Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convex Algebraic Geometry of Curvature Operators   We study the structure of the set of algebraic curvature operators satisfying
a sectional curvature bound under the light of the emerging field of Convex
Algebraic Geometry. More precisely, we determine in which dimensions $n$ this
convex semialgebraic set is a spectrahedron or a spectrahedral shadow; in
particular, for $n\geq5$, these give new counter-examples to the Helton--Nie
Conjecture. Moreover, efficient algorithms are provided if $n=4$ to test
membership in such a set. For $n\geq5$, algorithms using semidefinite
programming are obtained from hierarchies of inner approximations by
spectrahedral shadows and outer relaxations by spectrahedra.

5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con