Tootfinder

I guess Elon is getting his wish to lay off 20% of Tesla because sales fell 20% (which is an idiotic equivalence by the way).
“Tesla announces fourth round of layoffs in four weeks”
#cars #ev #tesla

Tesla announces fourth round of layoffs in four weeks
The latest cuts affect engineers, HR, and service advisers.

A 2-categorical analysis of context comprehension
Greta Coraglia, Jacopo Emmenegger
https://arxiv.org/abs/2403.03085 https://arxiv.or…

A 2-categorical analysis of context comprehension
We consider the equivalence between the two main categorical models for the type-theoretical operation of context comprehension, namely P. Dybjer's categories with families and B. Jacobs' comprehension categories, and generalise it to the non-discrete case. The classical equivalence can be summarised in the slogan: "terms as sections". By recognising "terms as coalgebras", we show how to use the structure-semantics adjunction to prove that a 2-category of comprehension categories is biequivalen…

VeriEQL: Bounded Equivalence Verification for Complex SQL Queries with Integrity Constraints
Yang He, Pinhan Zhao, Xinyu Wang, Yuepeng Wang
https://arxiv.org/abs/2403.03193

VeriEQL: Bounded Equivalence Verification for Complex SQL Queries with Integrity Constraints
The task of SQL query equivalence checking is important in various real-world applications (including query rewriting and automated grading) that involve complex queries with integrity constraints; yet, state-of-the-art techniques are very limited in their capability of reasoning about complex features (e.g., those that involve sorting, case statement, rich integrity constraints, etc.) in real-life queries. To the best of our knowledge, we propose the first SMT-based approach and its implementa…

This https://arxiv.org/abs/2104.02438 has been replaced.
link: https://scholar.google.com/scholar?q=a

Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata
We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata for infinite alphabets. The algorithm runs in exponential time, and in polynomial time for a fixed number of registers. As a special case, we can decide, with the same complexity, language equivalence for unambiguous register automata, which improves previou…

A remark on $\mathscr{C}^\infty$ definable equivalence
Anna Valette, Guillaume Valette
https://arxiv.org/abs/2403.03164 https://arxiv…

A remark on $\mathscr{C}^\infty$ definable equivalence
We establish that if a submanifold $M$ of $\mathbb{R}^n$ is definable in some o-minimal structure then any definable submanifold $N\subset \mathbb{R}^n$ which is $\mathscr{C}^\infty$ diffeomorphic to $M$, with a diffeomorphism $h:N\to M$ that is sufficiently close to the identity, must be $\mathscr{C}^\infty$ definably diffeomorphic to $M$. The definable diffeomorphism between $N$ and $M$ is then provided by a tubular neighborhood of $M$.

This https://arxiv.org/abs/2306.16974 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Approximate homomorphisms and sofic approximations of orbit equivalence relations
We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbit equivalence relation. Moreover, this orbit equivalence relation is uniquely determined by the invariant random subgroup of the approximate homomorphism. We record applications of this result to recover various known stability and conjugacy characterizations for almost homomorphisms of amenable groups.

This https://arxiv.org/abs/2402.07700 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

The noisy Landau-Streater or the Werner-Holevo channel in arbitrary dimensions
Two important classes of quantum channels, namly the Werner-Holevo and the Landau-Streater channels are known to be related only in three dimensions, i.e. when acting on qutrits. In this work, the definition of the Landau-Streater channel is extended in such a way which retains its equivalence to the Werner-Holevo channel in all dimensions. This channel is then modified to be representable as a model of noise acting on qudits. We then investigate propeties of the resulting noisy channel and det…

On dense orbits in the space of subequivalence relations
Fran\c{c}ois Le Ma\^itre
https://arxiv.org/abs/2405.01806 https://arxiv.org/…

On dense orbits in the space of subequivalence relations
We first explain how to endow the space of subequivalence relations of any non-singular countable equivalence relation with a Polish topology, extending the framework of Kechris' recent monograph on subequivalence relations of probability measure-preserving (p.m.p.) countable equivalence relations. We then restrict to p.m.p. equivalence relations and discuss dense orbits therein for the natural action of the full group and of the automorphism group of the relation. Our main result is a characte…

This https://arxiv.org/abs/2306.02568 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Latent Optimal Paths by Gumbel Propagation for Variational Bayesian Dynamic Programming
We propose the stochastic optimal path which solves the classical optimal path problem by a probability-softening solution. This unified approach transforms a wide range of DP problems into directed acyclic graphs in which all paths follow a Gibbs distribution. We show the equivalence of the Gibbs distribution to a message-passing algorithm by the properties of the Gumbel distribution and give all the ingredients required for variational Bayesian inference of a latent path, namely Bayesian dyna…

This https://arxiv.org/abs/2404.18835 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Degeneration in discrimintal arrangements
Discriminantal arrangements are hyperplane arrangements, which are generalized braid ones. They are constructed from given hyperplane arrangements, but their combinatorics are not invariant under combinatorial equivalence. However, it is known that the combinatorics of the discriminantal arrangement are constant on a Zariski open set of the space of hyperplane arrangements. In the present paper, we introduce non-very generic varieties in the space of hyperplane arrangements to classify discrimi…

Stability of the Ghurye-Olkin Characterization of Vector Gaussian Distributions
Mahdi Mahvari, Gerhard Kramer
https://arxiv.org/abs/2405.01707 https://

Stability of the Ghurye-Olkin Characterization of Vector Gaussian Distributions
The stability of the Ghurye-Olkin (GO) characterization of Gaussian vectors is analyzed using a partition of the vectors into equivalence classes defined by their matrix factors. The sum of the vectors in each class is near-Gaussian in the characteristic function (c.f.) domain if the GO independence condition is approximately met in the c.f. domain. All vectors have the property that any vector projection is near-Gaussian in the distribution function (d.f.) domain. The proofs of these c.f. and …

Some applications of the geometric Satake equivalence to modular representation theory
Simon Riche
https://arxiv.org/abs/2403.03734 https://

Some applications of the geometric Satake equivalence to modular representation theory
These notes present an application of the geometric Satake equivalence to the description of characters of indecomposable tilting modules for reductive algebraic groups over fields of positive characteristic, obtained in joint work with G. Williamson.

Cofinality Theorems of Infinity Categories and Algebraic K-Theory
Hisato Matsukawa
https://arxiv.org/abs/2405.03498 https://arxiv.org…

Cofinality Theorems of Infinity Categories and Algebraic K-Theory
In this paper, we establish a theorem that proves a condition when an inclusion morphism between simplicial sets becomes a weak homotopy equivalence. Additionally, we present two applications of this result. The first application demonstrates that cofinal full inclusion functors of (\infty)-categories are weak homotopy equivalences. For our second application, we provide an alternative proof of Barwick's cofinality theorem of algebraic (K)-theory.

Refining the grading of irreducible Lie colour algebra representations
Mitchell Ryan
https://arxiv.org/abs/2403.02855 https://arxiv.o…

Refining the grading of irreducible Lie colour algebra representations
We define the refining extension of representations for Lie colour algebras which simultaneously extends the representations and refines the grading to a larger grading group.We show that the refining extension provides a general method for deriving all finite-dimensional irreducible Lie colour algebra representations from those for Lie superalgebras. This method yields a bijection between equivalence classes but, despite this, Lie colour algebras maintain a non-trivial representation theory di…

Equivalence between VMO functions and Zero Lelong numbers functions
S\'everine Biard, Jujie Wu
https://arxiv.org/abs/2403.03568 https://

Equivalence between VMO functions and Zero Lelong numbers functions
We prove that a plurisbharmonic function on a bounded domain $Ω$ in $\mathbb{C}^n$ is a VMO (Vanishing Mean Oscillation) function if and only if its Lelong number at each point of $Ω$ vanishes. This result contributes to a better understanding of the behavior of singular plurisubharmonic functions.

Statistical Equivalence of Metrics for Meteor Dynamical Association
Eloy Pe\~na-Asensio, Juan Miguel S\'anchez-Lozano
https://arxiv.org/abs/2405.03308 …

Statistical Equivalence of Metrics for Meteor Dynamical Association
We statistically evaluate and compare four orbital similarity criteria within five-dimensional parameter space ($D_{SH}$, $D_D$, $D_H$, and $\varrho_2$) to study dynamical associations using the already classified meteors (manually by a human) in CAMS database as a benchmark. In addition, we assess various distance metrics typically used in Machine Learning with two different vectors: ORBIT, grounded in heliocentric orbital elements, and GEO, predicated on geocentric observational parameters. A…

This https://arxiv.org/abs/2205.06692 has been replaced.
link: https://scholar.google.com/scholar?q=a

Co-spectral radius for countable equivalence relations
We define the co-spectral radius of inclusions $\mathcal{S}\leq \mathcal{R}$ of discrete, probability measure-preserving equivalence relations, as the sampling exponent of a generating random walk on the ambient relation. The co-spectral radius is analogous to the spectral radius for random walks on $G/H$ for inclusion $H\leq G$ of groups. For the proof, we develop a more general version of the 2-3 method we used in another work on the growth of unimodular random rooted trees. We use this metho…

This https://arxiv.org/abs/2312.15470 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Dual theory of decaying turbulence
This paper investigates the recently found \cite{migdal2023exact} reduction of decaying turbulence in the Navier-Stokes equation to a Number Theory problem of finding the statistical limit of the Euler ensemble. We reformulate the Euler ensemble as a Markov chain and show the equivalence of this formulation to the quantum statistical theory of free fermions on a ring, with an external field related to the random fractions of $π$. We find the solution of this system in the statistical limit $N\…

This https://arxiv.org/abs/2311.10877 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Covariate adjustment in randomized experiments with missing outcomes and covariates
Covariate adjustment can improve precision in analyzing randomized experiments. With fully observed data, regression adjustment and propensity score weighting are asymptotically equivalent in improving efficiency over unadjusted analysis. When some outcomes are missing, we consider combining these two adjustment methods with inverse probability of observation weighting for handling missing outcomes, and show that the equivalence between the two methods breaks down. Regression adjustment no long…

This https://arxiv.org/abs/2306.00592 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Phase space analysis of spectral multipliers for the twisted Laplacian
We prove boundedness results on modulation and Wiener amalgam spaces for some families of spectral multipliers for the twisted Laplacian. We exploit the metaplectic equivalence relating the twisted Laplacian with a partial harmonic oscillator, leading to a general transference principle for the corresponding spectral multipliers. Our analysis encompasses powers of the twisted Laplacian and oscillating multipliers, with applications to the corresponding Schrödinger and wave flows. On the other …

This https://arxiv.org/abs/2303.16638 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Derived equivalence of elliptic K3 surfaces and Jacobians
We present a detailed study of elliptic fibrations on Fourier-Mukai partners of K3 surfaces, which we call derived elliptic structures. We fully classify derived elliptic structures in terms of Hodge-theoretic data, similar to the Derived Torelli Theorem that describes Fourier-Mukai partners. In Picard rank two, derived elliptic structures are fully determined by the Lagrangian subgroups of the discriminant group. As a consequence, we prove that for a large class of Picard rank 2 elliptic K3 su…

This https://arxiv.org/abs/2308.10359 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

Central Bank Digital Currency with Collateral-constrained Banks
We analyze the risks to financial stability following the introduction of a central bank digital currency (CBDC). The CBDC competes with commercial bank deposits as the household's source of liquidity. We revisit the result in the literature regarding the equivalence of payment systems by introducing a collateral constraint for banks when borrowing from the central bank. When comparing two equilibria with and without the CBDC, the central bank can ensure the same equilibrium allocation and pric…

Equivalence and Similarity Refutation for Probabilistic Programs
Krishnendu Chatterjee, Ehsan Kafshdar Goharshady, Petr Novotn\'y, {\DJ}or{\dj}e \v{Z}ikeli\'c
https://arxiv.org/abs/2404.03430

Equivalence and Similarity Refutation for Probabilistic Programs
We consider the problems of statically refuting equivalence and similarity of output distributions defined by a pair of probabilistic programs. Equivalence and similarity are two fundamental relational properties of probabilistic programs that are essential for their correctness both in implementation and in compilation. In this work, we present a new method for static equivalence and similarity refutation. Our method refutes equivalence and similarity by computing a function over program outpu…

This https://arxiv.org/abs/2305.03008 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Some aspects of vector valued de Branges spaces of entire functions
This paper deals with certain aspects of the vector valued de Branges spaces of entire functions that are based on pairs of Fredholm operator valued functions. Some factorization and isometric embedding results are extended from the scalar valued theory of de Branges spaces. In particular, global factorization of Fredholm operator valued entire functions and analytic equivalence of reproducing kernels of de Branges spaces are discussed. Additionally, the operator valued entire functions associa…

The Lanczos Tau Framework for Time-Delay Systems: Pad\'e Approximation and Collocation Revisited
Evert Provoost, Wim Michiels
https://arxiv.org/abs/2403.03895

The Lanczos Tau Framework for Time-Delay Systems: Padé Approximation and Collocation Revisited
We reformulate the Lanczos tau method for the discretization of time-delay systems in terms of a pencil of operators, allowing for new insights into this approach. As a first main result, we show that, for the choice of a shifted Legendre basis, this method is equivalent to Padé approximation in the frequency domain. We illustrate that Lanczos tau methods straightforwardly give rise to sparse, self nesting discretizations. Equivalence is also demonstrated with pseudospectral collocation, where…

Interpolant Existence is Undecidable for Two-Variable First-Order Logic with Two Equivalence Relations
Frank Wolter, Michael Zakharyaschev
https://arxiv.org/abs/2404.02683

Interpolant Existence is Undecidable for Two-Variable First-Order Logic with Two Equivalence Relations
The interpolant existence problem (IEP) for a logic L is to decide, given formulas P and Q, whether there exists a formula I, built from the shared symbols of P and Q, such that P entails I and I entails Q in L. If L enjoys the Craig interpolation property (CIP), then the IEP reduces to validity in L. Recently, the IEP has been studied for logics without the CIP. The results obtained so far indicate that even though the IEP can be computationally harder than validity, it is decidable when L is …

Refining the grading of irreducible Lie colour algebra representations
Mitchell Ryan
https://arxiv.org/abs/2403.02855 https://arxiv.o…

Refining the grading of irreducible Lie colour algebra representations
We define the refining extension of representations for Lie colour algebras which simultaneously extends the representations and refines the grading to a larger grading group.We show that the refining extension provides a general method for deriving all finite-dimensional irreducible Lie colour algebra representations from those for Lie superalgebras. This method yields a bijection between equivalence classes but, despite this, Lie colour algebras maintain a non-trivial representation theory di…

This https://arxiv.org/abs/2211.00544 has been replaced.
link: https://scholar.google.com/scholar?q=a

Igusa-Todorov distances of Artin algebras
We introduce Igsua-Todorov distances of Artin algebra, prove its invariance under derived equivalence, present its application to exterior algebra, and establish the link between the dimension of the singularity category and this distance.

Representations of quantum lattice vertex algebras
Fei Kong
https://arxiv.org/abs/2404.03552 https://arxiv.org/pdf/2404.03552<…

Representations of quantum lattice vertex algebras
Let $Q$ be a non-degenerated even lattice, let $V_Q$ be the lattice vertex algebra associated to $Q$, and let $V_Q^η$ be a quantum lattice vertex algebra. In this paper, we prove the equivalence between the category $V_Q$-modules and the category of $V_Q^η$-modules. As a consequence, we show that every $V_Q^η$-module is completely reducible, and the set of simple $V_Q^η$-modules are in one-to-one correspondence with the set of cosets of $Q$ in its dual lattice.

This https://arxiv.org/abs/2009.14801 has been replaced.
link: https://scholar.google.com/scholar?q=a

Birational Equivalences and Generalized Weyl Algebras
We calculate suitably localized Hochschild homologies of various quantum groups and Podleś spheres after realizing them as generalized Weyl algebras (GWAs). We use the fact that every GWA is birationally equivalent to a smash product with a 1-torus. We also address and solve the birational equivalence problem and the birational smoothness problem for GWAs.

Groups with few finite dimensional unitary representations
Mar\'ia V. Ferrer, S. Hern\'andez
https://arxiv.org/abs/2405.02627 https://

Groups with few finite dimensional unitary representations
The \emph{Bohr compactification} of an arbitrary topological group $G$ is defined as the group compactification $(bG,b)$ with the following universal property: for every continuous homomorphism $h$ from $G$ into a compact group $K$ there is a continuous homomorphism $h^{b}$ from $bG$ into $K$ extending $h$ in the sense that $h=h^b \circ b$. The Bohr compactification $(bG,b)$ is the unique (up to equivalence) largest compactification of $G$. Although, for locally compact Abelian groups, the Bohr…

Classification of 2-node Excitatory-Inhibitory Networks
Manuela Aguiar, Ana Dias, Ian Stewart
https://arxiv.org/abs/2403.02869 https://

Classification of 2-node Excitatory-Inhibitory Networks
We classify connected 2-node excitatory-inhibitory networks under various conditions. We assume that, as well as for connections, there are two distinct node-types, excitatory and inhibitory. In our classification we consider four different types of excitatory-inhibitory networks: restricted, partially restricted, unrestricted and completely unrestricted. For each type we give two different classifications. Using results on ODE-equivalence and minimality, we classify the ODE-classes and present…

The Extension dimension of syzygy module categories
Junling Zheng, Lulu Tian, Qianyu Shu, Jinbi Zhang
https://arxiv.org/abs/2405.02921 https://

The Extension dimension of syzygy module categories
In this paper, our primary focus is on investigating the extension dimensions of syzygy module categories associated with Artin algebras, particularly under various equivalences. We demonstrate that, for sufficiently large $i$, the $i$-th syzygy module categories of derived equivalent algebras exhibit identical extension dimensions. Furthermore, we establish that the extension dimension of the $i$-th syzygy module category is an invariant under both stable equivalence and separable equivalence …

This https://arxiv.org/abs/2312.00243 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

Low Revenue in Display Ad Auctions: Algorithmic Collusion vs. Non-Quasilinear Preferences
The transition of display ad exchanges from second-price to first-price auctions has raised questions about its impact on revenue, but evaluating these changes empirically proves challenging. Automated bidding agents play a significant role in this transition, often employing dynamic strategies that evolve through exploration and exploitation rather than using the static game-theoretical equilibrium strategies. Thus revenue equivalence between first- and second-price auctions might not hold. Re…

This https://arxiv.org/abs/2011.08808 has been replaced.
link: https://scholar.google.com/scholar?q=a

Lax monoidal adjunctions, two-variable fibrations and the calculus of mates
We provide a calculus of mates for functors to the $\infty$-category of $\infty$-categories and extend Lurie's unstraightening equivalences to show that (op)lax natural transformations correspond to maps of (co)cartesian fibrations that do not necessarily preserve (co)cartesian edges. As a sample application we obtain an equivalence between lax symmetric monoidal structures on right adjoint functors and oplax symmetric monoidal structures on the left adjoint functors between symmetric monoidal …

Proof of the geometric Langlands conjecture II: Kac-Moody localization and the FLE
D. Arinkin, D. Beraldo, J. Campbell, L. Chen, D. Gaitsgory J. Faergeman, K. Lin, S. Raskin, N. Rozenblyum
https://arxiv.org/abs/2405.03648

Proof of the geometric Langlands conjecture II: Kac-Moody localization and the FLE
This paper is the second in a series of five that together prove the geometric Langlands conjecture. Our goals are two-fold: (1) Formulate and prove the Fundamental Local Equivalence (FLE) at the critical level; (2) Study the interaction between Kac-Moody localization and the global geometric Langlands functor of ref. [GLC1]. This paper contains an extensive Appendix, whose primary goals are: (a) Development the theory of ind-coherent sheaves in infinite type; (b)Development of the fo…

An Infinite Family of Real Quadratic Fields with Three Classes of Perfect Unary Forms
Christian Porter
https://arxiv.org/abs/2404.01538 https://

An Infinite Family of Real Quadratic Fields with Three Classes of Perfect Unary Forms
In this paper, we revisit the theory of perfect unary forms over real quadratic fields. Specifically, we deduce an infinite family of real quadratic fields $\mathbb{Q}(\sqrt{d})$ when $d=2$ or $3$ mod $4$, such that there are three classes of perfect unary forms up to homothety and equivalence. This work, along with the work in \cite{unitred}, seems to suggest that the number of classes of perfect unary forms is related to the fundamental unit of $K$.

On free bases of Banach spaces
E. Perneck\'a, J. Sp\v{e}v\'ak
https://arxiv.org/abs/2405.03556 https://arxiv.org/pdf/2405.035…

On free bases of Banach spaces
We call a closed subset M of a Banach space X a free basis of X if it contains the null vector and every Lipschitz map from M to a Banach space Y, which preserves the null vectors can be uniquely extended to a bounded linear map from X to Y. We then say that two complete metric spaces M and N are Mol-equivalent if they admit bi-Lipschitz copies M' and N', respectively that are free bases of a common Banach space satisfying span M'=span N'. In this note, we compare Mol-equivalence with some ot…

The Lanczos Tau Framework for Time-Delay Systems: Pad\'e Approximation and Collocation Revisited
Evert Provoost, Wim Michiels
https://arxiv.org/abs/2403.03895

The Lanczos Tau Framework for Time-Delay Systems: Padé Approximation and Collocation Revisited
We reformulate the Lanczos tau method for the discretization of time-delay systems in terms of a pencil of operators, allowing for new insights into this approach. As a first main result, we show that, for the choice of a shifted Legendre basis, this method is equivalent to Padé approximation in the frequency domain. We illustrate that Lanczos tau methods straightforwardly give rise to sparse, self nesting discretizations. Equivalence is also demonstrated with pseudospectral collocation, where…

This https://arxiv.org/abs/1608.08462 has been replaced.
link: https://scholar.google.com/scholar?q=a

Garoufalidis-Levine's finite type invariants for $\mathbb{Z}π$-homology equivalences from 3-manifolds to the 3-torus
Garoufalidis and Levine defined a filtration for 3-manifolds equipped with some degree 1 map ($\mathbb{Z}π$-homology equivalence) to a fixed 3-manifold $N$ and showed that there is a natural surjection from a space of $π=π_1N$-decorated graphs to the graded quotient of the filtration over $\mathbb{Z}[\frac{1}{2}]$. In this paper, we show that in the case of $N=T^3$ the surjection of Garoufalidis--Levine is actually an isomorphism over $\mathbb{Q}$. For the proof, we construct a perturbative …

Well-posedness of Kolmogorov-Fokker-Planck equations with unbounded drift
Francesca Anceschi, Giacomo Ascione, Daniele Castorina, Francesco Solombrino
https://arxiv.org/abs/2405.01955

Well-posedness of Kolmogorov-Fokker-Planck equations with unbounded drift
We consider Kolmogorov-Fokker-Planck equations with unbounded drift terms which are only measurable in time and locally Hölder continuous in space. In particular, we extend the parametrix method to this setting and we prove existence and uniqueness of measure solutions to the associated Cauchy problem, as well as the equivalence with the corresponding stochastic formulation.

An order analysis of hyperfinite Borel equivalence relations
Su Gao, Ming Xiao
https://arxiv.org/abs/2404.17516 https://arxiv.org/pdf…

An order analysis of hyperfinite Borel equivalence relations
In this paper we first consider hyperfinite Borel equivalence relations with a pair of Borel $\mathbb{Z}$-orderings. We define a notion of compatibility between such pairs, and prove a dichotomy theorem which characterizes exactly when a pair of Borel $\mathbb{Z}$-orderings are compatible with each other. We show that, if a pair of Borel $\mathbb{Z}$-orderings are incompatible, then a canonical incompatible pair of Borel $\mathbb{Z}$-orderings of $E_0$ can be Borel embedded into the given pair.…

Representations of quantum lattice vertex algebras
Fei Kong
https://arxiv.org/abs/2404.03552 https://arxiv.org/pdf/2404.03552<…

Representations of quantum lattice vertex algebras
Let $Q$ be a non-degenerated even lattice, let $V_Q$ be the lattice vertex algebra associated to $Q$, and let $V_Q^η$ be a quantum lattice vertex algebra. In this paper, we prove the equivalence between the category $V_Q$-modules and the category of $V_Q^η$-modules. As a consequence, we show that every $V_Q^η$-module is completely reducible, and the set of simple $V_Q^η$-modules are in one-to-one correspondence with the set of cosets of $Q$ in its dual lattice.

This https://arxiv.org/abs/2005.08681 has been replaced.
link: https://scholar.google.com/scholar?q=a

Enumerative Geometry of Del Pezzo Surfaces
We prove an equivalence between the superpotential defined via tropical geometry and Lagrangian Floer theory for special Lagrangian torus fibres in del Pezzo surfaces constructed by Collins-Jacob-Lin. We also include some explicit calculations for the projective plane, which confirm some folklore conjecture in this case.

This https://arxiv.org/abs/2207.14684 has been replaced.
link: https://scholar.google.com/scholar?q=a

Two weight Sobolev norm inequalities for fractional vector Riesz transforms and doubling weights
We prove a T1 theorem for fractional vector Riesz transforms mapping one weighted Sobolev space to another, where the weights are doubling measures on Euclidean space. Boundedness is characterized by the classical A_2 condition and two dual testing conditions on indicators of cubes. We also show the equivalence of various weighted Sobolev norms when the measure is doubling, something that fails in general.

This https://arxiv.org/abs/2307.14826 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Graded Semantics and Graded Logics for Eilenberg-Moore Coalgebras
Coalgebra, as the abstract study of state-based systems, comes naturally equipped with a notion of behavioural equivalence that identifies states exhibiting the same behaviour. In many cases, however, this equivalence is finer than the intended semantics. Particularly in automata theory, behavioural equivalence of nondeterministic automata is essentially bisimilarity, and thus does not coincide with language equivalence. Language equivalence can be captured as behavioural equivalence on the det…

This https://arxiv.org/abs/2404.01286 has been replaced.
link: https://scholar.google.com/scholar?q=a

Beyond Linear Response: Equivalence between Thermodynamic Geometry and Optimal Transport
A fundamental result of thermodynamic geometry is that the optimal, minimal-work protocol that drives a nonequilibrium system between two thermodynamic states in the slow-driving limit is given by a geodesic of the friction tensor, a Riemannian metric defined on control space. For overdamped dynamics in arbitrary dimensions, we demonstrate that thermodynamic geometry is equivalent to $L^2$ optimal transport geometry defined on the space of equilibrium distributions corresponding to the control …

This https://arxiv.org/abs/2011.08808 has been replaced.
link: https://scholar.google.com/scholar?q=a

Lax monoidal adjunctions, two-variable fibrations and the calculus of mates
We provide a calculus of mates for functors to the $\infty$-category of $\infty$-categories and extend Lurie's unstraightening equivalences to show that (op)lax natural transformations correspond to maps of (co)cartesian fibrations that do not necessarily preserve (co)cartesian edges. As a sample application we obtain an equivalence between lax symmetric monoidal structures on right adjoint functors and oplax symmetric monoidal structures on the left adjoint functors between symmetric monoidal …

This https://arxiv.org/abs/2303.03765 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A survey of congruences and quotients of partially ordered sets
A quotient of a poset $P$ is a partial order obtained on the equivalence classes of an equivalence relation $θ$ on $P$; $θ$ is then called a congruence if it satisfies certain conditions, which vary according to different theories. The literature on congruences and quotients of partially ordered sets contains a large and profilerating array of approaches, but little in the way of systematic exposition and examination of the subject. We seek to rectify this by surveying the different theories …

This https://arxiv.org/abs/2402.16637 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Actions on classifiable C*-algebras without equivariant property (SI)
We exhibit examples of actions of countable discrete groups on both simple and non-simple nuclear stably finite C*-algebras that are tracially amenable but not amenable. We moreover obtain that, under the additional assumption of strict comparison, amenability is equivalent to tracial amenability plus the equivariant analogue of Matui--Sato's property (SI). By virtue of this equivalence, our construction yields the first known examples of actions on classifiable C*-algebras that do not have equ…

Equivalence: An analysis of artists' roles with Image Generative AI from Conceptual Art perspective through an interactive installation design practice
Yixuan Li, Dan C. Baciu, Marcos Novak, George Legrady
https://arxiv.org/abs/2404.18385

Equivalence: An analysis of artists' roles with Image Generative AI from Conceptual Art perspective through an interactive installation design practice
Over the past year, the emergence of advanced text-to-image Generative AI models has significantly impacted the art world, challenging traditional notions of creativity and the role of artists. This study explores how artists interact with these technologies, using a 5P model (Purpose, People, Process, Product, and Press) based on Rhodes' creativity framework to compare the artistic processes behind Conceptual Art and Image Generative AI. To exemplify this framework, a practical case study titl…

This https://arxiv.org/abs/2402.10354 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

A Heterotic Hermitian--Yang--Mills Equivalence
We consider N=1, d=4 vacua of heterotic theories in the large radius limit in which alpha' << 1. We construct a real differential operator $\mathcal{D}= D+\bar{D}$ on an extension bundle $(Q, \mathcal{D})$ with underlying topology $Q=(T^{1,0}X)^* \oplus {\rm End} \, E \oplus T^{1,0} X$ whose curvature is holomorphic and Hermitian-Yang-Mills with respect to the complex structure and metric on the underlying non-Kahler complex 3-fold X if and only if the heterotic supersymmetry equations and Bian…

This https://arxiv.org/abs/2311.07459 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On homogeneous plane waves
Plane waves are a special class of Lorentzian spaces with a parallel null vector field. They are of great importance in Geometry (e.g. Lorentzian holonomy) and in Physics (General Relativity as well as alternative gravity theories). Our contribution in the present paper aims at a rigorous mathematical treatment focusing on completeness of Killing fields, and globality of coordinates. Equivalence of different approaches to plane waves is by no means easy to handle. We use here cohomogeneity one …

This https://arxiv.org/abs/2401.16905 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Emulating dark energy models with known equation of state via the created cold dark matter scenario
In this work we establish only at background dynamics level, the equivalence between the Created Cold Dark Matter (CCDM) model and diverse dark energy (DE) models. We find that for a barotropic or linear equation of state (EoS) for the DE, $p=w ρ$, and standard matter sector the corresponding CCDM model is described by the same functional structure of the ratio of particle production, $Γ$. For a different EoS the functional form of the $Γ$ term is not longer maintained, however, in the case …

Linear degenerate symplectic flag varieties: symmetric degenerations and PBW locus
Magdalena Boos, Giovanni Cerulli Irelli, Xin Fang, Ghislain Fourier
https://arxiv.org/abs/2405.02739

Linear degenerate symplectic flag varieties: symmetric degenerations and PBW locus
We conceptualize in the paper the linear degenerate symplectic flag varieties as symmetric degenerations within the framework of type $A$ equioriented quivers. First, in the larger context of symmetric degenerations, we give a self-contained proof of the equivalence of different degeneration orders. Furthermore, we investigate the PBW locus: geometric properties of the degenerate varieties in this locus are proved by realizing them from different perspectives.

Overcoming model uncertainty -- how equivalence tests can benefit from model averaging
Niklas Hagemann, Kathrin M\"ollenhoff
https://arxiv.org/abs/2405.00827

Overcoming model uncertainty -- how equivalence tests can benefit from model averaging
A common problem in numerous research areas, particularly in clinical trials, is to test whether the effect of an explanatory variable on an outcome variable is equivalent across different groups. In practice, these tests are frequently used to compare the effect between patient groups, e.g. based on gender, age or treatments. Equivalence is usually assessed by testing whether the difference between the groups does not exceed a pre-specified equivalence threshold. Classical approaches are based…

This https://arxiv.org/abs/2312.15470 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Dual theory of decaying turbulence
This paper investigates the recently found \cite{migdal2023exact} reduction of decaying turbulence in the Navier-Stokes equation in $3 + 1$ dimensions to a Number Theory problem of finding the statistical limit of the Euler ensemble. We reformulate the Euler ensemble as a Markov chain and show the equivalence of this formulation to the quantum statistical theory of free fermions on a ring, with an external field related to the random fractions of $π$. We find the solution of this system in the…

This https://arxiv.org/abs/2308.04510 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Gromov-Hausdorff convergence of metric pairs and metric tuples
We study the Gromov-Hausdorff convergence of metric pairs and metric tuples and prove the equivalence of different natural definitions of this concept. We also prove embedding, completeness and compactness theorems in this setting. Finally, we get a relative version of Fukaya's theorem about quotient spaces under Gromov--Hausdorff equivariant convergence and a version of Grove-Petersen--Wu's finiteness theorem for stratified spaces.

A Dold-Kan Equivalence for Crossed Simplicial Groups
Atabey Kaygun, Haydar Can Kaya
https://arxiv.org/abs/2402.19291 https://arxiv.or…

A Dold-Kan Equivalence for Crossed Simplicial Groups
Using coinduction and restriction functors, we construct a Dold-Kan type equivalence for crossed simplicial groups. We first show that the original Dold-Kan equivalence is given by an adjoint pair of coinduction and restriction functors. Then we show that the category of simplicial vector spaces and the category of representations of a crossed simplicial group are similarly equivalent as model categories.

This https://arxiv.org/abs/2404.17116 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Topological remarks on end and edge-end spaces
The notion of ends in an infinite graph $G$ might be modified if we consider them as equivalence classes of infinitely edge-connected rays, rather than equivalence classes of infinitely (vertex-)connected ones. This alternative definition yields to the edge-end space $Ω_E(G)$ of $G$, in which we can endow a natural (edge-)end topology. For every graph $G$, this paper proves that $Ω_E(G)$ is homeomorphic to $Ω(H)$ for some possibly another graph $H$, where $Ω(H)$ denotes its usual end space.…

Learning Equivalence Relations on Polish Spaces
Dino Rossegger, Theodore Slaman, Tomasz Steifer
https://arxiv.org/abs/2403.17493 https://

Learning Equivalence Relations on Polish Spaces
We investigate natural variations of behaviourally correct learning and explanatory learning -- two learning paradigms studied in algorithmic learning theory -- that allow us to ``learn'' equivalence relations on Polish spaces. We give a characterization of the learnable equivalence relations in terms of their Borel complexity and show that the behaviorally correct and explanatory learnable equivalence relations coincide both in uniform and non-uniform versions of learnability and provide a cha…

This https://arxiv.org/abs/2401.02393 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A PDE approach for solving the characteristic function of the generalised signature process
The signature of a path, as a fundamental object in Rough path theory, serves as a generating function for non-commutative monomials on path space. It transforms the path into a grouplike element in the tensor algebra space, summarising the path faithfully up to a generalised form of re-parameterisation (a negligible equivalence class in this context). Our paper concerns stochastic processes and studies the characteristic function of the path signature of the stochastic process. In contrast to …

This https://arxiv.org/abs/2311.04043 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Gaitsgory's central functor and the Arkhipov-Bezrukavnikov equivalence in mixed characteristic
We show that the nearby cycles functor for the $p$-adic Hecke stack at parahoric level is perverse t-exact, by developing a theory of Wakimoto filtrations at Iwahori level, and that it lifts to the $\mathbb{E}_1$-center. We apply these tools to construct the Arkhipov--Bezrukavnikov functor for $p$-adic affine flag varieties at Iwahori level, and prove that it is an equivalence for type $A$ groups.

Kuroda's Translation for Higher-Order Logic
Thomas Traversi\'e (MICS, DEDUCTEAM)
https://arxiv.org/abs/2404.19503 https://arx…

Kuroda's Translation for Higher-Order Logic
In 1951, Kuroda defined an embedding of classical first-order logic into intuitionistic logic, such that a formula and its translation are equivalent in classical logic. Recently, Brown and Rizkallah extended this translation to higher-order logic, but did not prove the classical equivalence, and showed that the embedding fails in the presence of functional extensionality. We prove that functional extensionality and propositional extensionality are sufficient to derive the classical equivalence…

Gnosis
#Javascript #trinity

Fray functors and equivalence of colored HOMFLYPT homologies
Luke Conners
https://arxiv.org/abs/2405.00875 https://arxiv.org/pdf/2405…

Fray functors and equivalence of colored HOMFLYPT homologies
We construct several families of functors on the homotopy category of singular Soergel bimodules that mimic cabling and insertion of column-colored projectors. We use these functors to identify the intrinsically-colored homology of Webster--Williamson and the projector-colored homology of Elias--Hogancamp for an arbitrary link, up to multiplication by a polynomial in the quantum degree $q$. Combined with the results of arXiv:2303.16271, this establishes parity results for the intrinsic column-c…

Equivalence Checking of Parameterised Quantum Circuits
Xin Hong, Wei-Jia Huang, Wei-Chen Chien, Yuan Feng, Min-Hsiu Hsieh, Sanjiang Li, Mingsheng Ying
https://arxiv.org/abs/2404.18456

Equivalence Checking of Parameterised Quantum Circuits
Parameterised quantum circuits (PQCs) hold great promise for demonstrating quantum advantages in practical applications of quantum computation. Examples of successful applications include the variational quantum eigensolver, the quantum approximate optimisation algorithm, and quantum machine learning. However, before executing PQCs on real quantum devices, they undergo compilation and optimisation procedures. Given the inherent error-proneness of these processes, it becomes crucial to verify th…

This https://arxiv.org/abs/2403.07348 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Linear and smooth oriented equivalence of orthogonal representations of finite groups
Let $n\le 5$ be an integer, and let $Γ$ be a finite group. We prove that if $ρ, ρ': Γ\to O(n)$ are two representations that are conjugate by an orientation-preserving diffeomorphism, then they are conjugate by an element of $SO(n)$. In the process, we prove that if $G \subset O(4)$ is a finite group, then exactly one of the following is true: the elements of $G$ have a common invariant $1$-dimensional subspace in $\mathbb{R}^4$; some element of $G$ has no invariant $1$-dimensional subspace;…

This https://arxiv.org/abs/2208.10256 has been replaced.
link: https://scholar.google.com/scholar?q=a

Information-Theoretic Equivalence of Entropic Multi-Marginal Optimal Transport: A Theory for Multi-Agent Communication
In this paper, we propose our information-theoretic equivalence of entropic multi-marginal optimal transport (MOT). This equivalence can be easily reduced to the case of entropic optimal transport (OT). Because OT is widely used to compare differences between knowledge or beliefs, we apply this result to the communication between agents with different beliefs. Our results formally prove the statement that entropic OT is information-theoretically optimal given by Wang et al. [2020] and generaliz…

This https://arxiv.org/abs/2208.06281 has been replaced.
link: https://scholar.google.com/scholar?q=a

Bicategories of Action Groupoids
We prove that the 2-category of action Lie groupoids localised in the following three different ways yield equivalent bicategories: localising at equivariant weak equivalences à la Pronk, localising using surjective submersive equivariant weak equivalences and anafunctors à la Roberts, and localising at all weak equivalences. These constructions generalise the known case of representable orbifold groupoids. We also show that any weak equivalence between action Lie groupoids is isomorphic to t…

A sharp Sobolev trace inequality of order four on three-balls
Xuezhang Chen, Shihong Zhang
https://arxiv.org/abs/2403.00380 https://a…

A sharp Sobolev trace inequality of order four on three-balls
We establish a fourth order sharp Sobolev trace inequality on three-balls, and its equivalence to a third order sharp Sobolev inequality on two-spheres.

Effective Categorical Enumerative Invariants
Andrei Caldararu, Junwu Tu
https://arxiv.org/abs/2404.01499 https://arxiv.org/pdf/2404.0…

Effective Categorical Enumerative Invariants
We introduce enumerative invariants $F_{g,n}$ $(g\geq0$, $n \geq 1)$ associated to a cyclic $A_\infty$ algebra and a splitting of its non-commutative Hodge filtration. These invariants are defined by explicitly computable Feynman sums, and encode the same information as Costello's partition function of the corresponding field theory. Our invariants are stable under Morita equivalence, and therefore can be associated to a Calabi-Yau category with splitting data. This justifies the name categor…

This https://arxiv.org/abs/2310.09539 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

On the canonical equivalence between Jordan and Einstein frames
A longstanding issue is the classical equivalence between the Jordan and the Einstein frames, which is considered just a field redefinition of the metric tensor and the scalar field. In this work, based on the previous result that the Hamiltonian transformations from the Jordan to the Einstein frame are not canonical on the extended phase space, we study the possibility of the existence of canonical transformations. We show that on the reduced phase space -- defined by suitable gauge fixing of …

This https://arxiv.org/abs/2402.11644 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Grothendieck's theory of fibred categories for monoids
The aim of this paper is to interpret the Grothendieck construction in the monoidal world. That is to say, we restrict the equivalence between fibred categories and pseudo functors to the case of categories having only a single object. On other way of expressing this is to say that we are given a monoid homomorphism. Though only a specialisation, we discover many pleasant results and interpret many things in a new light. We also touch upon the case of finite groups as an example.

This https://arxiv.org/abs/2110.05388 has been replaced.
link: https://scholar.google.com/scholar?q=a

Quantitative Equality in Substructural Logic via Lipschitz Doctrines
Substructural logics naturally support a quantitative interpretation of formulas, as they are seen as consumable resources. Distances are the quantitative counterpart of equivalence relations: they measure how much two objects are similar, rather than just saying whether they are equivalent or not. Hence, they provide the natural choice for modelling equality in a substructural setting. In this paper, we develop this idea, using the categorical language of Lawvere's doctrines. We work in a mini…

This https://arxiv.org/abs/2310.16244 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Derived Satake category and Affine Hecke category in mixed characteristics
We construct a new affine Grassmannian which connects an equal characteristic affine Grassmannian and Zhu's Witt vector affine Grassmannian. As a result, we deduce the mixed characteristic version of the Bezrukavnikov-Finkelberg's derived Satake equivalence. By the same argument, we also obtain the mixed characteristic version of the Bezrukavnikov's equivalence between two categorifications of an affine Hecke algebra.

Effective Categorical Enumerative Invariants
Andrei Caldararu, Junwu Tu
https://arxiv.org/abs/2404.01499 https://arxiv.org/pdf/2404.0…

Effective Categorical Enumerative Invariants
We introduce enumerative invariants $F_{g,n}$ $(g\geq0$, $n \geq 1)$ associated to a cyclic $A_\infty$ algebra and a splitting of its non-commutative Hodge filtration. These invariants are defined by explicitly computable Feynman sums, and encode the same information as Costello's partition function of the corresponding field theory. Our invariants are stable under Morita equivalence, and therefore can be associated to a Calabi-Yau category with splitting data. This justifies the name categor…

This https://arxiv.org/abs/2312.16072 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Strong Nielsen equivalence on the punctured disc
Let $f$ be an orientation-preserving homeomorphism of the 2-disc $\mathbb{D}^2$ that fixes the boundary pointwise and leaves invariant a finite subset in the interior of $\mathbb{D}^2$. We study the strong Nielsen equivalence of periodic points of such homeomorphisms $f$ and we give a necessary and sufficient condition for two periodic points to be strong Nielsen equivalent in the context of braid theory. In addition, we present an application of our result to the trace formula given by Jiang--…

Equivalence between validity of the $p$-Poincar\'e inequality and finiteness of the strict $p$-capacitary inradius
A. -K. Gallagher
https://arxiv.org/abs/2404.19207 https://arxiv.org/pdf/2404.19207
arXiv:2404.19207v1 Announce Type: new
Abstract: It is shown that the $p$-Poincar\'e inequality holds on an open set $\Omega$ in $\mathbb{R}^n$ if and only if the strict $p$-capacitary inradius of $\Omega$ is finite. To that end, new upper and lower bounds for the infimum for the associated nonlinear Rayleigh quotients are derived.

Relativized universal algebra via partial Horn logic
Yuto Kawase
https://arxiv.org/abs/2403.19661 https://arxiv.org/pdf/2403.19661

Relativized universal algebra via partial Horn logic
Algebraic theories, sometimes called equational theories, are syntactic notions given by finitary operations and equations, such as monoids, groups, and rings. There is a well-known category-theoretic treatment of them that algebraic theories are equivalent to finitary monads on $\mathbf{Set}$. In this paper, using partial Horn theories, we syntactically generalize such an equivalence to arbitrary locally presentable categories from $\mathbf{Set}$; the corresponding algebraic concepts relative …

VERT: Verified Equivalent Rust Transpilation with Few-Shot Learning
Aidan Z. H. Yang, Yoshiki Takashima, Brandon Paulsen, Josiah Dodds, Daniel Kroening
https://arxiv.org/abs/2404.18852

VERT: Verified Equivalent Rust Transpilation with Few-Shot Learning
Rust is a programming language that combines memory safety and low-level control, providing C-like performance while guaranteeing the absence of undefined behaviors by default. Rust's growing popularity has prompted research on safe and correct transpiling of existing code-bases to Rust. Existing work falls into two categories: rule-based and large language model (LLM)-based. While rule-based approaches can theoretically produce correct transpilations that maintain input-output equivalence to t…

This https://arxiv.org/abs/2402.07696 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Synthesizing Strongly Equivalent Logic Programs: Beth Definability for Answer Set Programs via Craig Interpolation in First-Order Logic
We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs $P$ and $Q$ and vocabulary $V$ (set of predicates) the existence of a program $R$ in $V$ such that $P \cup R$ and $P \cup Q$ are strongly equivalent can be expressed as a first-order entailment. Moreover, our result is effective: A program $R$ can be constructed from a Craig interpolant for this entailment, using a known first-order encoding for testing strong equivalence, whic…

This https://arxiv.org/abs/2304.03007 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Classification of lattice triangles by their two smallest widths
We introduce the notion of the second lattice width of a lattice polytope and use this to classify lattice triangles by their width and second width. This is equivalent to classifying lattice triangles contained in a given rectangle (and no smaller rectangle) up to affine equivalence. Using this classification we investigate the automorphism groups and Ehrhart theory of lattice triangles. We also show that the sequence counting lattice triangles contained in dilations of the unit square has gen…

This https://arxiv.org/abs/2303.08267 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Koszul duality for Coxeter groups
We construct a "Koszul duality" equivalence relating the (diagrammatic) Hecke category attached to a Coxeter system and a given realization to the Hecke category attached to the same Coxeter system and the dual realization. This extends a construction of Beilinson-Ginzburg-Soergel and Bezrukavnikov-Yun in a geometric context, and of the first author with Achar, Makisumi and Williamson. As an application, we show that the combinatorics of the "tilting perverse sheaves" considered in arXiv:1802.0…

On Affinely Homogeneous Submanifolds: The Power Series Method of Equivalence
Julien HeydLM-Orsay, Joel MerkerLM-Orsay
https://arxiv.org/abs/2402.18437 http…

On Affinely Homogeneous Submanifolds: The Power Series Method of Equivalence
We determine all affinely homogeneous models for surfaces $S^2 \subset \mathbb{R}^4$, including the simply transitive models. We employ an improved power series method of equivalence, which captures invariants at the origin, creates branches, and infinitesimalizes calculations. We find several inequivalent terminal branches yielding each to some nonempty moduli space of homogeneous models, sometimes parametrized by a certain invariant algebraic variety. Three main features may be emphasized: 1)…

Relativized universal algebra via partial Horn logic
Yuto Kawase
https://arxiv.org/abs/2403.19661 https://arxiv.org/pdf/2403.19661

Relativized universal algebra via partial Horn logic
Algebraic theories, sometimes called equational theories, are syntactic notions given by finitary operations and equations, such as monoids, groups, and rings. There is a well-known category-theoretic treatment of them that algebraic theories are equivalent to finitary monads on $\mathbf{Set}$. In this paper, using partial Horn theories, we syntactically generalize such an equivalence to arbitrary locally presentable categories from $\mathbf{Set}$; the corresponding algebraic concepts relative …

This https://arxiv.org/abs/2304.10763 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finiteness of CAT(0) group actions
We prove some finiteness results for discrete isometry groups $Γ$ of uniformly packed CAT$(0)$-spaces $X$ with uniformly bounded codiameter (up to group isomorphism), and for CAT$(0)$-orbispaces $M = Γ\backslash X$ (up to equivariant homotopy equivalence or equivariant diffeomorphism); these results generalize, in nonpositive curvature, classical finiteness theorems of Riemannian geometry. As a corollary, the order of every torsion subgroup of $Γ$ is bounded above by a universal constant onl…

This https://arxiv.org/abs/2302.11030 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Log $p$-divisible groups and semi-stable representations
Let $\mathscr{O}_K$ be a henselian DVR with field of fractions $K$ and residue field of characteristic $p>0$. Let $S$ denote $\mathop{\mathrm{Spec}} \mathscr{O}_K$ endowed with the canonical log structure. We show that the generic fiber functor $\mathbf{BT}_{S, {\mathrm{d}}}^{\log}\to \mathbf{BT}^{\mathrm{st}}_K$ between the category of dual representable log $p$-divisible groups over $S$ and the category of $p$-divisible groups with semistable reduction over $K$ is an equivalence. If $\mathscr…

Characteristic tilting modules and Ringel duality in the Noetherian world
Tiago Cruz
https://arxiv.org/abs/2405.00729 https://arxiv.o…

Characteristic tilting modules and Ringel duality in the Noetherian world
The foundations of Ringel duality for split quasi-hereditary algebras over commutative Noetherian rings are strengthened. Several descriptions and properties of the smallest resolving subcategory containing all standard modules over split quasi-hereditary algebras over commutative Noetherian rings are provided. In particular, given two split quasi-hereditary algebras $A$ and $B$, we prove that any exact equivalence between the smallest resolving subcategory containing all standard modules ove…

This https://arxiv.org/abs/2312.09408 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Non-Abelian X-Ray Transform on Asymptotically Hyperbolic Spaces
In this paper we formulate and prove a gauge equivalence for connections and Higgs fields of suitable regularity that are mapped to the same function under the non-abelian X-ray transform on nontrapping asymptotically hyperbolic (AH) spaces with negative curvature and no nontrivial twisted conformal Killing tensor fields with certain regularity. If one furthermore fixes such a connection with zero curvature, a corollary provides an injectivity result for the non-abelian X-ray transform over Hig…

This https://arxiv.org/abs/2304.10763 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finiteness of CAT(0) group actions
We prove some finiteness results for discrete isometry groups $Γ$ of uniformly packed CAT$(0)$-spaces $X$ with uniformly bounded codiameter (up to group isomorphism), and for CAT$(0)$-orbispaces $M = Γ\backslash X$ (up to equivariant homotopy equivalence or equivariant diffeomorphism); these results generalize, in nonpositive curvature, classical finiteness theorems of Riemannian geometry. As a corollary, the order of every torsion subgroup of $Γ$ is bounded above by a universal constant onl…

Characteristic tilting modules and Ringel duality in the Noetherian world
Tiago Cruz
https://arxiv.org/abs/2405.00729 https://arxiv.o…

Characteristic tilting modules and Ringel duality in the Noetherian world
The foundations of Ringel duality for split quasi-hereditary algebras over commutative Noetherian rings are strengthened. Several descriptions and properties of the smallest resolving subcategory containing all standard modules over split quasi-hereditary algebras over commutative Noetherian rings are provided. In particular, given two split quasi-hereditary algebras $A$ and $B$, we prove that any exact equivalence between the smallest resolving subcategory containing all standard modules ove…

Prismatic $F$-Gauges and Fontaine--Laffaille modules
Gleb Terentiuk, Vadim Vologodsky, Yujie Xu
https://arxiv.org/abs/2402.17755 https://

Prismatic $F$-Gauges and Fontaine--Laffaille modules
Let $k$ be a perfect field of characteristic $p$ and $W(k)$ its ring of Witt vectors. We construct an equivalence of categories between the full subcategory of the derived category of quasi-coherent sheaves on the syntomification of $W(k)$ spanned by objects whose Hodge-Tate weights are between $[0,p-2]$ and an appropriate derived category of Fontaine-Laffaille modules.

This https://arxiv.org/abs/1706.04417 has been replaced.
link: https://scholar.google.com/scholar?q=a

On derived equivalence for Abuaf flop: mutation of non-commutative crepant resolutions and spherical twists
Recently, Segal constructed a derived equivalence for an interesting 5-fold flop that was provided by Abuaf. The aim of this article is to add some results for the derived equivalence for Abuaf's flop. Concretely, we study the equivalence for Abuaf's flop by using Toda-Uehara's tilting bundles and Iyama-Wemyss's mutation functors. In addition, we observe a "flop-flop=twist" result and a "multi-mutation=twist" result for Abuaf's flop.

On the Galois module structure of minus class groups
Cornelius Greither, Takenori Kataoka
https://arxiv.org/abs/2404.11823 https://ar…

On the Galois module structure of minus class groups
The main object of this paper is the minus class groups associated to CM-fields as Galois modules. In a previous article of the authors, we introduced a notion of equivalence for modules and determined the equivalence classes of the minus class groups. In this paper, we show a concrete application of this result. We also study how large a proportion of equivalence classes can be realized as classes of minus class groups.

Proving Behavioural Apartness
Ruben Turkenburg, Harsh Beohar, Clemens Kupke, Jurriaan Rot
https://arxiv.org/abs/2404.16588 https://ar…

Proving Behavioural Apartness
Bisimilarity is a central notion for coalgebras. In recent work, Geuvers and Jacobs suggest to focus on apartness, which they define by dualising coalgebraic bisimulations. This yields the possibility of finite proofs of distinguishability for a wide variety of state-based systems. We propose behavioural apartness, defined by dualising behavioural equivalence rather than bisimulations. A motivating example is the subdistribution functor, where the proof system based on bisimilarity requires a…

A model for the coherent walking $\omega$-equivalence
Amar Hadzihasanovic, F\'elix Loubaton, Viktoriya Ozornova, Martina Rovelli
https://arxiv.org/abs/2404.14509

A model for the coherent walking $ω$-equivalence
We prove that a certain $ω$-category, which was constructed in previous work by the third and fourth author, is a model for the fully coherent walking $ω$-equivalence. Further, appropriate truncations of it give models for the fully coherent walking $n$-equivalence for each $n\geq1$.

This https://arxiv.org/abs/1810.05991 has been replaced.
link: https://scholar.google.com/scholar?q=a

Invariance of non-vanishing of first $l^p$-cohomology under $L^q$-Measured Equivalence
The first $l^p$-cohomology is an algebro-analytical object attached to a finitely generated discrete group and introduced by M. Gromov. It is well known that it is invariant under quasi-isometry. In this article, we prove that the non-vanishing of the first $l^p$-cohomology of a non-amenable group is invariant under $L^q$-Measured Equiavalence (an equivalence relation introduced by Gromov), where $q\geq p$. We also discuss many applications of this result. We prove that for hyperbolic (in the s…

Character Sheaves on Reductive Lie Algebras in Positive Characteristic
Tong Zhou
https://arxiv.org/abs/2404.19210 https://arxiv.org/p…

Character Sheaves on Reductive Lie Algebras in Positive Characteristic
We prove a microlocal characterisation of character sheaves on a reductive Lie algebra over an algebraically closed field of sufficiently large positive characteristic: a perverse irreducible G-equivariant sheaf is a character sheaf if and only if it has nilpotent singular support and is quasi-admissible. We also present geometric proofs, in positive characteristic, of the equivalence between being admissible and being a character sheaf, and various characterisations of cuspidal sheaves, follow…

Character Sheaves on Reductive Lie Algebras in Positive Characteristic
Tong Zhou
https://arxiv.org/abs/2404.19210 https://arxiv.org/p…

Character Sheaves on Reductive Lie Algebras in Positive Characteristic
We prove a microlocal characterisation of character sheaves on a reductive Lie algebra over an algebraically closed field of sufficiently large positive characteristic: a perverse irreducible G-equivariant sheaf is a character sheaf if and only if it has nilpotent singular support and is quasi-admissible. We also present geometric proofs, in positive characteristic, of the equivalence between being admissible and being a character sheaf, and various characterisations of cuspidal sheaves, follow…