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Integrable Partial Differential Equations: Geometry, Asymptotics, and Numerics.

Deliverables

Public Lecture 1

By this date at least a public lecture on subjects related with the project and aimed at the wider public will be delivered at each node.

Conference at Unimib

First general Conference of the Project. The main focus will be on WP2( (Near-to) Integrable PDEs and Applications), state of the art review and novel developments. The state of the art concerning WP3 and WP4 will be also reviewed. The conference will be organized by Unimib. The entire network will participate, and attendance by experts outside the consortium will also be encouraged.

Conference at UBFC

Second general Conference of the project. The main focus will be on WP4 (Numerical Approaches), state of the art review and novel developments. The state of the art in WP2 and WP3 will also reviewed. The conference will be organized by UBFC (in particular University of Bourgogne). The entire network will participate, and attendance by experts outside the consortium will also be encouraged.

Monograph

Publication of a monograph directed to graduate students to present the research activities of the network to a larger audience in a more accessible way than journal publications In this monograph integrable systems techniques are compared to PDE methods for certain integrable equations This will allow to asses pros and cons of the two approaches to the same type of equations providing an important compendium accessible to both communities It will also help to identify strategies to apply integrable system techniques to nonintegrable PDEs which is at the heart of the present project

Release of Numerical code libraries

Libraries of numerical programs will be developed This will allow the participants of the project to use stateofart numerical techniques to be developed by those participants actively working in WP4 Numerical Methods These novel numerical approaches will allow to address questions which are up to now out of reach of standard numerical techniques During the first half of the project the use of this numerical library will be restricted also for testing reasons to the members of the Consortium By the end of the project the libraries will be made freely available to the scientific community at large An exception will be made for codes with potential commercial interest that will be protected by software patentsThe libraries are envisaged to comprise1 Implementation of geometric and symplectic integrators for integrable and almost integrable PDEs2 Development of boundary integral and multidomain spectral methods for coupled InternalSurface Wave systems3 Painlev equations4 Numerical treatment of compact Riemann surfaces

Web Page

Web page of the network, created and constantly updated with the description of the goals and the actions of the network, both scientific and organizational. The web page will also have a section devoted to the large public, for outreach purpose.

video gallery

Realization of an online video gallery with typical solutions of dispersive PDEs. This gallery will combine information in the form of wikipedia articles with videos illustrating solutions described in the text. The items of the gallery will be presented during the planned public lectures.

Table-top tank for water waves

Realization of a table-top size tank equipped with surface and possibly internal waves generators. This will make possible to perform small scale experiments aimed at popularizing our research.

Publications

Soliton Shielding of the Focusing Nonlinear Schrödinger Equation

Author(s): Marco Bertola, Tamara Grava, and Giuseppe Orsatti
Published in: Physical Review Letters, 2023, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/physrevlett.130.127201

The sharp quantitative isocapacitary inequality (the case of p-capacity)

Author(s): Ekaterina Mukoseeva
Published in: Advances in Calculus of Variations, 2021, ISSN 1864-8258
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/acv-2020-0106

Poisson quasi-Nijenhuis deformations of the canonical PN structure

Author(s): G. Falqui; I. Mencattini; M. Pedroni
Published in: Journal of Geometry and Physics, 2023, ISSN 0393-0440
Publisher: Elsevier BV
DOI: 10.1016/j.geomphys.2023.104773

Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals

Author(s): Massimo Gisonni; Tamara Grava; Tamara Grava; Giulio Ruzza; Giulio Ruzza
Published in: Annales Henri Poincaré, 2020, ISSN 1424-0637
Publisher: Birkhauser Verlag
DOI: 10.1007/s00023-020-00922-4

Integrable equations associated with the finite-temperature deformation of the discrete Bessel point process

Author(s): Mattia Cafasso, Giulio Ruzza
Published in: Journal of the London Mathematical Society, 2023, ISSN 0024-6107
Publisher: Oxford University Press
DOI: 10.1112/jlms.12745

Rigorous Asymptotics of a KdV Soliton Gas

Author(s): Manuela Girotti; Tamara Grava; Tamara Grava; Robert Jenkins; Kenneth D.T-R McLaughlin
Published in: Communications in Mathematical Physics, 2021, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-021-03942-1

On the Long-Time Asymptotic Behavior of the Modified Korteweg--de Vries Equation with Step-like Initial Data

Author(s): Tamara Grava and Alexander Minakov
Published in: SIAM Journal on Mathematical Analysis (SIMA), 2020, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m1279964

Evolution of interface singularities in shallow water equations with variable bottom topography

Author(s): R. Camassa, R. D'Onofrio, G. Falqui, G. Ortenzi, M. Pedroni
Published in: Studies in Applied Mathematics, 2022, ISSN 0022-2526
Publisher: Blackwell Publishing Inc.
DOI: 10.1111/sapm.12480

Simple two-layer dispersive models in the Hamiltonian reduction formalism

Author(s): R. Camassa, G. Falqui, M. Pedroni, G. Ortenzi & Vu Ho, T.T.
Published in: Nonlinearity, 2023, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ace3a0

Entanglement of Two Disjoint Intervals in Conformal Field Theory and the 2D Coulomb Gas on a Lattice.

Author(s): Tamara Grava; Tamara Grava; Andrew P. Kels; Erik Tonni
Published in: Physical Review Letters, 2021, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/physrevlett.127.141605

Integrable hierarchies, Frölicher–Nijenhuisbicomplexes and Lauricella bi-flat F-manifolds

Author(s): Paolo Lorenzoni and Sara Perletti
Published in: Nonlinearity, 2023, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ad05dc

Isomonodromic Tau Functions on a Torus as Fredholm Determinants, and Charged Partitions

Author(s): Fabrizio Del Monte, Harini Desiraju & Pavlo Gavrylenko
Published in: Communications in Mathematical Physics, 2023, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-022-04458-y

Miura-reciprocal transformations and localizable Poisson pencils

Author(s): P Lorenzoni; S Shadrin; R Vitolo
Published in: Nonlinearity, 2024, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ad1494

On blowups of vorticity for the homogeneous Euler equation

Author(s): B. G. Konopelchenko, G. Ortenzi
Published in: Studies in Applied Mathematics, 2023, ISSN 0022-2526
Publisher: Blackwell Publishing Inc.
DOI: 10.1111/sapm.12618

Large |k| Behavior of Complex Geometric Optics Solutions to d-bar Problems

Author(s): Christian Klein, Johannes Sjöstrand, Nikola Stoilov
Published in: Communications on Pure and Applied Mathematics, 2022, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/cpa.22075

Fredholm determinant representation of the homogeneous Painlevé II τ-function

Author(s): Harini Desiraju
Published in: Nonlinearity, 2021, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/abf84a

Hamiltonian Aspects of Three-Layer Stratified Fluids

Author(s): R. Camassa, G. Falqui, G. Ortenzi, M. Pedroni & T. T. Vu Ho
Published in: Journal of Nonlinear Science, 2021, ISSN 0938-8974
Publisher: Springer Verlag
DOI: 10.1007/s00332-021-09726-0

Adiabatic invariants for the FPUT and Toda chain in the thermodynamic limit

Author(s): Tamara Grava; Tamara Grava; Alberto Maspero; Guido Mazzuca; Antonio Ponno
Published in: Communications in Mathematical Physics, 2020, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-020-03866-2

Momenta spacing distributions in anharmonic oscillators and the higher order finite temperature Airy kernel

Author(s): Thomas Bothner; Mattia Cafasso; Sofia Tarricone
Published in: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Issue 3, 2022, ISSN 0246-0203
Publisher: Elsevier BV
DOI: 10.1214/21-aihp1211

On the mean density of states of some matrices related to the beta ensembles and an application to the Toda lattice

Author(s): Guido Mazzuca
Published in: Journal of Mathematical Physics, 2022, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/5.0076539

On the modified fractional Korteweg-de Vries and related equations

Author(s): Klein, C.; Saut, J. -C.; Wang, Yuexun
Published in: Nonlinearity, 2022, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ac4814

On numerical approaches to nonlinear Schrödinger and Korteweg–de Vries equations for piecewise smooth and slowly decaying initial data

Author(s): Christian KleinJuan Prada-Malagon, Nikola Stoilov
Published in: Physica D, 2023, ISSN 0167-2789
Publisher: Elsevier BV
DOI: 10.1016/j.physd.2023.133885

Tau-functions for the Ablowitz–Ladik hierarchy: the matrix-resolvent method

Author(s): Mattia Cafasso; Di Yang
Published in: Journal of Physics A: Mathematical and Theoretical, 2022, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/ac5e74

Discrete Integrable Systems and Random Lax Matrices

Author(s): Tamara Grava; Massimo Gisonni; Giorgio Gubbiotti; Guido Mazzuca
Published in: Journal of Statistical Physics, 2022, ISSN 0022-4715
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10955-022-03024-z

Higher-order degenerations of Fay’s identities and applications to integrable equations

Author(s): Christian Klein and Jordi Pillet
Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2023, ISSN 1364-5021
Publisher: Royal Society of London
DOI: 10.1098/rspa.2023.0031

Correlation Functions for a Chain of Short Range Oscillators

Author(s): Tamara Grava; Tamara Grava; T. Kriecherbauer; Guido Mazzuca; Kenneth D.T-R McLaughlin
Published in: Journal of Statistical Physics, 2021, ISSN 0022-4715
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10955-021-02735-z

A Riemann-Hilbert approach to the lower tail of the KPZ equation

Author(s): Cafasso, Mattia; Claeys, Tom
Published in: Communications on Pure and Applied Mathematics, 2022, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/cpa.21978

Matrix models for stationary Gromov–Witten invariants of the Riemann sphere

Author(s): M Bertola and G Ruzza
Published in: Nonlinearity, 2021, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/abd85e

Numerical Approach to Painlevé Transcendents on Unbounded Domains

Author(s): Christian Klein, Nikola Stoilov
Published in: Symmetry, Integrability and Geometry: Methods and Applications, 2018, ISSN 1815-0659
Publisher: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
DOI: 10.3842/sigma.2018.068

Drinfeld-Sokolov Hierarchies, Tau Functions, and Generalized Schur Polynomials

Author(s): Mattia Cafasso, Ann du Crest de Villeneuve, Di Yang
Published in: Symmetry, Integrability and Geometry: Methods and Applications, 2018, ISSN 1815-0659
Publisher: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
DOI: 10.3842/sigma.2018.104

The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type

Author(s): Mattia Cafasso, Manuel D. de la Iglesia
Published in: Symmetry, Integrability and Geometry: Methods and Applications, 2018, ISSN 1815-0659
Publisher: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
DOI: 10.3842/sigma.2018.076

Painlevé IV Critical Asymptotics for Orthogonal Polynomials in the Complex Plane

Author(s): Marco Bertola, José Gustavo Elias Rebelo, Tamara Grava
Published in: Symmetry, Integrability and Geometry: Methods and Applications, 2018, ISSN 1815-0659
Publisher: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
DOI: 10.3842/sigma.2018.091

Noncommutative Painlevé Equations and Systems of Calogero Type

Author(s): M. Bertola, M. Cafasso, V. Rubtsov
Published in: Communications in Mathematical Physics, Issue 363/2, 2018, Page(s) 503-530, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-018-3210-0

Hydrodynamic Models and Confinement Effects by Horizontal Boundaries

Author(s): R. Camassa, G. Falqui, G. Ortenzi, M. Pedroni, C. Thomson
Published in: Journal of Nonlinear Science, Issue 29/4, 2019, Page(s) 1445-1498, ISSN 0938-8974
Publisher: Springer Verlag
DOI: 10.1007/s00332-018-9522-6

Fredholm Determinant Solutions of the Painlevé II Hierarchy and Gap Probabilities of Determinantal Point Processes

Author(s): Mattia Cafasso, Tom Claeys, Manuela Girotti
Published in: International Mathematics Research Notices, 2019, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnz168

A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions

Author(s): Estelle Basor, Pavel Bleher, Robert Buckingham, Tamara Grava, Alexander Its, Elizabeth Its, Jonathan P Keating
Published in: Nonlinearity, Issue 32/10, 2019, Page(s) 4033-4078, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ab28c7

Spectral approach to the scattering map for the semi-classical defocusing Davey–Stewartson II equation

Author(s): Christian Klein, Ken McLaughlin, Nikola Stoilov
Published in: Physica D: Nonlinear Phenomena, Issue 400, 2019, Page(s) 132126, ISSN 0167-2789
Publisher: Elsevier BV
DOI: 10.1016/j.physd.2019.05.006

Quantum D 4 Drinfeld–Sokolov hierarchy and quantum singularity theory

Author(s): Ann du Crest de Villeneuve, Paolo Rossi
Published in: Journal of Geometry and Physics, Issue 141, 2019, Page(s) 29-44, ISSN 0393-0440
Publisher: Elsevier BV
DOI: 10.1016/j.geomphys.2019.02.011

Singularity formation as a wetting mechanism in a dispersionless water wave model

Author(s): R Camassa, G Falqui, G Ortenzi, M Pedroni, G Pitton
Published in: Nonlinearity, Issue 32/10, 2019, Page(s) 4079-4116, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ab2a1a

Multidomain spectral method for the Gauss hypergeometric function

Author(s): S. Crespo, M. Fasondini, C. Klein, N. Stoilov, C. Vallée
Published in: Numerical Algorithms, 2019, ISSN 1017-1398
Publisher: Baltzer Science Publishers B.V.
DOI: 10.1007/s11075-019-00741-7

On the Geometry of Extended Self-Similar Solutions of the Airy Shallow Water Equations

Author(s): Roberto Camassa, Gregorio Falqui, Giovanni Ortenzi, Marco Pedroni
Published in: Symmetry, Integrability and Geometry: Methods and Applications, 2019, ISSN 1815-0659
Publisher: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
DOI: 10.3842/sigma.2019.087

Brezin–Gross–Witten tau function and isomonodromic deformations

Author(s): Marco Bertola, Giulio Ruzza
Published in: Communications in Number Theory and Physics, Issue 13/4, 2019, Page(s) 827-883, ISSN 1931-4523
Publisher: International Press of Boston, Inc.
DOI: 10.4310/cntp.2019.v13.n4.a4

The τ -function of the Ablowitz-Segur family of solutions to Painlevé II as a Widom constant

Author(s): Harini Desiraju
Published in: Journal of Mathematical Physics, Issue 60/11, 2019, Page(s) 113505, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/1.5120357

On a class of derivative Nonlinear Schrödinger-type equations in two spatial dimensions

Author(s): Jack Arbunich, Christian Klein, Christof Sparber
Published in: ESAIM: Mathematical Modelling and Numerical Analysis, Issue 53/5, 2019, Page(s) 1477-1505, ISSN 0764-583X
Publisher: EDP Sciences
DOI: 10.1051/m2an/2019018

Numerical scattering for the defocusing Davey–Stewartson II equation for initial data with compact support

Author(s): Christian Klein, Nikola Stoilov
Published in: Nonlinearity, Issue 32/11, 2019, Page(s) 4258-4280, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ab28c6

A Study of the Direct Spectral Transform for the Defocusing Davey‐Stewartson II Equation the Semiclassical Limit

Author(s): O. Assainova, C. Klein, K. D. T.‐R. McLaughlin, P. D. Miller
Published in: Communications on Pure and Applied Mathematics, Issue 72/7, 2019, Page(s) 1474-1547, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/cpa.21822

On the “Vacuum” Dam-Break Problem: Exact Solutions and Their Long Time Asymptotics

Author(s): Roberto Camassa, Gregorio Falqui, Giovanni Ortenzi, Marco Pedroni, Giuseppe Pitton
Published in: SIAM Journal on Applied Mathematics, Issue 80/1, 2020, Page(s) 44-70, ISSN 0036-1399
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m1266836

Borodin–Okounkov formula, string equation and topological solutions of Drinfeld–Sokolov hierarchies

Author(s): Mattia Cafasso, Chao-Zhong Wu
Published in: Letters in Mathematical Physics, Issue 109/12, 2019, Page(s) 2681-2722, ISSN 0377-9017
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11005-019-01205-8

Weakly nonlocal Poisson brackets, Schouten brackets and supermanifolds

Author(s): P. Lorenzoni, R. Vitolo
Published in: Journal of Geometry and Physics, Issue 149, 2020, Page(s) 103573, ISSN 0393-0440
Publisher: Elsevier BV
DOI: 10.1016/j.geomphys.2019.103573

Three computational approaches to weakly nonlocal Poisson brackets

Author(s): Matteo Casati, Paolo Lorenzoni, Raffaele Vitolo
Published in: Studies in Applied Mathematics, 2020, ISSN 0022-2526
Publisher: Blackwell Publishing Inc.
DOI: 10.1111/sapm.12302

Tau Functions as Widom Constants

Author(s): M. Cafasso, P. Gavrylenko, O. Lisovyy
Published in: Communications in Mathematical Physics, Issue 365/2, 2019, Page(s) 741-772, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-018-3230-9

The classical β-ensembles with β proportional to 1/N: From loop equations to Dyson’s disordered chain

Author(s): Peter J. Forrester; G. Mazzuca
Published in: Journal of Mathematical Physics, 2021, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/5.0048481

Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

Author(s): Massimo Gisonni, Tamara Grava & Giulio Ruzza
Published in: Letters in Mathematical Physics, 2021, ISSN 0377-9017
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11005-021-01396-z

Failure of scattering for the NLSE with a point interaction in dimension two and three

Author(s): Claudio Cacciapuoti; Domenico Finco; Diego Noja
Published in: Nonlinearity, 2023, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/acf1ee

Airy Kernel Determinant Solutions to the KdV Equation and Integro-Differential Painlevé Equations

Author(s): Mattia Cafasso; Tom Claeys; Giulio Ruzza
Published in: Communications in Mathematical Physics, 2021, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-021-04108-9

Multidomain spectral approach to rational-order fractional derivatives

Author(s): Klein, Christian, Stoilov, Nikola
Published in: Studies in Applied Mathematics, 2024, ISSN 0022-2526
Publisher: Blackwell Publishing Inc.
DOI: 10.1111/sapm.12671

Numerical study of Davey–Stewartson I systems

Author(s): Jörg Frauendiener, Christian Klein, Umar Muhammad, Nikola Stoilov
Published in: Studies in applied mathematics, 2022, ISSN 0022-2526
Publisher: Blackwell Publishing Inc.
DOI: 10.1111/sapm.12491

On the spectral problem of the quantum KdV hierarchy

Author(s): Giulio Ruzza and Di Yang
Published in: Journal of Physics A: Mathematical and Theoretical, 2021, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/ac190a

Poisson Quasi-Nijenhuis Manifolds and the Toda System

Author(s): Gregorio Falqui; Igor Mencattini; Giovanni Ortenzi; Marco Pedroni
Published in: Mathematical Physics, Analysis and Geometry, 2020, ISSN 1385-0172
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11040-020-09352-4

Solutions and singularities of the semigeostrophic equations via the geometry of Lagrangian submanifolds

Author(s): Roberto D’Onofrio; Giovanni Ortenzi; Ian Roulstone; Volodya Rubtsov
Published in: Proceedings of the Royal Society A, 2023, ISSN 1364-5021
Publisher: Royal Society of London
DOI: 10.1098/rspa.2022.0682

Generalized Gibbs Ensemble of the Ablowitz–Ladik Lattice, Circular β-Ensemble and Double Confluent Heun Equation

Author(s): Tamara Grava & Guido Mazzuca
Published in: Communications in Mathematical Physics, 2023, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-023-04642-8

Well posedness of the nonlinear Schrödinger equation with isolated singularities

Author(s): Claudio Cacciapuoti; Domenico Finco; Diego Noja
Published in: Journal of Differential Equations, 2021, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2021.10.017

Flat F-Manifolds, F-CohFTs, and Integrable Hierarchies

Author(s): Alessandro Arsie; Alexandr Buryak; Alexandr Buryak; Alexandr Buryak; Paolo Lorenzoni; Paolo Lorenzoni; Paolo Rossi
Published in: Communications in Mathematical Physics, 2021, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-021-04109-8

Numerical study of fractional Camassa–Holm equations

Author(s): Christian Klein; Goksu Oruc
Published in: Physica D, 2024, ISSN 0167-2789
Publisher: Elsevier BV
DOI: 10.1016/j.physd.2023.133979

Stable vector bundles on the families of curves

Author(s): Fedor Bogomolov, Elena Lukzen
Published in: European Journal of Mathematics, 2022, ISSN 2199-675X
Publisher: Springer Nature
DOI: 10.1007/s40879-021-00527-z

Isomonodromic Laplace transform with coalescing eigenvalues and confluence of Fuchsian singularities

Author(s): Davide Guzzetti
Published in: Letters in Mathematical Physics, 2021, ISSN 0377-9017
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11005-021-01423-z

Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics

Author(s): Alessandro Arsie; Alexandr Buryak; Alexandr Buryak; Alexandr Buryak; Paolo Lorenzoni; Paolo Lorenzoni; Paolo Rossi
Published in: International Mathematics Research Notices, 2021, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnab203

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