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Symmetry, integrability and geometry: methods and applications
Volume 17 (2021)
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With Wronskian through the Looking Glass
Vassily Gorbounov; Vadim Schechtman

A Fully Noncommutative Painlevé II Hierarchy: Lax Pair and Solutions Related to Fredholm Determinants
Sofia Tarricone

The Expansion of Wronskian Hermite Polynomials in the Hermite Basis
Codruţ Grosu; Corina Grosu

The Arithmetic Geometry of AdS$_2$ and its Continuum Limit
Minos Axenides; Emmanuel Floratos; Stam Nicolis

Quantum Groups for Restricted SOS Models
Giovanni Felder; Muze Ren

Poisson Principal Bundles
Shahn Majid; Liam Williams

Harmonic Analysis in $d$-Dimensional Superconformal Field Theory
Ilija Burić

Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures
Shinji Koshida

Double Lowering Operators on Polynomials
Paul Terwilliger

$C$-Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type
Su Ji Hong

Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry
Felipe Leitner

Topological $\mathrm{T}$-Duality for Twisted Tori
Paolo Aschieri; Richard J. Szabo

Curvature-Dimension Condition Meets Gromov's $n$-Volumic Scalar Curvature
Jialong Deng

The Subelliptic Heat Kernel of the Octonionic Anti-De Sitter Fibration
Fabrice Baudoin; Gunhee Cho

Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics
Andreas Vollmer

Exceptional Legendre Polynomials and Confluent Darboux Transformations
María Ángeles García-Ferrero; David Gómez-Ullate; Robert Milson

Convergence to the Product of the Standard Spheres and Eigenvalues of the Laplacian
Masayuki Aino

Quantum $\mathrm{K}$-Theory of Grassmannians and Non-Abelian Localization
Alexander Givental; Xiaohan Yan

Computing Regular Meromorphic Differential Forms via Saito's Logarithmic Residues
Shinichi Tajima; Katsusuke Nabeshima

A Spectral Triple for a Solenoid Based on the Sierpinski Gasket
Valeriano Aiello; Daniele Guido; Tommaso Isola

Parameter Permutation Symmetry in Particle Systems and Random Polymers
Leonid Petrov

The Differential Geometry of the Orbit Space of Extended Affine Jacobi Group $A_1$
Guilherme F. Almeida

A Classification of Twisted Austere $3$-Folds
Thomas A. Ivey; Spiro Karigiannis

Space Curves and Solitons of the KP Hierarchy. I. The $l$-th Generalized KdV Hierarchy
Yuji Kodama; Yuancheng Xie

Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model
Vladimir V. Bazhanov; Gleb A. Kotousov; Sergii M. Koval; Sergei L. Lukyanov

Mixed vs Stable Anti-Yetter–Drinfeld Contramodules
Ilya Shapiro

From Orthocomplementations to Locality
Pierre Clavier; Li Guo; Sylvie Paycha; Bin Zhang

Stringy Kähler Moduli for the Pfaffian–Grassmannian Correspondence
Will Donovan

Twisted Traces and Positive Forms on Quantized Kleinian Singularities of Type A
Pavel Etingof; Daniil Klyuev; Eric Rains; Douglas Stryker

Prescribed Riemannian Symmetries
Alexandru Chirvasitu

Representations of the Lie Superalgebra $\mathfrak{osp}(1|2n)$ with Polynomial Bases
Asmus K. Bisbo; Hendrik De Bie; Joris Van der Jeugt

An Introduction to Motivic Feynman Integrals
Claudia Rella

Invariants of Surfaces in Three-Dimensional Affine Geometry
Örn Arnaldsson; Francis Valiquette

Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities
Boris Botvinnik; Mark G. Walsh

Functional Relations on Anisotropic Potts Models: from Biggs Formula to the Tetrahedron Equation
Boris Bychkov; Anton Kazakov; Dmitry Talalaev

Interplay between Opers, Quantum Curves, WKB Analysis, and Higgs Bundles
Olivia Dumitrescu; Motohico Mulase

Sobolev Lifting over Invariants
Adam Parusiński; Armin Rainer

The Primitive Derivation and Discrete Integrals
Daisuke Suyama; Masahiko Yoshinaga

Degree-One Rational Cherednik Algebras for the Symmetric Group
Briana Foster-Greenwood; Cathy Kriloff

CFT Correlators for Cardy Bulk Fields via String-Net Models
Christoph Schweigert; Yang Yang

A Decomposition of Twisted Equivariant $K$-Theory
José Manuel Gómez; Johana Ramírez

Linear Independence of Generalized Poincaré Series for Anti-de Sitter $3$-Manifolds
Kazuki Kannaka

The Holonomy Groupoids of Singularly Foliated Bundles
Lachlan Ewen Macdonald

On the Abuaf–Ueda Flop via Non-Commutative Crepant Resolutions
Wahei Hara

How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave
Iryna Egorova; Johanna Michor

On Scalar and Ricci Curvatures
Gerard Besson; Sylvestre Gallot

Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations II: Conservation Laws
Benjamin B. Mcmillan

Double Box Motive
Spencer Bloch

Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations
Jean-Louis Clerc; Khalid Koufany

On $q$-Isomonodromic Deformations and $q$-Nekrasov Functions
Hajime Nagoya

Spectra of Compact Quotients of the Oscillator Group
Mathias Fischer; Ines Kath

Centralizers of Rank One in the First Weyl Algebra
Leonid Makar-Limanov

Gauss Hypergeometric Representations of the Ferrers Function of the Second Kind
Howard S. Cohl; Justin Park; Hans Volkmer

Nonsymmetric Macdonald Superpolynomials
Charles F. Dunkl

Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations
Yuki Hirano

From Heun Class Equations to Painlevé Equations
Jan Dereziński; Artur Ishkhanyan; Adam Latosiński

Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of $K_{{\rm i}\nu}(z)$ with Respect to Order
Yuri Krynytskyi; Andrij Rovenchak

Integrable $\mathcal{E}$-Models, $4\mathrm{d}$ Chern–Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
Sylvain Lacroix; Benoît Vicedo

Families of Gröbner Degenerations, Grassmannians and Universal Cluster Algebras
Lara Bossinger; Fatemeh Mohammadi; Alfredo Nájera Chávez

Linear $\mathbb{Z}_2^n$-Manifolds and Linear Actions
Andrew James Bruce; Eduardo Ibarguëngoytia; Norbert Poncin

Extrinsic Geometry and Linear Differential Equations
Boris Doubrov; Yoshinori Machida; Tohru Morimoto

Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants
Boris Botvinnik; Paolo Piazza; Jonathan Rosenberg

Completeness of SoV Representation for $\mathrm{SL}(2,\mathbb R)$ Spin Chains
Sergey É. Derkachov; Karol K. Kozlowski; Alexander N. Manashov

Generalized Gross–Neveu Universality Class with Non-Abelian Symmetry
John A. Gracey

New Techniques for Worldline Integration
James P. Edwards; C. Moctezuma Mata; Uwe Müller; Christian Schubert

Manin Matrices for Quadratic Algebras
Alexey Silantyev

A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves
Peter H. van der Kamp

Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
Takuro Mochizuki

Separation of Variables, Quasi-Trigonometric $r$-Matrices and Generalized Gaudin Models
Taras Skrypnyk

Singularities of Schubert Varieties within a Right Cell
Martina Lanini; Peter J. McNamara

$\mathbb{Z}_2^3$-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics
Shunya Doi; Naruhiko Aizawa

A Framework for Geometric Field Theories and their Classification in Dimension One
Matthias Ludewig; Augusto Stoffel

Locality and General Vacua in Quantum Field Theory
Daniele Colosi; Robert Oeckl

Non-Integrability of the Kepler and the Two-Body Problems on the Heisenberg Group
Tomasz Stachowiak; Andrzej J. Maciejewski

Resurgent Analysis of Ward–Schwinger–Dyson Equations
Marc P. Bellon; Enrico I. Russo

Quantum Representation of Affine Weyl Groups and Associated Quantum Curves
Sanefumi Moriyama; Yasuhiko Yamada

Second-Order Differential Operators in the Limit Circle Case
Dmitri R. Yafaev

Minimal Kinematics: An All $k$ and $n$ Peek into $\mathrm{Trop}^+\mathrm{G}(k,n)$
Freddy Cachazo; Nick Early

Triality for Homogeneous Polynomials
Laura P. Schaposnik; Sebastian Schulz

An Expansion Formula for Decorated Super-Teichmüller Spaces
Gregg Musiker; Nicholas Ovenhouse; Sylvester W. Zhang

Quantization of Calogero–Painlevé System and Multi-Particle Quantum Painlevé Equations II–VI
Fatane Mobasheramini; Marco Bertola

Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank $1$
Claus Hertling

Resolvent Trace Formula and Determinants of $n$ Laplacians on Orbifold Riemann Surfaces
Lee-Peng Teo

Exponential Formulas, Normal Ordering and the Weyl–Heisenberg Algebra
Stjepan Meljanac; Rina Štrajn

Perturbative and Geometric Analysis of the Quartic Kontsevich Model
Johannes Branahl; Alexander Hock; Raimar Wulkenhaar

Algebraic Structures on Typed Decorated Rooted Trees
Loïc Foissy

Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson–Schwinger Equations: $\phi^3$ QFT in $6$ Dimensions
Michael Borinsky; Gerald V. Dunne; Max Meynig

Lax Pair for a Novel Two-Dimensional Lattice
Maria N. Kuznetsova

Virasoro Action on the $Q$-Functions
Kazuya Aokage; Eriko Shinkawa; Hiro-Fumi Yamada

Spinors, Twistors and Classical Geometry
Nigel J. Hitchin

Negative Times of the Davey–Stewartson Integrable Hierarchy
Andrei K. Pogrebkov

Cluster Configuration Spaces of Finite Type
Nima Arkani-Hamed; Song He; Thomas Lam

A Revisit to the ABS $\mathrm{H2}$ Equation
Aye Aye Cho; Maebel Mesfun; Da-Jun Zhang

Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme
Johannes Thürigen

Real Liouvillian Extensions of Partial Differential Fields
Teresa Crespo; Zbigniew Hajto; Rouzbeh Mohseni

Generically, Arnold–Liouville Systems Cannot be Bi-Hamiltonian
Hassan Boualem; Robert Brouzet

Liouville Action for Harmonic Diffeomorphisms
Jinsung Park

Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities
Asena Çetinkaya; Dmitrii Karp; Elena Prilepkina

Quot Schemes for Kleinian Orbifolds
Alastair Craw; Søren Gammelgaard; Ádám Gyenge; Balázs Szendrői

$c_2$ Invariants of Hourglass Chains via Quadratic Denominator Reduction
Oliver Schnetz; Karen Yeats

The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes
Hadleigh Frost

Twistors, Self-Duality, and Spin${}^c$ Structures
Claude LeBrun

Invariant Differential Forms on Complexes of Graphs and Feynman Integrals
Francis Brown

Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters
Masoumeh Koohestani; Nobuaki Obata; Hajime Tanaka

A Sharp Lieb–Thirring Inequality for Functional Difference Operators
Ari Laptev; Lukas Schimmer

How to Draw a Correlation Function
Nikolay Bogolyubov; Cyril Malyshev

Clean Single-Valued Polylogarithms
Steven Charlton; Claude Duhr; Herbert Gangl

The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System
Dmitry K. Demskoi

Scalar Curvatures of Invariant Almost Hermitian Structures on Generalized Flag Manifolds
Lino Grama; Ailton R. Oliveira

A Composite Order Generalization of Modular Moonshine
Satoru Urano

Boundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties
Mikhail D. Minin; Andrei G. Pronko

Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots
Nikolai Kitanine; Giridhar Kulkarni

Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP$(2j)$ and Multi-Species IRW
Zhengye Zhou
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