Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cyclic stratum of Frobenius manifolds, Borel-Laplace
  $(\boldsymbol\alpha,\boldsymbol\beta)$-multitransforms, and integral
  representations of solutions of Quantum Differential Equations   In the first part of this paper, we introduce the notion of "cyclic stratum"
of a Frobenius manifold $M$. This is the set of points of the extended manifold
$\mathbb C^*\times M$ at which the unit vector field is a cyclic vector for the
isomonodromic system defined by the flatness condition of the extended deformed
connection. The study of the geometry of the complement of the cyclic stratum
is addressed. We show that at points of the cyclic stratum, the isomonodromic
system attached to $M$ can be reduced to a scalar differential equation, called
the "master differential equation" of $M$. In the case of Frobenius manifolds
coming from Gromov-Witten theory, namely quantum cohomologies of smooth
projective varieties, such a construction reproduces the notion of quantum
differential equation.
  In the second part of the paper, we introduce two multilinear transforms,
called "Borel-Laplace $(\boldsymbol \alpha,\boldsymbol\beta)$-multitransforms",
on spaces of Ribenboim formal power series with exponents and coefficients in
an arbitrary finite dimensional $\mathbb C$-algebra $A$. When $A$ is
specialized to the cohomology of smooth projective varieties, the integral
forms of the Borel-Laplace $(\boldsymbol
\alpha,\boldsymbol\beta)$-multitransforms are used in order to rephrase the
Quantum Lefschetz Theorem. This leads to explicit Mellin-Barnes integral
representations of solutions of the quantum differential equations for a wide
class of smooth projective varieties, including Fano complete intersections in
projective spaces.
  In the third and final part of the paper, as an application, we show how to
use the new analytic tools, introduced in the previous parts, in order to study
the quantum differential equations of Hirzebruch surfaces. This finally leads
to the proof of Dubrovin Conjecture for all Hirzebruch surfaces.

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The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat