Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic embeddings of four-dimensional polydisks into half integer
  ellipsoids   We obtain new sharp obstructions to symplectic embeddings of four-dimensional
polydisks $P(a,1)$ into four-dimensional ellipsoids $E(bc,c)$ when $1\le a< 2$
and $b$ is a half-integer. When $1 \leq a < 2-O(b^{-1})$ we demonstrate that
$P(a,1)$ symplectically embeds into $E(bc,c)$ if and only if $a+b\le bc$. Our
results show that inclusion is optimal and extend the result by Hutchings
\cite{H} when $b$ is an integer. Our proof is based on a combinatorial
criterion developed by Hutchings \cite{H} to obstruct symplectic embeddings.

31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph