Tootfinder

This https://arxiv.org/abs/2501.01817 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Distributed Framework Construction for Affine Formation Control
In affine formation control problems, the construction of the framework with universal rigidity and affine localizability is a critical prerequisite, but it has not yet been well addressed, especially when additional agents join the formation or link/agent failures emerge. Motivated by this observation, we investigate the problem of constructing affine frameworks in three scenarios, including vertex addition, edge deletion and vertex deletion. Our approach starts from the original affine format…

This https://arxiv.org/abs/2404.14096 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The coproduct for the affine Yangian and the parabolic induction for non-rectangular $W$-algebras
By using the coproduct and evaluation map for the affine Yangian and the Miura map for non-rectangular $W$-algebras, we construct a homomorphism from the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ to the universal enveloping algebra of a non-rectangular $W$-algebra of type $A$, which is an affine analogue of the one given in De Sole-Kac-Valeri. As a consequence, we find that the coproduct for the affine Yangian is compatible with some of the parabolic induction for non-rectangu…

Affine connections for Galilean and Carrollian structures: a unified perspective
Quentin Vigneron, Hamed Barzegar, James Read
https://arxiv.org/abs/2506.03936

Affine connections for Galilean and Carrollian structures: a unified perspective
We develop a classification of general Carrollian structures, permitting affine connections with both torsion and non-metricity. We compare with a recent classification of general Galilean structures in order to present a unified perspective on both. Moreover, we demonstrate how both sets of structures emerge from the most general possible Lorentzian structures in their respective limits, and we highlight the role of global hyperbolicity in constraining both structures. We then leverage this wo…

Diffeomorphic approximation of piecewise affine homeomorphisms
Daniel Campbell, Luigi D'Onofrio, Tom\'a\v{s} V\'itek
https://arxiv.org/abs/2507.02854

Diffeomorphic approximation of piecewise affine homeomorphisms
Given any $f$ a locally finitely piecewise affine homeomorphism of $Ω\subset \mathbb{R}^d$ onto $Δ\subset \mathbb{R}^d$ (for $d=3, 4$) such that $f\in W^{1,p}(Ω, \mathbb{R}^d)$ and $f^{-1}\in W^{1,q}(Δ, \mathbb{R}^d)$, $1\leq p ,q < \infty$ and any $ε>0$ we construct a diffeomorphism $\tilde{f}$ such that $$\|f-\tilde{f}\|_{W^{1,p}(Ω,\mathbb{R}^d)} + \|f^{-1}-\tilde{f}^{-1}\|_{W^{1,q}(Δ,\mathbb{R}^d)} < ε.$$

Induction for extended affine type A Soergel bimodules from a maximal parabolic
Marco Mackaay, Vanessa Miemietz, Pedro Vaz
https://arxiv.org/abs/2507.02347

Induction for extended affine type A Soergel bimodules from a maximal parabolic
In this paper we take a first step towards the categorification of the Zelevinsky tensor product of finite dimensional representations of extended affine type A Hecke algebras.

This https://arxiv.org/abs/2111.14384 has been replaced.
link: https://scholar.google.com/scholar?q=a

Zero cycles, Mennicke symbols and $\mathrm{K}_1$-stability of certain real affine algebras
Let $R$ be a reduced real affine algebra of (Krull) dimension $d \ge 2$ such that either $R$ has no real maximal ideals, or the intersection of all real maximal ideals in $R$ has height at least one. In this article, we prove the following: (1) the $d$-th Euler class group $\text{E}^d(R)$, defined by Bhatwadekar-R.~Sridharan, is canonically isomorphic to the Levine-Weibel Chow group of zero cycles $\text{CH}_0(\text{Spec}(R))$; (2) the universal Mennicke symbol $\text{MS}_{d+1}(R)$ is canonical…

This https://arxiv.org/abs/2501.16263 has been replaced.
link: https://scholar.google.com/scholar?q=a

Rotation number and dynamics of 3-interval piecewise $λ$-affine contractions
We consider a family of piecewise contractions admitting a rotation number and defined for every $x\in[0,1)$ by $f(x)=λx + δ+ d θ_a(x) \pmod 1$, where $λ\in(0,1)$, $d\in(0,1-λ)$, $δ\in[0,1]$, $a\in[0,1]$ and $θ_a(x)=1$ if $x\geq a$ and $θ_a(x)=0$ otherwise. In the special case where $a=1$, the family reduces to the well studied ``contracted rotations" $x\mapsto λx + δ\pmod 1$, which are 2-interval piecewise $λ$-affine contractions when $δ\in(1-λ,1)$. Considering $a\in(0,1)$ allows …

Code-based $[3,1]$-avoiders in finite affine spaces $\mathrm{AG}(n,2)$
Benedek Kov\'acs
https://arxiv.org/abs/2505.24072 https://…

Code-based $[3,1]$-avoiders in finite affine spaces $\mathrm{AG}(n,2)$
The author, together with Nagy, studied the following problem on unavoidable intersections of given size in binary affine spaces. Given an $m$-element set $S\subseteq \mathbb{F}_2^n$, is there guaranteed to be a $[k,t]$-flat, that is, a $k$-dimensional affine subspace of $\mathbb{F}_2^n$ containing exactly $t$ points of $S$? Such problems can be viewed as generalizations of the cap set problem over the binary field. They conjectured that for every fixed pair $(k,t)$ with $k\ge 1$ and $0\le t\le…

EL-AGHF: Extended Lagrangian Affine Geometric Heat Flow
Sangmin Kim, Hae-Won Park
https://arxiv.org/abs/2505.24751 https://arxiv.org/…

EL-AGHF: Extended Lagrangian Affine Geometric Heat Flow
We propose a constrained Affine Geometric Heat Flow (AGHF) method that evolves so as to suppress the dynamics gaps associated with inadmissible control directions. AGHF provides a unified framework applicable to a wide range of motion planning problems, including both holonomic and non-holonomic systems. However, to generate admissible trajectories, it requires assigning infinite penalties to inadmissible control directions. This design choice, while theoretically valid, often leads to high com…

Rigid affine cones over singular del Pezzo surfaces
In-Kyun Kim, Jaehyun Kim, Joonyeong Won
https://arxiv.org/abs/2506.01310 https://…

Rigid affine cones over singular del Pezzo surfaces
We completely determine the existence of anticanonical polar cylinders in quasi-smooth log del Pezzo surfaces of index one.

A 10-bit S-box generated by Feistel construction from cellular automata
Thomas Pr\'evost (I3S), Bruno Martin (I3S)
https://arxiv.org/abs/2507.02489 htt…

A 10-bit S-box generated by Feistel construction from cellular automata
We propose a new 10-bit S-box generated from a Feistel construction. The subpermutations are generated by a 5-cell cellular automaton based on a unique well-chosen rule and bijective affine transformations. In particular, the cellular automaton rule is chosen based on empirical tests of its ability to generate good pseudorandom output on a ring cellular automaton. Similarly, Feistel's network layout is based on empirical data regarding the quality of the output S-box. We perform cryptanalysis o…

Monodromy groups and exceptional Hodge classes, II: Sato-Tate groups
Andrea Gallese, Heidi Goodson, Davide Lombardo
https://arxiv.org/abs/2507.02535 https:…

Monodromy groups and exceptional Hodge classes, II: Sato-Tate groups
Denote by $J_m$ the Jacobian variety of the hyperelliptic curve defined by the affine equation $y^2=x^m+1$ over $\mathbb{Q}$, where $m \geq 3$ is a fixed positive integer. In this paper, we compute the Sato-Tate group of $J_m$. Currently, there is no general algorithm that computes this invariant. We also describe the Sato-Tate group of an abelian variety, generalizing existing results that apply only to non-degenerate varieties, and prove an extension of a well-known formula of Gross-Koblitz t…

Choi-Wang inequality for affine connections
Yasuaki Fujitani
https://arxiv.org/abs/2507.00385 https://arxiv.org/pdf/2507.00385…

Choi-Wang inequality for affine connections
Choi-Wang established a lower bound for the first eigenvalue of the Laplacian on minimal hypersurfaces in manifolds with positive Ricci curvature. We extend this Choi-Wang type inequality to the setting of positive Ricci curvature with respect to the Li-Xia type affine connection.

This https://arxiv.org/abs/2505.11605 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On representations of quantum affine $\mathfrak{sl}_2$
We study tensor products of two-dimensional evaluation $U_q\widehat{\mathfrak{sl}}_2$-modules at generic values of $q$, $U_q\widehat{\mathfrak{sl}}_2$ homomorphisms between them, and closely related subjects.

This https://arxiv.org/abs/2209.14273 has been replaced.
link: https://scholar.google.com/scholar?q=a

Derived equivalences for trigonometric double affine Hecke algebras
The trigonometric double affine Hecke algebra $\mathbf{H}_c$ for an irreducible root system depends on a family of complex parameters $c$ Given two families of parameters $c$ and $c'$ which differ by integers, we construct the translation functor from $\mathbf{H}_{c}\operatorname{-Mod}$ to $\mathbf{H}_{c'}\operatorname{-Mod}$ and prove that it induces equivalence of derived categories. This is a trigonometric counterpart of a theorem of Losev on the derived equivalences for rational Cherednik a…

On Obtaining New MUBs by Finding Points on Complete Intersection Varieties over $\mathbb{R}$
Arindam Banerjee, Kanoy Kumar Das, Ajeet Kumar, Rakesh Kumar, Subhamoy Maitra
https://arxiv.org/abs/2507.02492

On Obtaining New MUBs by Finding Points on Complete Intersection Varieties over $\mathbb{R}$
Mutually Unbiased Bases (MUBs) are closely connected with quantum physics, and the structure has a rich mathematical background. We provide equivalent criteria for extending a set of MUBs for $C^n$ by studying real points of a certain affine algebraic variety. This variety comes from the relations that determine the extendability of a system of MUBs. Finally, we show that some part of this variety gives rise to complete intersection domains. Further, we show that there is a one-to-one correspon…

Digitaltag 2025: resilient, demokratisch, Teilhabe-orientiert
Der Digitaltag wirbt für eine digital-affine und resiliente Gesellschaft. Die destruktiven Seiten des Internets sollen bekämpft, die guten gefördert werden.

Affine-Invariant Global Non-Asymptotic Convergence Analysis of BFGS under Self-Concordance
Qiujiang Jin, Aryan Mokhtari
https://arxiv.org/abs/2507.00361 ht…

Affine-Invariant Global Non-Asymptotic Convergence Analysis of BFGS under Self-Concordance
In this paper, we establish global non-asymptotic convergence guarantees for the BFGS quasi-Newton method without requiring strong convexity or the Lipschitz continuity of the gradient or Hessian. Instead, we consider the setting where the objective function is strictly convex and strongly self-concordant. For an arbitrary initial point and any arbitrary positive-definite initial Hessian approximation, we prove global linear and superlinear convergence guarantees for BFGS when the step size is …

This https://arxiv.org/abs/2304.07859 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Affine Isoperimetric Inequalities for Higher-Order Projection and Centroid Bodies
In 1970, Schneider introduced the $m$th order difference body of a convex body, and also established the $m$th-order Rogers-Shephard inequality. In this paper, we extend this idea to the projection body, centroid body, and radial mean bodies, as well as prove the associated inequalities (analogues of Zhang's projection inequality, Petty's projection inequality, the Busemann-Petty centroid inequality and Busemann's random simplex inequality). We also establish a new proof of Schneider's $m$th-or…

The Generalized Dirac Equation in the Metric Affine Spacetime
Muzaffer Adak, Ali Bagci, Caglar Pala, Ozcan Sert
https://arxiv.org/abs/2506.23609 https://…

The Generalized Dirac Equation in the Metric Affine Spacetime
We discuss the most general form of Dirac equation in the non$-$Riemannian spacetimes containing curvature, torsion and non$-$metricity. It includes all bases of the Clifford algebra $cl(1,3)$ within the spinor connection. We adopt two approaches. First, the generalized Dirac equation is directly formulated by applying the minimal coupling prescription to the original Dirac equation. It is referred to as the {\it direct Dirac equation} for seek of clarity and to preserve the tractability. Secon…

Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions
Hank Chen, Joaquin Liniado
https://arxiv.org/abs/2507.01858 https://

Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions
We introduce a three-dimensional quantum field theory with an infinite-dimensional symmetry, realized explicitly through a centrally extended affine graded Lie algebra. This symmetry is a direct three-dimensional generalization of the chiral symmetry in the Wess-Zumino-Witten model. Accordingly, this setup provides a framework for extending the methods of two-dimensional conformal field theory to three dimensions, and we expect it to lay the groundwork for exact methods in three-dimensional qua…

Non-archimedean periods for log Calabi-Yau surfaces
Soham Karwa, Jonathan Lai
https://arxiv.org/abs/2506.01651 https://arxiv.org/pdf/…

Non-archimedean periods for log Calabi-Yau surfaces
We prove the first instance of a conjecture by Kontsevich-Soibelman that the non-archimedean period map recovers the analytic periods in the case of log Calabi-Yau surfaces. In particular, we show that the K-affine structure, a natural enhancement of the singular integral affine structure on the essential skeleton, determines the isomorphism type of the log Calabi-Yau surface.

Insights in $f(Q)$ cosmology: the relevance of the connection
Ismael Ayuso, Mariam Bouhmadi-L\'opez, Che-Yu Chen, Xiao Yan Chew, Konstantinos Dialektopoulos, Yen Chin Ong
https://arxiv.org/abs/2506.03506

Insights in $f(Q)$ cosmology: the relevance of the connection
We explore the role of the affine connection in $f(Q)$ gravity, a modified theory where gravity is governed by non-metricity within the symmetric teleparallel framework. Although the connection is constrained to be flat and torsionless, it is not uniquely determined by the metric, allowing for multiple physically distinct formulations. We analyze three such connections compatible with a homogeneous and isotropic universe to show that they yield markedly different cosmological dynamics, even und…

Affinization of algebraic structures: Leibniz algebras
Tomasz Brzezi\'nski, Krzysztof Radziszewski, Brais Ramos P\'erez
https://arxiv.org/abs/2506.23398

Affinization of algebraic structures: Leibniz algebras
A general procedure of affinization of linear algebra structures is illustrated by the case of Leibniz algebras. Specifically, the definition of an affine Leibniz bracket, that is, a bi-affine operation on an affine space that at each tangent vector space becomes a (bi-linear) Leibniz bracket in terms of a tri-affine operation called a Leibnizian, is given. An affine space together with such an operation is called a Leibniz affgebra. It is shown that any Leibniz algebra can be extended to a fam…

Conjugator length of locally compact groups of Euclidean isometries
Yuri Santos Rego, Petra Schwer
https://arxiv.org/abs/2507.01268 https://

Conjugator length of locally compact groups of Euclidean isometries
We consider locally compact subgroups $H$ of the full isometry group $\mathrm{Isom}(\mathbb{E}^n)$ of Euclidean $n$-space which respect the splitting into an orthogonal and a translation subgroup. We prove that the conjugator length function of such groups grows linearly. Our theorem applies, in particular, to the Lie group $\mathrm{Isom}(\mathbb{E}^n)$ itself but also to affine Coxeter groups and to split crystallographic groups.

Substructural Abstract Syntax with Variable Binding and Single-Variable Substitution
Marcelo Fiore, Sanjiv Ranchod
https://arxiv.org/abs/2505.24812 https:/…

Substructural Abstract Syntax with Variable Binding and Single-Variable Substitution
We develop a unified categorical theory of substructural abstract syntax with variable binding and single-variable (capture-avoiding) substitution. This is done for the gamut of context structural rules given by exchange (linear theory) with weakening (affine theory) or with contraction (relevant theory) and with both (cartesian theory). Specifically, in all four scenarios, we uniformly: define abstract syntax with variable binding as free algebras for binding-signature endofunctors over variab…

Non-affine Families of 8 x 8 Complex Hadamard Matrices
Tuomo Valtonen
https://arxiv.org/abs/2505.22947 https://arxiv.org/pdf/2505.229…

Non-affine Families of 8 x 8 Complex Hadamard Matrices
Six non-affine 3-parameter families of complex Hadamard matrices of order 8 are presented. These families contain Hadamard matrices that are not equivalent to any previously known Hadamard matrices in the literature. Each family arises from unimodular points of an affine variety defined by palindromic polynomials. The families are given as an image of a function that solves the corresponding system of polynomials on a domain that guarantees unimodularity of the solutions

This https://arxiv.org/abs/2410.23052 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the Tambara Affine Line
Tambara functors are the analogue of commutative rings in equivariant algebra. Nakaoka defined ideals in Tambara functors, leading to the definition of the Nakaoka spectrum of prime ideals in a Tambara functor. In this work, we continue the study of the Nakoaka spectra of Tambara functors. We describe, in terms of the Zariski spectra of ordinary commutative rings, the Nakaoka spectra of many Tambara functors. In particular: we identify the Nakaoka spectrum of the fixed point Tambara functor of …

Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- Definable Lipschitz selections for affine-set valued maps
Adam Parusi\'nski, Armin Rainer

Prym varieties and projective structures on Riemann surfaces
Indranil Biswas, Alessandro Ghigi, Luca Vai
https://arxiv.org/abs/2506.02871 https://

Prym varieties and projective structures on Riemann surfaces
Given an étale double covering $π\, :\, \widetilde{C}\, \longrightarrow\, C$ of compact Riemannsurfaces with $C$ of genus at least two, we use the Prym variety of the cover to construct canonical projective structures on both $\widetilde C$ and $C$. This construction can be interpreted as a section of an affine bundle over the moduli space of étale double covers. The $\overline{\partial}$--derivative of this section is a (1,1)--form on the moduli space. We compute this derivative in terms of…

Replaced article(s) found for math.FA. https://arxiv.org/list/math.FA/new
[1/1]:
- Affine Gateaux Differentials and the von Mises Statistical Calculus
Simone Cerreia-Vioglio, Fabio Maccheroni, Massimo Marinacci, Luigi Montrucchio, Lorenzo Stanca

This https://arxiv.org/abs/2403.16434 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The classification of complete improper affine spheres with singularities of low total curvature and new examples
We provide a classification of complete improper affine spheres with singularities (say \emph{improper affine fronts}) in unimodular affine three-space $\boldsymbol{R}^3$ whose total curvature is greater than or equal to $-6π$, and a partial classification in the case of total curvature $-8π$. For the case of total curvature $-8π$, we give a complete classification for genus $0$ case and show the existence of an example and a one parameter family with genus $1$. We also study the asymptotic …

$(d,\sigma)$-twisted Affine-Virasoro superalgebras
Rencai L\"u, Xizhou You, Kaiming Zhao
https://arxiv.org/abs/2507.00349 https://

$(d,σ)$-twisted Affine-Virasoro superalgebras
For any finite dimensional Lie superalgebra $\dot{\mathfrak{g}}$ (maybe a Lie algebra) with an even derivation $d$ and a finite order automorphism $σ$ that commutes with $d$, we introduce the $(d,σ)$-twisted Affine-Virasoro superalgebra $\mathfrak{L}=\mathfrak{L}(\dot{\mathfrak{g}},d,σ)$ and determine its universal central extension $\hat{\mathfrak{L}}=\hat{\mathfrak{L}}(\dot{\mathfrak{g}},d,σ)$. This is a huge class of infinite-dimensional Lie superalgebras. Such Lie superalgebras consist …

A Compact 16-bit S-box over Tower Field $\F_{(((2^2)^2)^2)^2}$ with High Security
Bahram Rashidi, Behrooz Khadem
https://arxiv.org/abs/2507.01423 https://

A Compact 16-bit S-box over Tower Field $\F_{(((2^2)^2)^2)^2}$ with High Security
This paper introduces a compact and secure 16-bit substitution box (S-box) designed over the composite field $\F_{(((2^2)^2)^2)^2}$, optimized for both hardware efficiency and cryptographic robustness. The proposed S-box decomposes operations into subfields, leveraging a tower field architecture. This enables significant hardware reduction through optimized field inversion and a low-cost affine transformation. Security evaluations confirm resilience against linear, differential, algebraic and D…

Classifying soft elastic lattices using higher-order homogenization
Basile Audoly, Claire Lestringant, Hussein Nassar
https://arxiv.org/abs/2507.00630 http…

Classifying soft elastic lattices using higher-order homogenization
We propose a methodology for the homogenization of periodic elastic lattices that covers the case of unstable lattices, having affine (macroscopic) or periodic (microscopic) mechanisms. The singular cell problems that are encountered when a periodic mechanism is present are naturally solved by treating the amplitude $θ(X)$ of the mechanism as an enrichment variable. We use asymptotic second-order homogenization to derive an effective energy capturing both the strain-gradient effect $\nabla \va…

Low-Complexity Receiver Design for Affine Filter Bank Modulation
Kuranage Roche Rayan Ranasinghe, Bruno S. Chang, Giuseppe Thadeu Freitas de Abreu
https://arxiv.org/abs/2506.17010

Low-Complexity Receiver Design for Affine Filter Bank Modulation
We propose a low-complexity receiver structure for the recently introduced Affine Filter Bank Modulation (AFBM) scheme, which is a novel waveform designed for integrated sensing and communications (ISAC) systems operating in doubly-dispersive (DD) channels. The proposed receiver structure is based on the Gaussian Belief Propagation (GaBP) framework, making use of only element-wise scalar operations to perform detection of the transmitted symbols. Simulation results demonstrate that AFBM in conj…

Some inequalities of isoperimetric type for the c-affine surface area
Shiri Artstein-Avidan, Arnon Chor
https://arxiv.org/abs/2505.19172 https://

Some inequalities of isoperimetric type for the c-affine surface area
We study the c-affine surface area $Ω^c$, recently introduced by Schütt, Werner and Yalikun. We show that on the class of ball-bodies, $Ω^c$ is maximized by a ball of radius $\frac{n}{n+1}$, and that a Santaló-type inequality holds: $Ω^c(K) Ω^c(K^c) \leq Ω^c(\frac{1}{2} B_2^n)^2$.

Lefschetz morphisms on singular cohomology and local cohomological dimension of toric varieties
Hyunsuk Kim, Sridhar Venkatesh
https://arxiv.org/abs/2506.03026

Lefschetz morphisms on singular cohomology and local cohomological dimension of toric varieties
Given a proper toric variety and a line bundle on it, we describe the morphism on singular cohomology given by the cup product with the Chern class of that line bundle in terms of the data of the associated fan. Using that, we relate the local cohomological dimension of an affine toric variety with the Lefschetz morphism on the singular cohomology of a projective toric variety of one dimension lower. As a corollary, we show that the local cohomological defect is not a combinatorial invariant. W…

Robust Aperiodic Sampled-Data Washout Control for Uncertain Affine Systems
Folco Giorgetti, Francesco Crocetti, Mario Luca Fravolini, Francesco Ferrante
https://arxiv.org/abs/2505.23534

Robust Aperiodic Sampled-Data Washout Control for Uncertain Affine Systems
In this paper, we address the problem of designing an aperiodic sampled-data controller stabilizing the zero-input equilibrium of an uncertain affine plant. The closed-loop system is modeled as a hybrid dynamical system incorporating a timer triggering the occurrence of the sampling events and two memory states storing the value of the controller state and controller output at each sampling time. Necessary and sufficient conditions on the controller parameters are given to establish the sought …

Generic graded contractions of Lie algebras
Mikhail V. Kochetov, Serhii D. Koval
https://arxiv.org/abs/2506.00610 https://arxiv.org/p…

Generic graded contractions of Lie algebras
We study generic graded contractions of Lie algebras from the perspectives of group cohomology, affine algebraic geometry and monoidal categories. We show that generic graded contractions with a fixed support are classified by a certain abelian group, which we explicitly describe. Analyzing the variety of generic graded contractions as an affine algebraic variety allows us to describe which generic graded contractions define graded degenerations of a given graded Lie algebra. Using the interpre…

On Generalised Danielewski Surfaces over fields of arbitrary characteristic
Debojyoti Saha
https://arxiv.org/abs/2506.01457 https://a…

On Generalised Danielewski Surfaces over fields of arbitrary characteristic
In this paper we study exponential maps ($\mathbb{G}_a$-actions) on the family of affine two dimensional surfaces of the form $f(x)y=ϕ(x,z)$ over arbitrary fields, describe the Makar-Limanov invariant and Derksen invariant of these surfaces, give a complete characterization of isomorphisms between such surfaces and display a subfamily which provides counterexamples to the cancellation problem.

Group schemes and their Lie algebras over a symmetric tensor category
Dave Benson, Julia Pevtsova
https://arxiv.org/abs/2507.02031 https://

Group schemes and their Lie algebras over a symmetric tensor category
We investigate the theory of affine group schemes over a symmetric tensor category, with particular attention to the tangent space at the identity. We show that this carries the structure of a restricted Lie algebra, and can be viewed as the degree one distributions on the group scheme, or as the right invariant derivations on the coordinate ring. In the second half of the paper, we illustrate the theory in the particular case of the symmetric tensor category $\mathsf{Ver}_4^+$ in characteristi…

Dimension of Besicovitch-Eggleston sets for non-autonomous systems with countable symbolic dynamics
Jonny Imbierski, Charlene Kalle
https://arxiv.org/abs/2506.01803

Dimension of Besicovitch-Eggleston sets for non-autonomous systems with countable symbolic dynamics
In this article we derive a formula for the Hausdorff dimension of Besicovitch-Eggleston level sets associated with non-autonomous dynamics constructed from families of countable affine iterated function systems. The formula obtained shows that the universal-lower-bound phenomenon present in the autonomous case studied by Fan et al. (2010) persists in this non-autonomous setting.

Affine invariant interacting Langevin dynamics in Markov chain importance sampling for rare event estimation
Jason Beh, J\'er\^ome Morio, Florian Simatos, Simon Weissmann
https://arxiv.org/abs/2506.20185

Affine invariant interacting Langevin dynamics in Markov chain importance sampling for rare event estimation
This work considers the framework of Markov chain importance sampling~(MCIS), in which one employs a Markov chain Monte Carlo~(MCMC) scheme to sample particles approaching the optimal distribution for importance sampling, prior to estimating the quantity of interest through importance sampling. In rare event estimation, the optimal distribution admits a non-differentiable log-density, thus gradient-based MCMC can only target a smooth approximation of the optimal density. We propose a new gradie…

Pure Gaps at Many Places and Multi-point AG Codes from Arbitrary Kummer Extensions
Huachao Zhang, Chang-An Zhao
https://arxiv.org/abs/2505.23274 https://…

Pure Gaps at Many Places and Multi-point AG Codes from Arbitrary Kummer Extensions
For a Kummer extension defined by the affine equation $y^{m}=\prod_{i=1}^{r} (x-\a_i)^{λ_i}$ over an algebraic extension $K$ of a finite field $\fq$, where $\la_i\in \Z\backslash\{0\}$ for $1\leq i\leq r$, $\gcd(m,q) = 1$, and $\a_1,\cdots,\a_r\in K$ are pairwise distinct elements, we propose a simple and efficient method to find all pure gaps at many totally ramified places. We introduce a bottom set of pure gaps and indicate that the set of pure gaps is completely determined by the bot…

Neural Network-based Universal Formulas for Control
Pol Mestres, Jorge Cort\'es, Eduardo D. Sontag
https://arxiv.org/abs/2505.24744 https://

Neural Network-based Universal Formulas for Control
We study the problem of designing a controller that satisfies an arbitrary number of affine inequalities at every point in the state space. This is motivated by the use of guardrails in autonomous systems. Indeed, a variety of key control objectives, such as stability, safety, and input saturation, are guaranteed by closed-loop systems whose controllers satisfy such inequalities. Many works in the literature design such controllers as the solution to a state-dependent quadratic program (QP) who…

Chevalley property and discriminant ideals of Cayley-Hamilton Hopf Algebras
Yimin Huang, Zhongkai Mi, Tiancheng Qi, Quanshui Wu
https://arxiv.org/abs/2506.21879

Chevalley property and discriminant ideals of Cayley-Hamilton Hopf Algebras
For any affine Hopf algebra $H$ which admits a large central Hopf subalgebra, $H$ can be endowed with a Cayley-Hamilton Hopf algebra structure in the sense of De Concini-Procesi-Reshetikhin-Rosso. The category of finite-dimensional modules over any fiber algebra of $H$ is proved to be an indecomposable exact module category over the tensor category of finite-dimensional modules over the identity fiber algebra $H/\mathfrak{m}_{\overline{\varepsilon}}H$ of $H$. For any affine Cayley-Hamilton Hopf…

A proof of the Fields Conjectures
Satoshi Murai, Brendon Rhoades, Andy Wilson
https://arxiv.org/abs/2505.24027 https://arxiv.org/pdf/…

A proof of the Fields Conjectures
The {\em superspace ring} of rank $n$ is the algebra $Ω_n$ of differential forms on affine $n$-space. The algebra $Ω_n$ is bigraded with respect to polynomial and exterior degree and carries a natural action of the symmetric group $\mathfrak{S}_n$. Modding out by $\mathfrak{S}_n$-invariants with vanishing constant term yields the {\em superspace coinvariant ring} $SR_n$. We prove that, as an ungraded $\mathfrak{S}_n$-module, the space $SR_n$ is isomorphic to the sign-twisted permutation actio…

CHIP: Chameleon Hash-based Irreversible Passport for Robust Deep Model Ownership Verification and Active Usage Control
Chaohui Xu, Qi Cui, Chip-Hong Chang
https://arxiv.org/abs/2505.24536

CHIP: Chameleon Hash-based Irreversible Passport for Robust Deep Model Ownership Verification and Active Usage Control
The pervasion of large-scale Deep Neural Networks (DNNs) and their enormous training costs make their intellectual property (IP) protection of paramount importance. Recently introduced passport-based methods attempt to steer DNN watermarking towards strengthening ownership verification against ambiguity attacks by modulating the affine parameters of normalization layers. Unfortunately, neither watermarking nor passport-based methods provide a holistic protection with robust ownership proof, hig…

Global Convergence of Iteratively Reweighted Least Squares for Robust Subspace Recovery
Gilad Lerman, Kang Li, Tyler Maunu, Teng Zhang
https://arxiv.org/abs/2506.20533

Global Convergence of Iteratively Reweighted Least Squares for Robust Subspace Recovery
Robust subspace estimation is fundamental to many machine learning and data analysis tasks. Iteratively Reweighted Least Squares (IRLS) is an elegant and empirically effective approach to this problem, yet its theoretical properties remain poorly understood. This paper establishes that, under deterministic conditions, a variant of IRLS with dynamic smoothing regularization converges linearly to the underlying subspace from any initialization. We extend these guarantees to affine subspace estima…

Quasi-isometric embeddings of Ramanujan complexes
Hyein Choi
https://arxiv.org/abs/2506.23585 https://arxiv.org/pdf/2506.23585…

Quasi-isometric embeddings of Ramanujan complexes
Ramanujan complexes were defined as high dimensional analogues of the optimal expanders, Ramanujan graphs. They were constructed as quotients of the Euclidean building (also called the affine building and the Bruhat-Tits building) of $\mathrm{PGL}_d(\mathbb{F}_p((y)))$ for any prime $p$ by Lubotzky-Samuels-Vishne. We distinguish the Ramanujan complexes up to large-scale geometry. More precisely, we show that if $p$ and $q$ are distinct primes, then the associated Ramanujan complexes do not quas…

Affine Deformations of Divisible Convex Cones and Affine Spacetimes
Antoine Ablondi
https://arxiv.org/abs/2506.12172 https://arxiv.or…

Affine Deformations of Divisible Convex Cones and Affine Spacetimes
Given a subgroup of $\mathrm{SL}(\mathbb{R}^{d+1})\ltimes\mathbb{R}^{d+1}$ obtained by adding a translation part to a torsion-free discrete subgroup of $\mathrm{SL}(\mathbb{R}^{d+1})$ dividing a convex domain in the sense of Benoist, we construct two maximal convex domains on which the affine action of that subgroup is free and properly continuous. We also introduce a notion of "affine spacetime" structure, with which quotients of those domains are naturally endowed. In that setting, we show th…

Paradoxical decompositions of finite-dimensional non-Archimedean normed spaces
Kamil Orzechowski
https://arxiv.org/abs/2506.01528 https://

Paradoxical decompositions of finite-dimensional non-Archimedean normed spaces
We show that any normed space $(K^n,\|\cdot\|)$, $n\ge 2$, over a field $K$ equipped with a nontrivial non-Archimedean valuation admits a paradoxical decomposition using four pieces with respect to the group of its affine isometries, provided that the norm $\|\cdot\|$ is equivalent to the maximum norm. It follows that any finite-dimensional normed space $(X,\|\cdot\|)$ with $\dim{X}\ge 2$ over a complete non-Archimedean nontrivially valued field $(K,|\cdot&#…

This https://arxiv.org/abs/2407.17366 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Automorphisms of the DAHA of type $\check{C_1}C_1$ and non-symmetric Askey-Wilson functions
In this paper we consider the automorphisms of the double affine Hecke algebra (DAHA) of type $\check{C_1}C_1$ which have a relatively simple action on the generators and on the parameters, notably a symmetry $t_4$ which sends the Askey-Wilson parameters $(a,b,c,d)$ to $(a,b,qd^{-1},qc^{-1})$. We study how these symmetries act on the basic representation and on the symmetric and non-symmetric Askey-Wilson (AW) polynomials and functions. Interestingly $t_4$ maps AW polynomials to functions. We t…

Controller Design for Bilinear Neural Feedback Loops
Dhruv Shah, Jorge Cort\'es
https://arxiv.org/abs/2505.24106 https://arxiv.or…

Controller Design for Bilinear Neural Feedback Loops
This paper considers a class of bilinear systems with a neural network in the loop. These arise naturally when employing machine learning techniques to approximate general, non-affine in the input, control systems. We propose a controller design framework that combines linear fractional representations and tools from linear parameter varying control to guarantee local exponential stability of a desired equilibrium. The controller is obtained from the solution of linear matrix inequalities, whic…

New presentation of the twisted Yangian of type $D$
Shuichi Harako, Mamoru Ueda
https://arxiv.org/abs/2507.00350 https://arxiv.org/pd…

New presentation of the twisted Yangian of type $D$
We construct a new presentation of the twisted Yangian of type $D$ with a finite number of generators. By using this presentation, we propose a new definition of the twisted affine Yangian of type $D$.

On the Unimodular Isomorphism Problem of Convex Lattice Polytopes
Qiuyue Liu, Zhanyuan Cai
https://arxiv.org/abs/2506.23846 https://a…

On the Unimodular Isomorphism Problem of Convex Lattice Polytopes
This paper studies the \emph{unimodular isomorphism problem} (UIP) of convex lattice polytopes: given two convex lattice polytopes $P$ and $P'$, decide whether there exists a unimodular affine transformation mapping $P$ to $P'$. We show that UIP is graph isomorphism hard, while the polytope congruence problem and the combinatorial polytope isomorphism problem (Akutsu, 1998; Kaibel, Schwartz, 2003) were shown to be graph isomorphism complete, and both the lattice isomorphism problem ( $\mathrm{S…

Replaced article(s) found for cs.CV. https://arxiv.org/list/cs.CV/new
[3/3]:
Niagara: Normal-Integrated Geometric Affine Field for Scene Reconstruction from a Single View

Affine semigroups without consecutive small elements
J. C. Rosales, R. Tapia-Ramos, A. Vigneron-Tenorio
https://arxiv.org/abs/2506.17152 https://

Affine semigroups without consecutive small elements
An $\mathcal{A}$-semigroup is a numerical semigroup without consecutive small elements. This work generalizes this concept to finite-complement submonoids of an affine cone $\mathcal{C}$. We develop algorithmic procedures to compute all $\mathcal{A}$-semigroups with a given Frobenius element (denoted by $\mathcal{A}(f)$), and with fixed Frobenius element and multiplicity. Moreover, we analyze the $\mathcal{A}(f)$-systems of generators. Furthermore, we study $\mathcal{A}$-numerical semigroups wi…

Replaced article(s) found for cs.NE. https://arxiv.org/list/cs.NE/new
[1/1]:
- Stable Learning Using Spiking Neural Networks Equipped With Affine Encoders and Decoders
A. Martina Neuman, Dominik Dold, Philipp Christian Petersen

A new addition to the zoo of isolated symplectic singularities
Callum Berry
https://arxiv.org/abs/2505.24524 https://arxiv.org/pdf/25…

A new addition to the zoo of isolated symplectic singularities
We give details of a new isolated symplectic singularity found in an affine chart in a crepant partial resolution of $\mathbb{C}^4/G_5$, which is 4-dimensional, isolated, and locally simply-connected. We distinguish the new singularity among all known such by the fact that the projective tangent cone at the singularity is non-reduced. We also find all 12 of its $\mathbb{Q}$-factorial terminalisations, in the process finding 24 for the quotient singularity $\mathbb{C}^4/G_5$.

Some Characteristics of Almost $\omega$-Bach Solitons
Paritosh Ghosh, Hemangi Madhusudan Shah, Arindam Bhattacharyya
https://arxiv.org/abs/2505.24316 https…

Some Characteristics of Almost $ω$-Bach Solitons
In this article, we introduce $ω$-Bach tensor corresponding to one form $ω$ and correspondingly introduce almost $ω$-Bach solitons, thereby generalizing the existing notion of Bach tensor and almost Bach solitons. We characterize almost $ω$-Bach solitons, when the potential vector field of the soliton generates an infinitesimal harmonic transformation or is an affine conformal vector field, or is a projective vector field or is a Killing vector field, when the $ω$-Bach tensor is divergence…

Shuffle algebras, lattice paths and quantum toroidal $\mathfrak{gl}_{n|m}$
Alexandr Garbali, Andrei Negu\c{t}
https://arxiv.org/abs/2507.00538 https://

Shuffle algebras, lattice paths and quantum toroidal $\mathfrak{gl}_{n|m}$
We describe and compute various families of commuting elements of the matrix shuffle algebra of type $\mathfrak{gl}_{n|m}$, which is expected to be isomorphic to quantum toroidal $\mathfrak{gl}_{n|m}$. Our formulas are given in terms of partial traces of products of $R$-matrices of the quantum affine algebra $U_t(\dot{\mathfrak{gl}}_{n|m})$, and have a lattice path interpretation. Our calculations are based on the machinery of the quantum toroidal algebras and a new anti-homomorp…

On flexibility of trinomial varieties
Mikhail Ignatev, Timofey Vilkin
https://arxiv.org/abs/2506.20524 https://arxiv.org/pdf/2506.205…

On flexibility of trinomial varieties
Trinomial varieties are affine varieties given by a system of equations consisting of polynomials with three terms. Such varieties are total coordinate spaces of normal varieties with torus action of complexity one. For an affine variety $X$ we consider the subgroup $\mathrm{SAut}(X)$ of the automorphism group generated by all algebraic subgroups isomorphic to the additive group of the ground field. By definition, an affine variety is flexible if $\mathrm{SAut}(X)$ acts transitively on its regu…

A Two-Operator Calculus for Arithmetic-Progression Paths in the Collatz Graph
Sebastian Angermund
https://arxiv.org/abs/2506.19115 https://

A Two-Operator Calculus for Arithmetic-Progression Paths in the Collatz Graph
A recast of the standard residue-class analysis of the 3x+1 (Collatz) map in terms of two elementary operators on arithmetic progressions. The resulting calculus (i) splits any progression into its even and odd subsequences in a single step, (ii) gives a closed formula for every set of seeds that realises a prescribed parity word, (iii) yields a one line affine invariant that forbids trajectories consisting of infinitely many odd moves, and (iv) reduces the non-trivial-cycle problem to a pair o…

Indefinite theta functions arising from affine Lie superalgebras and sums of triangular numbers
Toshiki Matsusaka, Miyu Suzuki
https://arxiv.org/abs/2506.04722

Indefinite theta functions arising from affine Lie superalgebras and sums of triangular numbers
We extend the recently developed theory of Roehrig and Zwegers on indefinite theta functions to prove certain power series are modular forms. As a consequence, we obtain several power series identities for powers of the generating function of triangular numbers. We also show that these identities arise as specializations of denominator identities of affine Lie superalgebras.

This https://arxiv.org/abs/2206.00444 has been replaced.
link: https://scholar.google.com/scholar?q=a

Affine Pavings of Quiver Flag Varieties
In this article, we construct affine pavings for quiver partial flag varieties when the quiver is of Dynkin type. To achieve our results, we extend methods from Cerulli-Irelli-Esposito-Franzen-Reineke and Maksimau as well as techniques from Auslander-Reiten theory.

This https://arxiv.org/abs/2505.21332 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Carrollian $\mathbb{R}^\times$-bundles: Connections and Beyond
We propose an approach to Carrollian geometry using principal $\mathbb{R}^\times$-bundles ($\mathbb{R}^\times := \mathbb{R} \setminus \{0\}$) equipped with a degenerate metric whose kernel is the module of vertical vector fields. The constructions allow for non-trivial bundles and a large class of Carrollian manifolds can be analysed in this formalism. Alongside other results, we show that once an $\mathbb{R}^\times$-connection has been chosen, there is a canonical affine connection that is tor…

Synthesizing Min-Max Control Barrier Functions For Switched Affine Systems
Sara Kamali, Guillaume O. Berger, Sriram Sankaranarayanan
https://arxiv.org/abs/2506.10296

Synthesizing Min-Max Control Barrier Functions For Switched Affine Systems
We study the problem of synthesizing non-smooth control barrier functions (CBFs) for continuous-time switched affine systems. Switched affine systems are defined by a set of affine dynamical modes, wherein the control consists of a state-based switching signal that determines the current operating mode. The control barrier functions seek to maintain the system state inside a control invariant set that excludes a given set of unsafe states. We consider CBFs that take the form of pointwise minima…

Perversity of coinvariants of affine Springer sheaves
Alexis Bouthier, David Kazhdan, Yakov Varshavsky
https://arxiv.org/abs/2506.19390 https://

Perversity of coinvariants of affine Springer sheaves
Using techniques of [BKV], we construct a perverse t-structure on the infinity-category of l-adic LG-equivariant sheaves on the regular-semisimple bounded locus of the loop group LG and prove that the derived $τ$-coinvariants of affine Grothendieck--Springer sheaves are perverse. Our main new ingredient is a theorem of Yun on compatibility of actions.

Dynamics for affine composition operators on weighted Bergman space of a half plane
Artur Blois, Osmar R. Severiano
https://arxiv.org/abs/2506.15822 https:…

Dynamics for affine composition operators on weighted Bergman space of a half plane
In this article, we completely characterize the positive expansive and absolutely Cesàro composition operators $C_ϕf=f\circ ϕ$ induced by affine self-maps $ϕ$ of the right half-plane $\mathbb{C}_+$ on the weighted Bergman space $\mathcal{A}^2_α(\mathbb{C}_+)$. Furthermore, we characterize which of these operators have the positive shadowing property.

Weakly separated self-affine carpets
Bal\'azs B\'ar\'any, Levente David
https://arxiv.org/abs/2506.06851 https://arxiv.or…

Weakly separated self-affine carpets
In this paper, we study the Hausdorff and box-counting dimensions of diagonally aligned self-affine carpets whose projections onto the $x$ and $y$-axes satisfy the weak separation condition. In particular, we will see that the Hausdorff dimension equals the limit of the Barański formula, and the box-counting dimension is the limit of the Feng-Wang formula taken over the $n$th level functions. We also prove various equivalent formulas for the box-counting dimension, and we provide an alternativ…

Generalized Frobenius Manifold Structures on the Orbit Spaces of Affine Weyl Groups I
Lingrui Jiang, Si-Qi Liu, Yingchao Tian, Youjin Zhang
https://arxiv.org/abs/2506.13656

Generalized Frobenius Manifold Structures on the Orbit Spaces of Affine Weyl Groups I
We present an approach to construct a class of generalized Frobenius manifold structures on the orbit spaces of affine Weyl groups, and prove that their monodromy groups are proper subgroups of the associated affine Weyl groups.

Mass Functions and Asymptotic Behavior of Caloric Functions on Affine Buildings
Effie Papageorgiou, Bartosz Trojan
https://arxiv.org/abs/2506.17042 https:/…

Mass Functions and Asymptotic Behavior of Caloric Functions on Affine Buildings
We study the large-time asymptotic behavior of solutions to the discrete-time heat equation, i.e., caloric functions, on affine buildings, including those without transitive group actions. For each $p \in [1, \infty]$, we introduce a notion of a $p$-mass function and prove that caloric functions with initial data belonging to certain weighted-$\ell^1$ spaces or to the radial $\ell^1$ class, asymptotically decouple as the product of this mass function and the heat kernel. These results extend cl…

Automatic Generation of Explicit Quadratic Programming Solvers
Maximilian Schaller, Daniel Arnstr\"om, Alberto Bemporad, Stephen Boyd
https://arxiv.org/abs/2506.11513

Automatic Generation of Explicit Quadratic Programming Solvers
We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a parametrized quadratic program is a piecewise affine function of the parameter. The number of (polyhedral) regions in the solution map can grow exponentially in problem size, but when the number of regions is moderate, a so-called explicit solver is practical. Such a so…

Proper polyhedral divisors and torus actions over arbitrary fields
Gary Martinez-Nunez
https://arxiv.org/abs/2506.22734 https://arxiv…

Proper polyhedral divisors and torus actions over arbitrary fields
We provide a algebro-geometric combinatorial description of geometrically integral geometrically normal affine varieties endowed with an effective action of an algebraic torus over arbitrary fields. This description is achieved in terms of proper polyhedral divisors endowed with a Galois semilinear action.

Cascade at local yield strain for silica and metallic glass
Nandlal Pingua, Himani Rautela, Roni Chatterjee, Smarajit Karmakar, Pinaki Chaudhuri, Shiladitya Sengupta
https://arxiv.org/abs/2506.17129

Cascade at local yield strain for silica and metallic glass
We report observations of unusal \emph{first} plastic events in silica and metallic glasses in the shear startup regime at applied strain two orders of magnitude smaller than yield strain. The (non-Affine) particle displacement field during these events have complex real space structure with multiple disconnected cores of high displacement appearing at the \emph{same} applied strain under athermal quasistatic simple shear deformation, and identified by a ``cell based cluster analysis'' method. …

$\mathbb{E}_2$-algebra structures on the derived center of an algebraic scheme
Sonja Farr
https://arxiv.org/abs/2506.14069 https://ar…

$\mathbb{E}_2$-algebra structures on the derived center of an algebraic scheme
This paper provides an explicit interface between J. Lurie's work on higher centers, and the Hochschild cohomology of an algebraic $\mathbb{k}$-scheme within the framework of deformation quantization. We first recover a canonical solution to Deligne's conjecture on Hochschild cochains in the affine and global cases, even for singular schemes, by exhibiting the Hochschild complex as an $\infty$-operadic center. We then prove that this universal $\mathbb{E}_2$-algebra structure precisely agrees w…

The higher order partial derivatives of Okamoto's function with respect to the parameter
Pieter Allaart, Nathan Dalaklis, Kiko Kawamura, Matthew Ortiz, Jiajie Zheng
https://arxiv.org/abs/2506.17737

The higher order partial derivatives of Okamoto's function with respect to the parameter
Let $\{F_a: a\in(0,1)\}$ be Okamoto's family of continuous self-affine functions, introduced in [{\em Proc. Japan Acad. Ser. A Math. Sci.} {\bf 81} (2005), no. 3, 47--50]. This family includes well-known ``pathological" examples such as Cantor's devil's staircase and Perkins' continuous but nowhere differentiable function. It is well known that $F_a(x)$ is real analytic in $a$ for every $x\in[0,1]$. We introduce the functions \[ M_{k,a}(x):=\frac{\partial^k}{\partial a^k}F_a(x), \qquad k\in\mat…

A Riemannian Characterization of Compact Affine Manifolds with Parallel Volume
Mihail Cocos
https://arxiv.org/abs/2506.14778 https://…

A Riemannian Characterization of Compact Affine Manifolds with Parallel Volume
We establish that any affine manifold $(M,\nabla)$ endowed with a parallel volume form $ω,$ admits, in any conformal class of Riemannian metrics, a representative $H$ for which $\nabla$ is the Levi-Civita connection. This provides a constructive proof that such manifolds are necessarily complete, generalizing the "if" direction of Markus' conjecture \cite{markus1962}. Moreover, our result demonstrates that these structures are intrinsically Riemannian-flat, a stronger conclusion than the affin…

Stability of the centers of group algebras of general affine groups $GA_n(q)$
Jinkui Wan, Lan Zhou
https://arxiv.org/abs/2506.05652 https://

Stability of the centers of group algebras of general affine groups $GA_n(q)$
The general affine group $GA_n(q)$ consisting of invertible affine transformations of an affine space of codimension one in the vector space $\mathbb{F}_q^n$ over a finite field $\mathbb{F}_q$, can be viewed as a subgroup of the general linear group $GL_{n}(q)$ over $\mathbb{F}_q$. In the article, we introduce the notion of the type of each matrix in $GA_n(q)$ and give an explicit representative for each conjugacy class. Then the center $\mathscr{A}_n(q)$ of the integral group algebra $\mathbb{…

This https://arxiv.org/abs/2505.10439 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Interpolating Feigin-Frenkel Duality at the Critical Level to Matrices of Complex Size
In this paper, we extend Feigin-Frenkel duality at the critical level to the setting of complex rank. This is accomplished by considering the center of a vertex algebra in Deligne's interpolating categories, along with Feigin's Lie algebras of complex rank, $\mathfrak{gl}_λ$ and $\mathfrak{po}_λ$. More precisely, we define the universal affine vertex algebras associated with Lie algebras in $\underline{\mathrm{Re}}\mathrm{p}(\mathrm{GL}_α,\mathbb{F})$, $\underline{\mathrm{Re}}\mathrm{p}(\mat…

Replaced article(s) found for math.AC. https://arxiv.org/list/math.AC/new
[1/1]:
- Zero cycles, Mennicke symbols and $\mathrm{K}_1$-stability of certain real affine algebras
Sourjya Banerjee

This https://arxiv.org/abs/2503.03076 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Non-Affine Extensions of the Raychaudhuri Equation in the K-essence Framework
We present a new avenue of the Raychaudhuri Equation (RE) by introducing a non-affine parametrization within the k-essence framework. This modification accounts for non-geodesic flow curves, leading to emergent repulsive effects in cosmic evolution. Using a DBI-type k-essence Lagrangian, we derive a modified RE and demonstrate its ability to address the Hubble tension while predicting a natural emergence of a dynamical dark energy equation of state. Our Bayesian analysis, constrained by cosmolo…

Examples of complete Calabi--Yau metrics on affine smoothings of irregular toric Calabi--Yau cones
Ronan J. Conlon, Tran-Trung Nghiem
https://arxiv.org/abs/2506.14118

Examples of complete Calabi--Yau metrics on affine smoothings of irregular toric Calabi--Yau cones
We present new examples of affine Calabi--Yau manifolds of Euclidean volume growth and quadratic curvature decay, whose tangent cones at infinity are irregular and have smooth links. In the process, we demonstrate (and provide the relevant computer code) how to explicitly compute the Reeb field and all Minkowski decompositions of a given toric Calabi--Yau cone with smooth link from the data of its toric polytope. Minkowski decompositions of this polytope into lattice segments and/or triangles g…

Affine web of type Q
Linliang Song, Xingyu Wang
https://arxiv.org/abs/2506.09729 https://arxiv.org/pdf/2506.09729

Affine web of type Q
We introduce a new diagrammatic $\Bbbk$-linear monoidal supercategory $QWeb^\bullet$, the affine web supercategory of type $Q$, where $\Bbbk$ is a commutative ring of characteristic not two. This category is the affinization of the web category of type $Q$, originally introduced by Brown and Kujawa. It serves as the type $Q$ analog of the affine web category introduced by Davidson, Kujawa, Muth and Zhu, and independently by Wang and one of the authors. We obtain diagrammatic integral bases for …

Compatibility between truncation and coproducts for quantum affine algebra and Yangian of $\mathfrak{sl}_2(\mathbb{C})$
J\'er\^ome Milot
https://arxiv.org/abs/2506.10544

Compatibility between truncation and coproducts for quantum affine algebra and Yangian of $\mathfrak{sl}_2(\mathbb{C})$
We prove that the standard Drinfeld-Jimbo coproducts for Yangians and quantum affine algebras factorize through their truncated quotients in the case of $\mathfrak{sl}_2(\mathbb{C})$.

Moduli spaces for $\Theta$-strata and non-reductive quotients
Ludvig Modin
https://arxiv.org/abs/2505.22812 https://arxiv.org/pdf/250…

Moduli spaces for $Θ$-strata and non-reductive quotients
We give a new proof of the $\hat{U}$-theorem of Bérczi, Doran, Hawes and Kirwan on the existence of geometric quotients for actions of graded unipotent groups in terms of stacks of filtrations and gradings introduced by Halpern-Leistner. Our proof works over any affine Noetherian base, in particular it simultaneously generalizes the previous results to arbitrary characteristic, actions in families and to general $Θ$-strata.

Profinite rigidity of crystallographic groups arising from Lie theory
Davide Carolillo, Gianluca Paolini
https://arxiv.org/abs/2506.15494 https://

Profinite rigidity of crystallographic groups arising from Lie theory
We prove that every finite direct product of crystallographic groups arising from an irreducible root system (in the sense of Lie theory) is profinitely rigid (equiv. first-order rigid). This is a generalization of recent proofs of profinite rigidity of affine Coxeter groups [1, 7, 22]. Our proof uses model theory.

Partially-Supervised Neural Network Model For Quadratic Multiparametric Programming
Fuat Can Beylunioglu, Mehrdad Pirnia, P. Robert Duimering
https://arxiv.org/abs/2506.05567

Partially-Supervised Neural Network Model For Quadratic Multiparametric Programming
Neural Networks (NN) with ReLU activation functions are used to model multiparametric quadratic optimization problems (mp-QP) in diverse engineering applications. Researchers have suggested leveraging the piecewise affine property of deep NN models to solve mp-QP with linear constraints, which also exhibit piecewise affine behaviour. However, traditional deep NN applications to mp-QP fall short of providing optimal and feasible predictions, even when trained on large datasets. This study propos…

Quantum cohomology, shift operators, and Coulomb branches
Ki Fung Chan, Kwokwai Chan, Chin Hang Eddie Lam
https://arxiv.org/abs/2505.23340 https://

Quantum cohomology, shift operators, and Coulomb branches
Given a complex reductive group $G$ and a $G$-representation $\mathbf{N}$, there is an associated quantized Coulomb branch algebra $\mathcal{A}_{G,\mathbf{N}}^\hbar$ defined by Braverman, Finkelberg and Nakajima. In this paper, we give a new interpretation of $\mathcal{A}_{G,\mathbf{N}}^\hbar$ as the largest subalgebra of the equivariant Borel--Moore homology of the affine Grassmannian on which shift operators can naturally be defined. As a main application, we show that if $X$ is a smooth semi…

Geometry of Yang-Baxter matrix equations over finite fields
Yin Chen, Shaoping Zhu
https://arxiv.org/abs/2506.17893 https://arxiv.org…

Geometry of Yang-Baxter matrix equations over finite fields
Let $A$ be a $2\times 2$ matrix over a finite field and consider the Yang-Baxter matrix equation $XAX=AXA$ with respect to $A$. We use a method of computational ideal theory to explore the geometric structure of the affine variety of all solutions to this equation. In particular, we exhibit all solutions explicitly and determine cardinality formulas for these varieties.

Higher-order affine Sobolev inequalities
Tristan Bullion-Gauthier (ICJ, EDPA)
https://arxiv.org/abs/2506.10473 https://arxiv.org/pdf/…

Higher-order affine Sobolev inequalities
Zhang refined the classical Sobolev inequality $\|f\|_{L^{Np/(N-p)}} \lesssim \| \nabla f \|_{L^p}$, where $1\leq p \lt N$, by replacing $\|\nabla f\|_{L^p}$ with a smaller quantity invariant by unimodular affine transformations. The analogue result in homogeneous fractional Sobolev spaces $\mathring{W}^{s,p}$, with $0 \lt s \lt 1$ and $sp \lt N$, was obtained by Haddad and Ludwig. We generalize their results to the case where $s \gt 1$. Our approach, based on the …

A short note on application of $G$-theory on Epimorphism Problem in Affine Geometry
Parnashree Ghosh
https://arxiv.org/abs/2506.09166 https://

A short note on application of $G$-theory on Epimorphism Problem in Affine Geometry
In this note we show application of $G$ theory in the Epimorphsm Problem for hypersurfaces in $\mathbb{A}^n$, by exhibiting a family of hypersurfaces satisfying Abhyankar-Sathaye's Epimorphism conjecture.

The Geometry of Extended Kalman Filters on Manifolds with Affine Connection
Yixiao Ge, Pieter van Goor, Robert Mahony
https://arxiv.org/abs/2506.05728 http…

The Geometry of Extended Kalman Filters on Manifolds with Affine Connection
The extended Kalman filter (EKF) has been the industry standard for state estimation problems over the past sixty years. The classical formulation of the EKF is posed for nonlinear systems defined on global Euclidean spaces. The design methodology is regularly applied to systems on smooth manifolds by choosing local coordinates, however, it is well known that this approach is not intrinsic to the manifold and performance depends heavily on choosing 'good' coordinates. In this paper, we propose …

Replaced article(s) found for math.QA. https://arxiv.org/list/math.QA/new
[1/1]:
- 2-categorical affine symmetries of quantum enveloping algebras
Sam Qunell

This https://arxiv.org/abs/2505.12357 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The geometric K-theory of quotient stacks
Given a quotient of a regular noetherian separated algebraic space $X$ over a field by an affine algebraic group $G$ having finite stabilizers (with some mild technical conditions), G. Vezzosi and A. Vistoli defined the \emph{geometric part} of the rational equivariant K-theory $K(X,G)$ and conjectured that it is isomorphic to the rational K-theory of the quotient $X/G$. In this paper we refine the construction of geometric K-theory to the rational K-theory of a quotient stack $[X/G]$ over an a…

This https://arxiv.org/abs/2011.02575 has been replaced.
link: https://scholar.google.com/scholar?q=a

The group of affine transformations of homogeneous spaces with discrete isotropy
We present a method to compute the group of affine transformations of a homogeneous $G$-space under specific conditions: when the group $G$ and the homogeneous $G$-space admit linear connections so that the natural projection is affine, and with discrete isotropy group. If $G$ admits a bi-invariant linear connection, we establish conditions under which the homogeneous space admits an invariant linear connection. As a consequence, when the isotropy group is discrete, their respective groups of a…

This https://arxiv.org/abs/2406.19303 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Compatibility of Drinfeld presentations for split affine Kac-Moody quantum symmetric pairs
Let $(\mathbf{U}, \mathbf{U}^\imath)$ be a split affine quantum symmetric pair of type $\mathsf{B}_n^{(1)}, \mathsf{C}_n^{(1)}$ or $\mathsf{D}_n^{(1)}$. We prove factorization and coproduct formulae for the Drinfeld-Cartan operators $Θ_i(z)$ in the Lu-Wang Drinfeld-type presentation, generalizing the type $\mathsf{A}_n^{(1)}$ result from [Prz23]. As an application, we show that a boundary analogue of the $q$-character map, defined via the spectra of these operators, is compatible with the usua…

Effective bounds for polynomial systems defined over the rationals
Teresa Krick
https://arxiv.org/abs/2506.18144 https://arxiv.org/pd…

Effective bounds for polynomial systems defined over the rationals
This survey paper was primarily written as as the support for a course pesented at the JNCF2025: it aims to present some material that illustrates the kind of estimates one can obtain in effective algebraic geometry, for affine polynomial equation systems defined over the rational numbers Q, and focuses on the case of finite varieties.