Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mirror symmetry for P^2 and tropical geometry   This paper explores the relationship between mirror symmetry for P^2, at the
level of big quantum cohomology, and tropical geometry. The mirror of P^2 is
typically taken to be ((C^*)^2,W), where W is a Landau-Ginzburg potential of
the form x+y+1/xy. The complex moduli space of the mirror is the universal
unfolding of W, and oscillatory integrals produce a Frobenius manifold
structure on this universal unfolding. We show that W can be deformed by
counting Maslov index two tropical disks, and the natural paramaters appearing
in this deformation are then the flat coordinates on the moduli space.
Furthermore, the oscillatory integrals are shown to read off directly tropical
curve counts from the potential. Thus we show in fact that mirror symmetry for
P^2 is equivalent in a strong sense to tropical curve counting formulas,
including tropical formulas for gravitational descendent invariants.

4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph