29 citations · 107 across the 17 of their papers we have counts for
17 papers
On the Betti numbers, Poincaré polynomials, and Euler characteristics of
Giordano Cotti
In this paper, we revisit the Poincaré polynomials, Betti numbers, and Euler characteristics of the Deligne-Mumford moduli spaces of stable -pointe…
Fiberwise Gromov-Witten theory, quantum spectra of flag bundles, and prime factorization of integers
Giordano Cotti
This work investigates the vertical quantum cohomology and quantum spectra of flag bundles, uncovering new links between the Gromov-Witten theory of homogeneous fibrations and anal…
Generalized Mittag-Leffler functions, Borel-Laplace multitransforms, and quantum differential equations of Fano varieties
Giordano Cotti
This paper addresses the integration problem for the isomonodromic system of quantum differential equations associated with smooth projective Fano varieties. We begin by introducin…
On the Satake correspondence for the equivariant quantum differential equations and qKZ difference equations of Grassmannians
Giordano Cotti, Alexander Varchenko
We consider the joint system of equivariant quantum differential equations (qDE) and qKZ difference equations for the Grassmannian , which parametrizes -dimensional subs…
Asymptotic solutions for linear ODEs with not-necessarily meromorphic coefficients: a Levinson type theorem on complex domains, and applications
Giordano Cotti, Davide Guzzetti, Davide Masoero
In this paper, we consider systems of linear ordinary differential equations, with analytic coefficients on big sectorial domains, which are asymptotically diagonal for large value…
Borel -multitransforms and Quantum Leray-Hirsch: integral representations of solutions of quantum differential equations for -bundles
Giordano Cotti
In this paper, we address the integration problem of the isomonodromic system of quantum differential equations (s) associated with the quantum cohomology of -bun…
On the universality of integrable deformations of solutions of degenerate Riemann-Hilbert-Birkhoff problems
Giordano Cotti
This paper addresses the classification problem of integrable deformations of solutions of "degenerate" Riemann-Hilbert-Birkhoff (RHB) problems. These consist of those RHB problems…
Riemann-Hilbert-Birkhoff inverse problem for semisimple flat -manifolds, and convergence of oriented associativity potentials
Giordano Cotti
In this paper, we address the problem of classification of quasi-homogeneous formal power series providing solutions of the oriented associativity equations. Such a classification…
Degenerate Riemann-Hilbert-Birkhoff problems, semisimplicity, and convergence of WDVV-potentials
Giordano Cotti
In the first part of this paper, we give a new analytical proof of a theorem of C. Sabbah on integrable deformations of meromorphic connections on with coalescing irr…
The -Markov equation for Laurent polynomials
Giordano Cotti, Alexander Varchenko
We consider the -Markov equation for the symmetric Laurent polynomials in three variables with integer coefficients, which is an equivariant analog of the classical Markov equat…
Cyclic stratum of Frobenius manifolds, Borel-Laplace -multitransforms, and integral representations of solutions of Quantum Differential Equations
Giordano Cotti
In the first part of this paper, we introduce the notion of "cyclic stratum" of a Frobenius manifold . This is the set of points of the extended manifold a…
Quantum differential equations and helices
Giordano Cotti
These notes partly touch the topic of the talk given by the author at the XXXVIII Workshop on Geometric Methods in Physics, hold in June-July 2019 in Białowieża, Poland. They consi…
Equivariant quantum differential equation and equations for a projective space: Stokes bases as exceptional collections, Stokes matrices as Gram matrices, and B-Theorem
Giordano Cotti, Alexander Varchenko
In arXiv:1901.02990v1 the equivariant quantum differential equation () for a projective space was considered and a compatible system of difference equations was introduc…
Helix Structures in Quantum Cohomology of Fano Varieties
Giordano Cotti, Boris Dubrovin, Davide Guzzetti
In this paper we consider a conjecture formulated by the second author in occasion of the 1998 ICM in Berlin (arXiv:math/9807034v2). This conjecture states the equivalence, for a F…
Local Moduli of Semisimple Frobenius Coalescent Structures
Giordano Cotti, Boris Dubrovin, Davide Guzzetti
We extend the analytic theory of Frobenius manifolds to semisimple points with coalescing eigenvalues of the operator of multiplication by the Euler vector field. We clarify which…
Isomonodromy Deformations at an Irregular Singularity with Coalescing Eigenvalues
Giordano Cotti, Boris Dubrovin, Davide Guzzetti
We consider an linear system of ODEs with an irregular singularity of Poincaré rank 1 at , holomorphically depending on parameter within a polydisc in $\m…
Coalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers
Giordano Cotti
The occurrence and frequency of a phenomenon of resonance (namely the coalescence of some Dubrovin canonical coordinates) in the locus of Small Quantum Cohomology of complex Grassm…