{y_i}$. This gives a trivialization of the tangent space over each point in our coordinate chart. Now, finally, $J(x_1, y_1, \dots, x_n, y_n)$ is a matrix that tells you what $J$ does to the local vector fields $\partial_{x_i}$, $\partial_{y_i}$.
Feb
14
answered On the definition/notation for pseudoholomorphic curves