Tootfinder

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…

Linear Geometry and Algebra
Taras Banakh
https://arxiv.org/abs/2506.14060 https://arxiv.org/pdf/2506.14060

Linear Geometry and Algebra
Linear Geometry studies geometric properties which can be expressed via the notion of a line. All information about lines is encoded in a ternary relation called a line relation. A set endowed with a line relation is called a liner. So, Linear Geometry studies liners. Imposing some additional axioms on a liner, we obtain some special classes of liners: regular, projective, affine, proaffine, etc. Linear Geometry includes Affine and Projective Geometries and is a part of Incidence Geometry. The …

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.

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

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…

Serre's question on thin sets in projective space
Tijs Buggenhout, Raf Cluckers, Tim Santens, Floris Vermeulen
https://arxiv.org/abs/2506.13471 https:/…

Serre's question on thin sets in projective space
We answer a question of Serre on rational points of bounded height on projective thin sets in degree at least $4$. For degrees $2$ and $3$ we improve the known bounds in general. The focus is on thin sets of type II, namely corresponding to the images of ramified dominant quasi-finite covers of projective space, as thin sets of type I are already well understood via dimension growth results. We obtain a uniform affine variant of Serre's question which implies the projective case and for which t…

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…

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…

Replaced article(s) found for gr-qc. https://arxiv.org/list/gr-qc/new
[1/2]:
Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II:...

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 $\mathfrak{sl}_2(\mathbb{C})$.

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 …

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…

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.

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…

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…

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…

Nash equilibria in semidefinite games and Lemke-Howson paths
Constantin Ickstadt, Thorsten Theobald, Elias Tsigaridas, Antonios Varvitsiotis
https://arxiv.org/abs/2506.11940

Nash equilibria in semidefinite games and Lemke-Howson paths
We consider an algorithmic framework for two-player non-zero-sum semidefinite games, where each player's strategy is a positive semidefinite matrix with trace one. We formulate the computation of Nash equilibria in such games as semidefinite complementarity problems and develop symbolic-numeric techniques to trace generalized Lemke-Howson paths. These paths generalize the piecewise affine-linear trajectories of the classical Lemke-Howson algorithm for bimatrix games, replacing them with nonline…

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{…

Symbolic Generation and Modular Embedding of High-Quality abc-Triples
Michael A. Idowu
https://arxiv.org/abs/2506.10039 https://arxiv…

Symbolic Generation and Modular Embedding of High-Quality abc-Triples
We present a symbolic identity for generating integer triples $(a, b, c)$ satisfying $a + b = c$, inspired by structural features of the \emph{abc conjecture}. The construction uses powers of $2$ and $3$ in combination with modular inversion in $\mathbb{Z}/3^p\mathbb{Z}$, leading to a parametric identity with residue constraints that yield abc-triples exhibiting low radical values. Through affine transformations, these symbolic triples are embedded into a broader space of high-quality examples,…

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…

Antithetic Noise in Diffusion Models
Jing Jia, Sifan Liu, Bowen Song, Wei Yuan, Liyue Shen, Guanyang Wang
https://arxiv.org/abs/2506.06185 https://

Antithetic Noise in Diffusion Models
We initiate a systematic study of antithetic initial noise in diffusion models. Across unconditional models trained on diverse datasets, text-conditioned latent-diffusion models, and diffusion-posterior samplers, we find that pairing each initial noise with its negation consistently yields strongly negatively correlated samples. To explain this phenomenon, we combine experiments and theoretical analysis, leading to a symmetry conjecture that the learned score function is approximately affine an…

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.

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

Reflexive dg categories in algebra and topology
Matt Booth, Isambard Goodbody, Sebastian Opper
https://arxiv.org/abs/2506.11213 https://

Reflexive dg categories in algebra and topology
Reflexive dg categories were introduced by Kuznetsov and Shinder to abstract the duality between bounded and perfect derived categories. In particular this duality relates their Hochschild cohomologies, autoequivalence groups, and semiorthogonal decompositions. We establish reflexivity in a variety of settings including affine schemes, simple-minded collections, chain and cochain dg algebras of topological spaces, Ginzburg dg algebras, and Fukaya categories of cotangent bundles and surfaces as …

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…

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…

Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification
Matthias Beckmann, Robert Beinert, Jonas Bresch
https://arxiv.org/abs/2506.08761

Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification
The Radon cumulative distribution transform (R-CDT), is an easy-to-compute feature extractor that facilitates image classification tasks especially in the small data regime. It is closely related to the sliced Wasserstein distance and provably guaranties the linear separability of image classes that emerge from translations or scalings. In many real-world applications, like the recognition of watermarks in filigranology, however, the data is subject to general affine transformations originating…

Complex harmonic maps and rank 2 higher Teichm\"uller theory
Christian El Emam, Nathaniel Sagman
https://arxiv.org/abs/2506.11746 https://

Complex harmonic maps and rank 2 higher Teichmüller theory
We initiate and develop the theory of complex harmonic maps to holomorphic Riemannian symmetric spaces, which we make use of to study complex analytic aspects of higher Teichmüller theory, with a focus on rank $2$ Hitchin components. Complex harmonic maps lead to various generalizations of objects from the theory of Higgs bundles; for instance, the Hitchin fibration, cyclic Higgs bundles, and the affine Toda equations. Beyond such generalizations, we also find a relation between complex harm…

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: $Ω^c(K) Ω^c(K^c) \leq Ω^c(\frac{1}{2} B_2^n)^2$.

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.

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…

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 …

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 …

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…

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…

Flag-transitive point-primitive quasi-symmetric $2$-designs and exceptional groups of Lie type
Jianbing Lu
https://arxiv.org/abs/2506.10266 https://…

Flag-transitive point-primitive quasi-symmetric $2$-designs and exceptional groups of Lie type
Let $\mathcal{D}$ be a non-trivial quasi-symmetric $2$-design with two block intersection numbers $x=0$ and $2\leq y\leq10$, and suppose that $G$ is an automorphism group of $\mathcal{D}$. If $G$ is flag-transitive and point-primitive, then it is known that $G$ is either of affine type or almost simple type. In this paper, we show that the socle of $G$ cannot be a finite simple exceptional group of Lie type.

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 …

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…

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…

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…

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.

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 …

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…

Characterizations of Faces of Convex Sets in Infinite-dimensional Vector Spaces
Valentin V. Gorokhovik
https://arxiv.org/abs/2506.08742 https://

Characterizations of Faces of Convex Sets in Infinite-dimensional Vector Spaces
In the paper three different characterizations of faces of convex sets, belonging to infinite-dimensional real vector spaces, are presented. The first one is formulated in the terms of generalized semispaces, the second -- in the terms of compatible complete (total) preorders, and the third -- in the terms of step-affine functions. All three characterization are equivalent each other and extend to infinite-dimensional vector spaces the lexicographical characterization of faces established in fi…

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 …

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…

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…

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…

Replaced article(s) found for math.RT. https://arxiv.org/list/math.RT/new/
[1/1]:
Level-Rank Dualities from $\Phi$-Cuspidal Pairs and Affine Springer Fibers

Stochastic Quadratic Dynamic Programming
Vincent Guigues, Adriana Washington
https://arxiv.org/abs/2506.07314 https://arxiv.org/pdf/2…

Stochastic Quadratic Dynamic Programming
We introduce an algorithm called SQDP (Stochastic Quadratic Dynamic Programming) to solve some multistage stochastic optimization problems having strongly convex recourse functions. The algorithm extends the classical Stochastic Dual Dynamic Programming (SDDP) method replacing affine cuts by quadratic cuts. We provide conditions ensuring strong convexity of the recourse functions and prove the convergence of SQDP. In the special case of a single stage deterministic problem, we call QCSC (Quadra…

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.

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.

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…

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…

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…

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.

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.

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…

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&#…

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 $\mathbb{C}^4/G_5$.

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…

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…

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…

On the geometry of synthetic null hypersurfaces
Fabio Cavalletti, Davide Manini, Andrea Mondino
https://arxiv.org/abs/2506.04934 https://

On the geometry of synthetic null hypersurfaces
This paper develops a synthetic framework for the geometric and analytic study of null (lightlike) hypersurfaces in non-smooth spacetimes. Drawing from optimal transport and recent advances in Lorentzian geometry and causality theory, we define a synthetic null hypersurface as a triple $(H, G, \mathfrak{m})$: $H$ is a closed achronal set in a topological causal space, $G$ is a gauge function encoding affine parametrizations along null generators, and $\mathfrak{m}$ is a Radon measure serving as…

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…

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…

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.

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…

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…