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c5e98418c0bfb8fc73a6d7a2084ee2a6e56ffd0a292fa1c9e78798cd1ef176da | 2026-01-07T00:00:00-05:00 | Boundary operators in the Brownian loop soup | arXiv:2601.02755v1 Announce Type: new Abstract: We obtain infinitely many boundary operators in the Brownian loop soup in the subcritical phase by analyzing the conformal block expansion of the two-point function that computes the probability of having two marked points on the upper half-plane being separated by Browni... | https://arxiv.org/abs/2601.02755 | Academic Papers | svg |
7e4b330f8aeba298b44f83ee0ecc8ee2a916b53d030caeb411de0158cce7aacd | 2026-01-07T00:00:00-05:00 | The automorphism groups of generalized Kausz compactifications and spaces of complete collineations | arXiv:2601.02768v1 Announce Type: new Abstract: In this paper, we determine the automorphism groups of generalized Kausz compactifications $\mathcal T_{s,p,n}$. By establishing the (semi-)positivity of the anticanonical bundles of $\mathcal T_{s,p,n}$, we also determine the automorphism groups of generalized spaces of ... | https://arxiv.org/abs/2601.02768 | Academic Papers | svg |
e537fe73f04e0684e1673ff9841483f7ecc39548efc8cf968a3273125d2dd684 | 2026-01-07T00:00:00-05:00 | On rates of convergence in central limit theorems of Selberg and Bourgade | arXiv:2601.02781v1 Announce Type: new Abstract: Based on the recent works of Radziwill-Soundararajan and Roberts, we establish a rate of convergence in Bourgade's central limit theorem for shifted Dirichlet $L$-functions. Our results also indicate that the dependence structure in the components of a random vector could... | https://arxiv.org/abs/2601.02781 | Academic Papers | svg |
91da5c97877bbdf99cadacfc147058956988cec1069fa4e0730940ee6de0b33d | 2026-01-07T00:00:00-05:00 | Minimal Sets of Involution Generators for Big Mapping Class Groups | arXiv:2601.02784v1 Announce Type: new Abstract: Let $S(n)$, for $n \in \mathbb{N}$, be the infinite-type surface of infinite genus with $n$ ends, each of which is accumulated by genus. The mapping class groups of these types of surfaces are not countably generated. However, they are Polish groups, so they can be topolo... | https://arxiv.org/abs/2601.02784 | Academic Papers | svg |
aeb6893195ce3f269932d1fc60eebabccd9af7ec83d7398327f9d07211bc5699 | 2026-01-07T00:00:00-05:00 | Approximate Birkhoff-James orthogonality preserver on Lebesgue-Bochner spaces | arXiv:2601.02786v1 Announce Type: new Abstract: In this article, we examine an approximate version of Koldobsky-Blanco-Turn\v{s}ek theorem (namely, Property P) in the space of vector-valued integrable functions. More precisely, we prove that the Lebesgue-Bochner spaces $L^p(\mu,X),\;(1\leq p<\infty)$, do not have Prope... | https://arxiv.org/abs/2601.02786 | Academic Papers | svg |
9cfef55e7f19eb5366bc173412f72e5cabca756663d7dcfeb5f651ba290a57d5 | 2026-01-07T00:00:00-05:00 | On Liouiville Type Theorem for the 3D Isentropic Navier-Stokes System without D-condition | arXiv:2601.02791v1 Announce Type: new Abstract: In this paper, we establish Liouville-type theorems for the steady compressible Navier-Stokes system. Assuming a smooth solution \(u \in L^p(\mathbb{R}^3)\), \(3 \le p \le \frac{9}{2}\), with bounded density, one obtains \(u \equiv0\). This generalizes the result of Li-Yu... | https://arxiv.org/abs/2601.02791 | Academic Papers | svg |
67804c32563a4ae7d3a95d98232126f1183b8314b00d0beb2a657875a28b08e9 | 2026-01-07T00:00:00-05:00 | Adapting Polyhedral Dominance Cones to Ordinal Preference Structures | arXiv:2601.02796v1 Announce Type: new Abstract: In combinatorial optimization, ordinal costs can be used to model the quality of elements whenever numerical values are not available. When considering, for example, routing problems for cyclists, the safety of a street can be ranked in ordered categories like safe (separ... | https://arxiv.org/abs/2601.02796 | Academic Papers | svg |
05b6f16a0e46d4a90e1fe0a05ed8510e3155abf1c9e848e95aab6738a9d1b741 | 2026-01-07T00:00:00-05:00 | Log-Polynomial Optimization | arXiv:2601.02797v1 Announce Type: new Abstract: We study an optimization problem in which the objective is given as a sum of logarithmic-polynomial functions. This formulation is motivated by statistical estimation principles such as maximum likelihood estimation, and by loss functions including cross-entropy and Kullb... | https://arxiv.org/abs/2601.02797 | Academic Papers | svg |
2f825ddc4bb808d236cc89e4cc736f5aa1a7dd1f78edaa6bf90cbdfe66f5313f | 2026-01-07T00:00:00-05:00 | An extended symmetric union with multiple tangle regions and its Alexander polynomial | arXiv:2601.02800v1 Announce Type: new Abstract: The authors recently introduced a new construction of a knot as an extended symmetric union of a knot with a single tangle region. In this paper, we generalize the construction to include multiple tangle regions. The constructed knot $K$ with a partial knot $\hat{K}$ and ... | https://arxiv.org/abs/2601.02800 | Academic Papers | svg |
9e135923d14a2527fbfeb5020c1b309221309cdac1e2c9c61743053f44fed7bb | 2026-01-07T00:00:00-05:00 | Diffusion on homogeneous ultrametric spaces: the contributions of Alessandro Fig\`a-Talamanca | arXiv:2601.02809v1 Announce Type: new Abstract: Alessandro Fig\`a-Talamanca (1938-2023) was an influential Italian mathematician, scientific leader of the Italian group of harmonic analysis for many years. Since the late 1970ies, his interest focussed on harmonic analysis on free groups and trees. In the later years of... | https://arxiv.org/abs/2601.02809 | Academic Papers | svg |
e7a3c1c9ecf04fa2e387687f2e13f4430daa94f5af05c0dedc36b5bb79e39f7e | 2026-01-07T00:00:00-05:00 | Decision-Theoretic Robustness for Network Models | arXiv:2601.02811v1 Announce Type: new Abstract: Bayesian network models (Erdos Renyi, stochastic block models, random dot product graphs, graphons) are widely used in neuroscience, epidemiology, and the social sciences, yet real networks are sparse, heterogeneous, and exhibit higher-order dependence. How stable are net... | https://arxiv.org/abs/2601.02811 | Academic Papers | svg |
24481205a3555ecb378e2a14b4f8ebd4f9c983a5c3332e3b6f310ecb2bbf3e14 | 2026-01-07T00:00:00-05:00 | An introduction of Berezin sectorial operators and its application to Berezin number inequalities | arXiv:2601.02817v1 Announce Type: new Abstract: We introduce a new class of operators, called Berezin sectorial operators, which generalizes classical sectorial operators. We provide examples on the Hardy-Hilbert space showing that there exist operators that are Berezin sectorial but not sectorial and that the Berezin ... | https://arxiv.org/abs/2601.02817 | Academic Papers | svg |
33730baaf3a5ca0519cb3252acf1dcd5c382bb5ff143a95b84372300edee925e | 2026-01-07T00:00:00-05:00 | Effective Disjunction and Effective Interpolation in Suffciently Strong Proof Systems | arXiv:2601.02821v1 Announce Type: new Abstract: In this article, we deal with the uniform effective disjunction property and the uniform effective interpolation property, which are weaker versions of the classical effective disjunction property and the effective interpolation property.\\ The main result of the paper is... | https://arxiv.org/abs/2601.02821 | Academic Papers | svg |
2b47d1bfea3ad99d84646ab315509f0dd0db52a3513183fadd6d19d2b51eaf04 | 2026-01-07T00:00:00-05:00 | Collapsed Structured Block Models for Community Detection in Complex Networks | arXiv:2601.02828v1 Announce Type: new Abstract: Community detection seeks to recover mesoscopic structure from network data that may be binary, count-valued, signed, directed, weighted, or multilayer. The stochastic block model (SBM) explains such structure by positing a latent partition of nodes and block-specific edg... | https://arxiv.org/abs/2601.02828 | Academic Papers | svg |
5131fd500d9811e8c866bdea65ad3a28b94d98654f41ab2506a626dbacefcdbd | 2026-01-07T00:00:00-05:00 | Varadhan Functions, Variances, and Means on Compact Riemannian Manifolds | arXiv:2601.02832v1 Announce Type: new Abstract: Motivated by Varadhan's theorem, we introduce Varadhan functions, variances, and means on compact Riemannian manifolds as smooth approximations to their Fr\'echet counterparts. Given independent and identically distributed samples, we prove uniform laws of large numbers f... | https://arxiv.org/abs/2601.02832 | Academic Papers | svg |
3c1a3685ec87841ad004061a0df7febe1ad3ffa20debb8d8dce08e5337d67db4 | 2026-01-07T00:00:00-05:00 | Une br\`eve histoire des perturbations non-hermitiennes de rang un | arXiv:2601.02834v1 Announce Type: new Abstract: Les perturbations de faible rang de matrices al\'eatoires ont \'et\'e au c{\oe}ur de nombreux travaux ces vingt derni\`eres ann\'ees. En particulier, les cas non-hermitiens, moins repr\'esent\'es dans la litt\'erature en r\`egle g\'en\'erale, font ici l'objet d'une attent... | https://arxiv.org/abs/2601.02834 | Academic Papers | svg |
656bdd2f485fb400ee8075bc5566a2c7955c9429fe4059770f093cf9b6165e13 | 2026-01-07T00:00:00-05:00 | Quantum isometry groups of log-Laplacians on Cuntz--Krieger algebras | arXiv:2601.02835v1 Announce Type: new Abstract: We compute the quantum isometry groups of Cuntz--Krieger algebras endowed with the spectral triples coming from the Ahlfors regular structure of the underlying topological Markov chain. This allows us to exhibit a new family of compact quantum groups, mixing features from... | https://arxiv.org/abs/2601.02835 | Academic Papers | svg |
6fcb7bbd38e34556c24afe01046d07491cbcac14d16f6bfacec519d4c9a4b349 | 2026-01-07T00:00:00-05:00 | Data-Driven Modeling of Global Bifurcations and Chaos in a Mechanical System under Delayed and Quantized Control | arXiv:2601.02838v1 Announce Type: new Abstract: We illustrate how the recent theory of Spectral Submanifolds (SSM) can capture global bifurcations and complex dynamics in mechanical systems even under delay and spatial discretization. Specifically, we build a parameter-dependent SSM-reduced model that predicts global h... | https://arxiv.org/abs/2601.02838 | Academic Papers | svg |
ff585903d326b09418fac1c1cb085944040585cc15cf8fdbb5fd025520cad6c6 | 2026-01-07T00:00:00-05:00 | Large-scale geometry of graphs interpolating between curve graphs and pants graphs | arXiv:2601.02839v1 Announce Type: new Abstract: We study two types of graphs interpolating between the curve graph and the pants graph from the viewpoint of large-scale geometry. One was introduced by Erlandsson and Fanoni, and the other by Mahan Mj. These graphs were developed independently in different contexts. In t... | https://arxiv.org/abs/2601.02839 | Academic Papers | svg |
e916abf198ea8c4e456c7ea4177609d0ba8bc806e196b027cf7478a5b74f50d9 | 2026-01-07T00:00:00-05:00 | Constructing $\lambda$-Angenent curve by flow method | arXiv:2601.02853v1 Announce Type: new Abstract: Using a modified curve shortening flow, we construct $\lambda$-Angenent curve, which was first constructed by the shooting method. | https://arxiv.org/abs/2601.02853 | Academic Papers | svg |
6e096ff023f368db7421b7420c536c596a1237b2ae2938e27506719055554a8d | 2026-01-07T00:00:00-05:00 | Higher order H{\"o}lder approximation by solutions of second order elliptic equations | arXiv:2601.02859v1 Announce Type: new Abstract: For a given second order elliptic operation $\mathcal{L}$ in a domain $\Omega\subset{\mathbb{R}}^\mathbf{N}$, $\mathbf{N}\ $, and a compact set $\mathbf{K}\subset\Omega$, order $\mathbf{N}$-$2$-Ahlfors-David regular, we define the space $\mathcal{H}^{\mathbf{r}+\omega}_{\... | https://arxiv.org/abs/2601.02859 | Academic Papers | svg |
cbc8e8c6e054338a49e0cac2897a2590bdb639c251246a6205190c3bf3a5d785 | 2026-01-07T00:00:00-05:00 | Morse index of min-max stationary integral varifolds | arXiv:2601.02860v1 Announce Type: new Abstract: We prove an upper bound for the Morse index of min-max stationary integral varifolds realizing the $d$-dimensional $p$-width of a closed Riemannian manifold. | https://arxiv.org/abs/2601.02860 | Academic Papers | svg |
16f1d0d4e0b48643cdc92eb3a8803c037fa914b83dd8f391a6e31020d76c2897 | 2026-01-07T00:00:00-05:00 | Global H\"{o}lder Solvability of parabolic equations on domains with capacity density conditions | arXiv:2601.02863v1 Announce Type: new Abstract: We investigate the Cauchy-Dirichlet problem for linear parabolic equations in divergence form. Under mild assumptions on the source term and the domain, we prove the existence of globally H\"{o}lder continuous solutions. Notably, our results accommodate data exhibiting si... | https://arxiv.org/abs/2601.02863 | Academic Papers | svg |
5f5742dd1c76adc3baf8eb37da3fd4cc383255fc503a78c5306cf58dbc36ee79 | 2026-01-07T00:00:00-05:00 | New biorthogonal sequences generated by index integrals of the weight functions | arXiv:2601.02866v1 Announce Type: new Abstract: We exhibit new biorthogonal sequences generated by index integrals of the squares of the modified Bessel functions and gamma functions. The composition orthogonality, involving differential operators is employed. Generalized Wilson polynomials are introduced. Some propert... | https://arxiv.org/abs/2601.02866 | Academic Papers | svg |
e44ae5161f58a3c4665e4778de6e7c5a0bee4211ef5d95e2a417b2b7c4d698a9 | 2026-01-07T00:00:00-05:00 | The W-Operator: A Volterra Fractional Time Operator with Non-Bernstein Symbol | arXiv:2601.02876v1 Announce Type: new Abstract: We introduce a new two-parameter fractional time operator with Volterra structure, denoted by the W-operator, defined through a generalized Laplace symbol. The operator preserves the Caputo-type high-frequency behavior while allowing a controlled modification of the low-f... | https://arxiv.org/abs/2601.02876 | Academic Papers | svg |
f07df46536d7ed269622d34a1c8f2c11b2895c3843742fa1e9fa9376cecfe8ce | 2026-01-07T00:00:00-05:00 | Constructing Cospectral Vertices Through Orbits of Subgraphs | arXiv:2601.02892v1 Announce Type: new Abstract: A constructive method is given for obtaining cospectral vertices in undirected graphs, along with an operation that preserves this construction. We prove that the construction yields cospectral vertices, as well as strongly cospectral vertices under additional conditions.... | https://arxiv.org/abs/2601.02892 | Academic Papers | svg |
2d0be67941feec74d9299abf69cea590f995e6be1e89737ff64177ecc1b426d0 | 2026-01-07T00:00:00-05:00 | Rational-Kernel Fractional Evolution Equations with Almost Sectorial Operators: A Resolvent Framework Unifying ABC and W Dynamics | arXiv:2601.02894v1 Announce Type: new Abstract: We study fractional evolution equations driven by rational-kernel time operators with non-singular memory, including the Atangana-Baleanu-Caputo operator and a generalized W-operator. These operators are characterized by Laplace symbols that do not necessarily belong to t... | https://arxiv.org/abs/2601.02894 | Academic Papers | svg |
9442a3b9983da52a5eb07b89c6a25855b426aa4ae98ce86145878be3e29335d0 | 2026-01-07T00:00:00-05:00 | Homotopical algebra of Lie-Rinehart pairs | arXiv:2601.02895v1 Announce Type: new Abstract: Dwyer-Kan localization at pairs of quasi-isomorphisms of the category of dg Lie-Rinehart pairs $(A,M)$, where $A$ is a semi-free cdga over a field $k$ of characteristic zero and $M$ a cell complex in $A$-modules, is shown to be equivalent to that of strong homotopy Lie-Ri... | https://arxiv.org/abs/2601.02895 | Academic Papers | svg |
c402b3fb593ad2b8f473c4b15d55f102c9240fcf9264770861d34d4041b45ada | 2026-01-07T00:00:00-05:00 | Relating Checkpoint Update Probabilities to Momentum Parameters in Single-Loop Variance Reduction Methods | arXiv:2601.02899v1 Announce Type: new Abstract: Variance reduction (VR) is a crucial tool for solving finite-sum optimization problems, including the composite general convex setting, which is the focus of this work. On the one hand, denoting the number of component functions as $n$ and the target accuracy as $\epsilon... | https://arxiv.org/abs/2601.02899 | Academic Papers | svg |
0f416996c44894a8ee597d2847d25a044fdd2bdf5fc269322e3746444ce115df | 2026-01-07T00:00:00-05:00 | The 2-systole on compact K\"ahler surfaces with positive scalar curvature | arXiv:2601.02901v1 Announce Type: new Abstract: We study the 2-systole on compact K\"ahler surfaces of positive scalar curvature. For any such surface $(X,\omega)$, we prove the sharp estimate \(\min_X S(\omega)\cdot\syst_2(\omega)\le12\pi\), with equality if and only if $X=\PP^2$ and $\omega$ is the Fubini--Study metr... | https://arxiv.org/abs/2601.02901 | Academic Papers | svg |
ad84e38d78e63bc1efc195609d93b531d733a5dd5038320341ad3805cd96e044 | 2026-01-07T00:00:00-05:00 | Inhomogeneous nonlinear Schr\"odinger equations with competing singular nonlinearities | arXiv:2601.02909v1 Announce Type: new Abstract: We study nonlinear elliptic equations arising as stationary states of inhomogeneous nonlinear Schr\"odinger equations with competing singular nonlinearities. Working in a weighted Sobolev space that combines the homogeneous Sobolev space with a weighted Lebesgue term, we ... | https://arxiv.org/abs/2601.02909 | Academic Papers | svg |
330c68525498fcf04a58a9ebb7e2f4b386cffff94d6d865ad11baaefacbf4267 | 2026-01-07T00:00:00-05:00 | Diamond Open Access: The AMR Experiment | arXiv:2601.02910v1 Announce Type: new Abstract: Diamond open access journals charge neither readers nor authors. Despite long-standing support for this ideal within mathematics, relatively few such journals exist. This article documents the Association for Mathematical Research's experience building and operating diamo... | https://arxiv.org/abs/2601.02910 | Academic Papers | svg |
21902fa44663817ed24c4fe7cdc5343ef7fe6d31e4751f6e7dc0ba38765a582b | 2026-01-07T00:00:00-05:00 | Characteristic quasi-polynomials of truncated arrangements | arXiv:2601.02912v1 Announce Type: new Abstract: Given an (affine) integral arrangement $\mathcal{A}$ in $\mathbb{R}^n$, the reduction of $\mathcal{A}$ modulo an arbitrary positive integer $q$ naturally yields an arrangement $\mathcal{A}_q$ in $\mathbb{Z}_q^n$. Our primary objective is to study the combinatorial aspects... | https://arxiv.org/abs/2601.02912 | Academic Papers | svg |
7c301da9c6ed2aa91290a7239aa9b257121b0f55a67ea989a64ca93b85c95085 | 2026-01-07T00:00:00-05:00 | The compositional inverses of some permutation polynomials of the form $x+\gamma\operatorname{Tr}_q^{q^2}(h(x))$ | arXiv:2601.02919v1 Announce Type: new Abstract: Recently, Jiang et al. \cite{JIANG2025102522} obtained several classes of Permutation Polynomial of the form $x+\gamma\operatorname{Tr}_q^{q^2}(h(x))$ over finite fields $\mathbb{F}_{q^2},q=2^n$. In this paper, we find the compositional inverse of six classes of permutati... | https://arxiv.org/abs/2601.02919 | Academic Papers | svg |
03acd3d8c0d3d1e0517c939642a2d5dbdaf4a02388ad50d264a718a0c71104df | 2026-01-07T00:00:00-05:00 | Ramaswami Type translation formulae for the polylogarithm functions | arXiv:2601.02921v1 Announce Type: new Abstract: In 1934, Ramaswami proved a number of curious translation formulae satisfied by the Riemann zeta function. Such translation formulae, in turn give the meromorphic extension of the Riemann zeta function. In 1954, Apostol extended those identities to establish a family of s... | https://arxiv.org/abs/2601.02921 | Academic Papers | svg |
6937b1efcc32dbb8cd058857f9575552637a882b5c5273e50f4a69063898c4df | 2026-01-07T00:00:00-05:00 | Consistency of square bracket partition relation | arXiv:2601.02923v1 Announce Type: new Abstract: Characteristic earlier results were of the form CON$(2^{\aleph_0} \to [\lambda]^2_{n, 2})$, with $2^{\aleph_0} $ an ex-large cardinal, in the best case the first weakly Mahlo cardinal. Characteristic new results are CON$((2^{\aleph_0} = \aleph_m) + \aleph_l \to [\aleph_k]... | https://arxiv.org/abs/2601.02923 | Academic Papers | svg |
ae1098812694085265652e8a4be4b009b66a0a52a786c7f7b7289a554effee73 | 2026-01-07T00:00:00-05:00 | With what probability does an inscribed triangle contain a given point? | arXiv:2601.02929v1 Announce Type: new Abstract: Three points uniformly selected on the unit circle form a triangle containing a point $X$ at distance $r \in [0; 1]$ from its center with probability $P(r) = \frac{1}{4} - \frac{3}{2 \pi^2}\textrm{Li}_2(r^2)$, where $\textrm{Li}_2$ is the dilogarithm function (Jeremy Tan ... | https://arxiv.org/abs/2601.02929 | Academic Papers | svg |
c5a62380cce1cb2deb9aa69f75bbde40fc3c4e8b3e7ed537f0fc03cfe847489d | 2026-01-07T00:00:00-05:00 | Dimension-decaying diffusion processes as the scaling limit of condensing zero-range processes | arXiv:2601.02935v1 Announce Type: new Abstract: In this article, we prove that, on the diffusive time scale, condensing zero-range processes converge to a dimension-decaying diffusion process on the simplex \[ \Sigma = \{(x_1,\dots,x_S) : x_i \ge 0,\; \sum_{i\in S} x_i = 1\}, \] where $S$ is a finite set. This limiting... | https://arxiv.org/abs/2601.02935 | Academic Papers | svg |
8fb76e3a177e0f60992db2e321ae34c251d48fef84b93213852c6ee19022a81a | 2026-01-07T00:00:00-05:00 | On a theorem Dan Rudolph: Part II: Amenable groups | arXiv:2601.02939v1 Announce Type: new Abstract: We prove an analog of Rudolph's theorem for actions of countable amenable groups, which asserts that among invariant measures with entropy at least c on the $G$-shift $(\Lambda^G,\sigma)$, a typical measure has entropy $c$ and is Bernoulli. We also address a relative vers... | https://arxiv.org/abs/2601.02939 | Academic Papers | svg |
58888382a270b8bc2c332aaede791c5e3878a3685b64799b09f3f65f90c5bdc9 | 2026-01-07T00:00:00-05:00 | Rational stable homotopy type of equivariant projective spaces and Grassmannians | arXiv:2601.02940v1 Announce Type: new Abstract: We prove explicit rational stable splittings of equivariant complex projective spaces $\mathbb{C}P(V)$ and Grassmannians $Gr_n(V)$, for complex representations $V$. When $V$ is a sum of one-dimensional representations, both $\mathbb{C}P(V)$ and $Gr_n(V)$ are rationally a ... | https://arxiv.org/abs/2601.02940 | Academic Papers | svg |
a58fadc362ceb58c6f81d156b545b71a13d8789b04957b6a1c239617cc381222 | 2026-01-07T00:00:00-05:00 | Hopfield neural networks as port-Hamiltonian and gradient systems | arXiv:2601.02951v1 Announce Type: new Abstract: The structure of continuous Hopfield networks is revisited from a system-theoretic point of view. After adopting a novel electrical network interpretation involving nonlinear capacitors, it is shown that Hopfield networks admit a port-Hamiltonian formulation provided an e... | https://arxiv.org/abs/2601.02951 | Academic Papers | svg |
65994d3ec30248924b1c91c19bdf746aede554648440494f0f6c6de90d36fe18 | 2026-01-07T00:00:00-05:00 | The left-to-right minima basis of the group algebra of the symmetric group (updated version) | arXiv:2601.02952v1 Announce Type: new Abstract: We introduce a new basis of the group algebra of the symmetric group, built using the left-to-right minima sets of permutations. We show that on this basis, the descent algebra acts by triangular operators, thus making it an analogue of a cellular basis. The proof involve... | https://arxiv.org/abs/2601.02952 | Academic Papers | svg |
640ed5bec7460c46a50a4d20bcaeadf730b7e633fad93d5d4e9d1b61d7783dfb | 2026-01-07T00:00:00-05:00 | K-stability of Fano weighted hypersurfaces via plt flags and convex geometry | arXiv:2601.02974v1 Announce Type: new Abstract: We develop a framework to study the K-stability of weighted Fano hypersurfaces based on a combination of birational and convex-geometric techniques. As an application, we prove that all quasi-smooth weighted Fano hypersurfaces of index 1 with at most two weights greater t... | https://arxiv.org/abs/2601.02974 | Academic Papers | svg |
5ecc6ff8440f714bad4dff7e6c5d77d29828590e9d6f4b98e8cf346e93373d74 | 2026-01-07T00:00:00-05:00 | Uniform distribution of saddle connection lengths in all $\mathsf{SL}(2,\mathbb{R})$ orbits | arXiv:2601.02979v1 Announce Type: new Abstract: For every flat surface, almost every flat surface in its $\mathsf{SL}(2,\mathbb{R})$ orbit has the following property: the sequence of its saddle connection lengths in non-decreasing order is uniformly distributed in the unit interval. | https://arxiv.org/abs/2601.02979 | Academic Papers | svg |
4122b22ed6eaf5b15cdbfc40181127213e36d6c95a0469f6e6574dd9532cbc49 | 2026-01-07T00:00:00-05:00 | Coupling Brownian loop soups and random walk loop soups at all polynomial scales | arXiv:2601.02992v1 Announce Type: new Abstract: Lawler and Trujillo Ferreras constructed a well-known coupling between the Brownian loop soups in $\mathbb{R}^2$ and the random walk loop soups on $\mathbb{Z}^2$ (one rescales the random walk loops by $1/N$, their time parametrizations by $1/(2N^2)$, and let $N\to \infty$... | https://arxiv.org/abs/2601.02992 | Academic Papers | svg |
68c07c0cb651c716982aa234866a4217a126074d6cc79233491e3a17698b55de | 2026-01-07T00:00:00-05:00 | Remarks on $d$-independent topological groups | arXiv:2601.03000v1 Announce Type: new Abstract: A non-trivial topological group is called \emph{$d$-independent} if for every subgroup of cardinality less than the continuum there exists a countable dense subgroup intersecting it trivially. This notion was introduced by M\'arquez and Tkachenko and has been intensively ... | https://arxiv.org/abs/2601.03000 | Academic Papers | svg |
144041ca3e66e24bb52050f67bded3458174b67053000623e33cf75d70420035 | 2026-01-07T00:00:00-05:00 | G-BSDEs with time-varying monotonicity condition | arXiv:2601.03006v1 Announce Type: new Abstract: In this paper, we study backward stochastic differential equations driven by G-Brownian motion where the generator has time-varying monotonicity with respect to y and Lipsitz property with respect to z. Through the Yosida approximation, we have proved the existence and un... | https://arxiv.org/abs/2601.03006 | Academic Papers | svg |
828bc2566f5eedd04dda87ef992b8f581f48eba8b698177cd286a60f7f8bf6c2 | 2026-01-07T00:00:00-05:00 | A Relaxation Method for Nonsmooth Nonlinear Optimization with Binary Constraints | arXiv:2601.03008v1 Announce Type: new Abstract: We study binary optimization problems of the form \( \min_{x\in\{-1,1\}^n} f(Ax-b) \) with possibly nonsmooth loss \(f\). Following the lifted rank-one semidefinite programming (SDP) approach\cite{qian2023matrix}, we develop a majorization-minimization algorithm by using ... | https://arxiv.org/abs/2601.03008 | Academic Papers | svg |
c334bd4d2739da9e51bf78b5475dd616561a6f0280e94c108cfbf63437c95d62 | 2026-01-07T00:00:00-05:00 | Adaptive Control of Unknown Linear Switched Systems via Policy Gradient Methods | arXiv:2601.03016v1 Announce Type: new Abstract: We consider the policy gradient adaptive control (PGAC) framework, which adaptively updates a control policy in real time, by performing data-based gradient descent steps on the linear quadratic regulator cost. This method has empirically shown to react to changing circum... | https://arxiv.org/abs/2601.03016 | Academic Papers | svg |
6333d8f15a311bdf6d274666a7f5640dc47e6b2f439a7acfa2a36c39f8a297b9 | 2026-01-07T00:00:00-05:00 | Periodicity of traces of Hecke operators modulo prime powers | arXiv:2601.03029v1 Announce Type: new Abstract: We study traces of Hecke operators on spaces of elliptic cusp forms and Drinfeld cusp forms and show that, modulo any prime power, these traces are periodic in the weight. | https://arxiv.org/abs/2601.03029 | Academic Papers | svg |
57bfe1b6bb6bb63f5a92bbd1c29346959ea634d0dfc4bd4c30be73ba84e6be69 | 2026-01-07T00:00:00-05:00 | On the Hilbert-Chow crepant resolution conjecture | arXiv:2601.03036v1 Announce Type: new Abstract: We prove the Hilbert-Chow crepant resolution conjecture in the exceptional curve classes for all projective surfaces and all genera. In particular, this confirms Ruan's cohomological Hilbert-Chow crepant resolution conjecture. The proof exploits Fulton-MacPherson compacti... | https://arxiv.org/abs/2601.03036 | Academic Papers | svg |
ae4c91d860b7513da78cf5aac5eb1861869933f813d9af7cc55afffee6567f51 | 2026-01-07T00:00:00-05:00 | Generalized Toeplitz determinants for Starlike Mappings in Several Complex Variables | arXiv:2601.03039v1 Announce Type: new Abstract: This paper establishes sharp bounds for the second and third-order Toeplitz determinants associated with starlike functions $f$ in the unit disk such that $f(z)-z$ has a zero of order $k+1$ at $z=0$. These bounds are further extended to starlike mappings defined on the un... | https://arxiv.org/abs/2601.03039 | Academic Papers | svg |
8c20d1513e559641d35b3337e9e0fd42d63b83639a0ec34d535fe78f984379b8 | 2026-01-07T00:00:00-05:00 | Egorov-Type Semiclassical Limits for Open Quantum Systems with a Bi-Lindblad Structure | arXiv:2601.03041v1 Announce Type: new Abstract: This paper develops a bridge between bi-Hamiltonian structures of Poisson-Lie type, contact Hamiltonian dynamics, and the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) formalism for quantum open systems. On the classical side, we consider bi-Hamiltonian systems defined by ... | https://arxiv.org/abs/2601.03041 | Academic Papers | svg |
44c451154e690d15111f01ec68ffcf629a34f637c75b9c8fe3e72fac4593eaa4 | 2026-01-07T00:00:00-05:00 | Classification of reductive homogeneous spaces satisfying strict inequality for Benoist-Kobayashi's $\rho$ functions | arXiv:2601.03049v1 Announce Type: new Abstract: Let $G$ be a real reductive Lie group and $H$ a reductive subgroup of $G$. Benoist-Kobayashi studied when $L^2(G/H)$ is a tempered representation of $G$. They introduced the functions $\rho$ on Lie algebras and gave a necessary and sufficient condition for the temperednes... | https://arxiv.org/abs/2601.03049 | Academic Papers | svg |
d518d1c30be3aac20ac5aa773e0f7fd9744e1ee6c150e9d1fe9c34be2aa50ba4 | 2026-01-07T00:00:00-05:00 | Existence and concentration of ground state solutions for an exponentially critical Choquard equation involving mixed local-nonlocal operators | arXiv:2601.03060v1 Announce Type: new Abstract: We study the Choquard equation involving mixed local and nonlocal operators \[-\varepsilon^{2}\Delta u+\varepsilon^{2s}(-\Delta)^{s}u+V(x)u=\varepsilon^{\mu-2}\left(\frac{1}{|x|^{\mu}}*F(u)\right)f(u)\quad \text{in }\R^{2},\] where \(\varepsilon>0\), \(s\in(0,1)\), \(0<\m... | https://arxiv.org/abs/2601.03060 | Academic Papers | svg |
901bebe7ee3c81235be75f39ff45d211bc5b5b7e7a3ce9cef34b23ad1876ba82 | 2026-01-07T00:00:00-05:00 | Hamiltonian reductions as affine closures of cotangent bundles | arXiv:2601.03068v1 Announce Type: new Abstract: For an irreducible non-singular affine $G$-variety $Y$ whose action is $2$-large, we prove that the Hamiltonian reduction $T^*Y/\!\!/\!\!/G$ is a symplectic variety with terminal singularities, isomorphic to the affine closure of $T^*Z_{\text{reg}}$ for $Z:=Y/\!/G$. As ap... | https://arxiv.org/abs/2601.03068 | Academic Papers | svg |
abc0518b046ff40045475ec64f3747495cc0ccb9a927a24e6775b5bb079e08ca | 2026-01-07T00:00:00-05:00 | Average gradient localisation for degenerate elliptic equations in the plane | arXiv:2601.03078v1 Announce Type: new Abstract: We consider Lipschitz solutions to the possibly highly degenerate elliptic equation $ \dv G(\nabla u)=0 $ in $B_1\subset\R^2 $, for any continuous strictly monotone vector field $ G\colon\R^2\to\R^2$. We show that $u$ is either $C^1$ at $0$, or any blowup limit $v(x)=\lim... | https://arxiv.org/abs/2601.03078 | Academic Papers | svg |
bc0c8783484824c1cf62a30a4d2826afcada04390c8cbaddde398af87b2c484e | 2026-01-07T00:00:00-05:00 | A proof of Xin-Zhang's tridiagonal determinant conjecture | arXiv:2601.03082v1 Announce Type: new Abstract: We confirm a recent conjecture by Xin and Zhang, which establishes a simple product formula for the characteristic polynomial of an $(n-1) \times (n-1)$ tridiagonal matrix $C$. This characteristic polynomial arises from a recurrence relation that enumerates $n \times n$ n... | https://arxiv.org/abs/2601.03082 | Academic Papers | svg |
8edb5d51a9b88d0d6237f9fb4d210b59f6bad94e41dbcccbd6a120877fbed569 | 2026-01-07T00:00:00-05:00 | Pseudo-differential operators associated with the fractional Hankel-Bessel transform | arXiv:2601.03091v1 Announce Type: new Abstract: We introduce and study a new class of pseudo-differential operators associated with a fractional Hankel--Bessel transform. Motivated by the classical Hankel transform and the pseudo-differential operators associated with Bessel operators studied by Pathak and Pandey \cite... | https://arxiv.org/abs/2601.03091 | Academic Papers | svg |
7d3cf3fb14c230f4e5073b872e1b5ddeb0af4f0c83b06df1028bfd8cf39914ce | 2026-01-07T00:00:00-05:00 | Stability of Hyperk\"ahler Flow | arXiv:2601.03092v1 Announce Type: new Abstract: In this work, we discuss the stability of Donaldson's flow of surfaces in a hyperk\"ahler 4-manifold. In \cite{WT2}, Wang and Tsai proved a uniqueness theorem and $C^1$ dynamic stability theorem of the mean curvature flow for minimal surface. We extend their results and o... | https://arxiv.org/abs/2601.03092 | Academic Papers | svg |
721295af6650ab11d0a01da58a0ede9aed908c5bb1fc7ee89fef0cc3a28e0f41 | 2026-01-07T00:00:00-05:00 | Submanifolds of almost quaternionic skew-Hermitian manifolds | arXiv:2601.03094v1 Announce Type: new Abstract: We investigate several classes of submanifolds of almost quaternionic skew-Hermitian manifolds $(M^{4n}, Q, \omega)$, including almost symplectic, almost complex, almost pseudo-Hermitian and almost quaternionic submanifolds. In the torsion-free case, we realize each type ... | https://arxiv.org/abs/2601.03094 | Academic Papers | svg |
740d6ea0a1a59ff6369cb1e5efc5477886d8274c952a026fb4caeea8ccb33df4 | 2026-01-07T00:00:00-05:00 | A Kirchhoff equation with infinite conservation laws | arXiv:2601.03095v1 Announce Type: new Abstract: We show here that the quasilinear Kirchhoff-Pokhozhaev equation $$u_{tt}-\big(a\int_{\mathbb{R}^n} |\nabla u |^2 dx + b \big)^{-2} \Delta u = 0,$$ with $a\neq0$, admits conservation laws of all orders. | https://arxiv.org/abs/2601.03095 | Academic Papers | svg |
64f180e2fb860b224d6ba47915f775467de499eb39e9e5daf7121a337f6172d1 | 2026-01-07T00:00:00-05:00 | Spherical Ricci tori with rotational symmetry | arXiv:2601.03096v1 Announce Type: new Abstract: In this article, we study $c$-spherical Ricci metrics, that is, Riemannian metrics whose Gaussian curvature $K$ satisfies \begin{equation*} (K - c)\Delta K - |\nabla K|^2 - 4K(K - c)^2 = 0, \end{equation*} for some $c>0$. We explicitly construct a two-parameter family of ... | https://arxiv.org/abs/2601.03096 | Academic Papers | svg |
8e93f5d90478eea26dbf23d492c7cac7a30e5c4aeecc49ae69e8107fb936174d | 2026-01-07T00:00:00-05:00 | Point-set models for homotopy coherent coalgebras | arXiv:2601.03101v1 Announce Type: new Abstract: We show a first rectification result for homotopy chain coalgebras over a field. On the one hand, we consider the $\infty$-category obtained by localizing differential graded coalgebras over an operad with respect to quasi-isomorphisms; on the other, we give a general def... | https://arxiv.org/abs/2601.03101 | Academic Papers | svg |
a5eef2adeefb91f185f47047128a982b25dd48110fda3f1e20c214e5655ab433 | 2026-01-07T00:00:00-05:00 | On the monotonicity of the entropy production in the Landau-Maxwell equation | arXiv:2601.03107v1 Announce Type: new Abstract: We study the homogeneous Landau equation with Maxwell molecules and prove that the entropy production is non-increasing provided the directional temperatures are well-distributed and the solution admits a moment of order $\ell$, for some $\ell$ arbitrarily close to $2$. I... | https://arxiv.org/abs/2601.03107 | Academic Papers | svg |
87172bd9801233ce48af36fc44bdc447f8f568aa25ebd4b970ddbc5d8e8f8821 | 2026-01-07T00:00:00-05:00 | First passage times for decoupled random walks | arXiv:2601.03109v1 Announce Type: new Abstract: Motivated by a connection to the infinite Ginibre point process, decoupled random walks were introduced in a recent article Alsmeyer, Iksanov and Kabluchko (2025). The decoupled random walk is a sequence of independent random variables, in which the $n$th variable has the... | https://arxiv.org/abs/2601.03109 | Academic Papers | svg |
1c8f7ea48ce83b189e523a361abe225db508ec58155ab991d34372e38cc5461e | 2026-01-07T00:00:00-05:00 | On derived categories of module categories over multiring categories | arXiv:2601.03128v1 Announce Type: new Abstract: Let $\mathcal{A}$ and $\mathcal{B}$ be subcategories of tensor categories $\mathcal{C}$ and $\mathcal{D}$, respectively, both of which are abelian categories with finitely many isomorphism classes of simple objects. We prove that if their derived categories $\mathbf{D}^b(... | https://arxiv.org/abs/2601.03128 | Academic Papers | svg |
94ea655b5c73385ab0fc79c7d2515dc4fd20a4063494b35bd8cf04c34e96bd03 | 2026-01-07T00:00:00-05:00 | Lipschitz extension and Lipschitz-free spaces over nets in normed spaces | arXiv:2601.03131v1 Announce Type: new Abstract: We consider subsets $S$ of a metric space $M$ such that Lipschitz mappings defined on $S$ can be extended to Lipschitz mappings on $M$, and we show that the union of such subsets has the same property under appropriate geometric conditions. We then derive several conseque... | https://arxiv.org/abs/2601.03131 | Academic Papers | svg |
edc4b01e789fee1f13114d60e8bc503262741e96974266552e8f78c206941122 | 2026-01-07T00:00:00-05:00 | Freely floating cylinder on a 3D fluid governed by the Boussinesq equations in the axisymmetric without swirl case | arXiv:2601.03133v1 Announce Type: new Abstract: This paper deals with the interactions of waves governed by a non-linear dispersive Boussinesq type system with the vertical displacement of a cylindrical floating structure in an axisymmetric without swirl situation. The Boussinesq regime is a good approximation of free ... | https://arxiv.org/abs/2601.03133 | Academic Papers | svg |
982bcb0336c3c41331b8a1d8af7319ef8b41e967e6d279523555443b0e1232e0 | 2026-01-07T00:00:00-05:00 | Classifying the Fine Polyhedral Spectrum | arXiv:2601.03145v1 Announce Type: new Abstract: In this paper, we examine an analogue of the recently solved spectrum conjecture by Fujita in the setting of Fine polyhedral adjunction theory. We present computational results for lower-dimensional polytopes, which lead to a complete classification of the highest numbers... | https://arxiv.org/abs/2601.03145 | Academic Papers | svg |
9e04caf8d701fe1ddb44c772bc2d3ded50a00b84bed39c5680187ab791f79df7 | 2026-01-07T00:00:00-05:00 | Normalization flow and Poincar\'e-Dulac theory | arXiv:2601.03147v1 Announce Type: new Abstract: In this article, we develop a new approach to the Poincar\'e--Dulac normal form theory for a system of differential equations near a singular point. Using the continuous averaging method, we construct a normalization flow that moves a vector field to its normal form. We p... | https://arxiv.org/abs/2601.03147 | Academic Papers | svg |
93274f67a3eae7ae85fa06cf9db4c0447940238509b7c6dd07eedf78f7152f0c | 2026-01-07T00:00:00-05:00 | Vaught's Conjecture and Theories of Partial Order Admitting a Finite Lexicographic Decomposition | arXiv:2601.03155v1 Announce Type: new Abstract: A complete theory ${\mathcal T}$ of partial order is an FLD$_1$-theory iff some (equivalently, any) of its models ${\mathbb X}$ admits a finite lexicographic decomposition ${\mathbb X} =\sum _{{\mathbb I}}{\mathbb X} _i$, where ${\mathbb I}$ is a finite partial order and ... | https://arxiv.org/abs/2601.03155 | Academic Papers | svg |
723c42934027505c329dc9e78aebdf2d7427232ffbb77187338cb724026439a8 | 2026-01-07T00:00:00-05:00 | Valuations on polyhedra and topological arrangements | arXiv:2601.03176v1 Announce Type: new Abstract: We revisit a classical theme of (general or translation invariant) valuations on convex polyhedra. Our setting generalizes the classical one, in a ``dual'' direction to previously considered generalizations: while previous research was mostly concerned with variations of ... | https://arxiv.org/abs/2601.03176 | Academic Papers | svg |
32ece18920e50f938ba4344b0de5eced1588f2fe26b619b437710560fa2a0a48 | 2026-01-07T00:00:00-05:00 | Deformations of the connected sum of Gorenstein algebras | arXiv:2601.03179v1 Announce Type: new Abstract: We prove that the Gorenstein locus of the Hilbert scheme of points on $\mathbb A^n$ is non-reduced for $n>9$; we construct examples of non-reduced points that come from apolar algebras of the sum of general cubics. As a corollary, we get a non-reducedness result for the c... | https://arxiv.org/abs/2601.03179 | Academic Papers | svg |
e3fef4f4dec769b6a6dd2a44d2179f898071f9e9bf82fb70a03b620ec9df94f4 | 2026-01-07T00:00:00-05:00 | Strongly finitary metric monads are too strong | arXiv:2601.03180v1 Announce Type: new Abstract: Varieties of quantitative algebras are fully described by their free-algebra monads on the category Met of metric spaces. For a longer time it has been an open problem whether the resulting enriched monads are precisely the strongly finitary ones (determined by their valu... | https://arxiv.org/abs/2601.03180 | Academic Papers | svg |
44e0428a79f9e19f95db4b744f71598f815f3a3eea09b25614bb077f6a080763 | 2026-01-07T00:00:00-05:00 | Subjective-Objective Median-based Importance Technique (SOMIT) to Aid Multi-Criteria Renewable Energy Evaluation | arXiv:2601.03182v1 Announce Type: new Abstract: Accelerating the renewable energy transition requires informed decision-making that accounts for the diverse financial, technical, environmental, and social trade-offs across different renewable energy technologies. A critical step in this multi-criteria decision-making (... | https://arxiv.org/abs/2601.03182 | Academic Papers | svg |
fe43da79bdb6c50c1802669ee313b85344860e4d60a7316733831c60e3f3f702 | 2026-01-07T00:00:00-05:00 | Flat simplices and kissing polytopes | arXiv:2601.03183v1 Announce Type: new Abstract: We consider how flat a lattice simplex contained in the hypercube $[0,k]^d$ can be. This question is related to the notion of kissing polytopes: two lattice polytopes contained in the hypercube $[0,k]^d$ are kissing when they are disjoint but their distance is as small as... | https://arxiv.org/abs/2601.03183 | Academic Papers | svg |
b81b8879be58cf71e14bcf11154cf69ffc5e19af2855ef1f13c24a0eb046358e | 2026-01-07T00:00:00-05:00 | Subprincipal Controlled Quasimodes and Spectral Instability | arXiv:2601.03188v1 Announce Type: new Abstract: Here we explore, in a series of articles, semiclassical quasimodes u(h,b), approximative solutions P(h)u(h,b)\sim 0, depending on $0<1$, and on b, the subprincipal symbol. We study a pseudodifferential operator with transversal intersections of bicharacteristics, where th... | https://arxiv.org/abs/2601.03188 | Academic Papers | svg |
a4f4bb386e74d89007361d089e8ebc59f85206822a3d82e82ad1e2ae9b68dbb7 | 2026-01-07T00:00:00-05:00 | HOMFLY parabolic restriction, defect skein theory and the Turaev coproduct | arXiv:2601.03196v1 Announce Type: new Abstract: We define a HOMFLY version of the category $\text{Rep}_q\text{P}$ of quantum representations of a parabolic subgroup $\text{P}\subseteq\text{GL}_{m+n}$ of block triangular matrices. Alongside this category, we construct functors that interpolate the usual restriction func... | https://arxiv.org/abs/2601.03196 | Academic Papers | svg |
56eb58e4001074db3c74273417d6f81fe3acd2762069c5b1945421ad3cbbb537 | 2026-01-07T00:00:00-05:00 | Signature invariants of monomial ideals | arXiv:2601.03208v1 Announce Type: new Abstract: Let $I$ be a monomial ideal of a polynomial ring $R=K[x_1,\ldots,x_n]$ over a field $K$ and let ${\rm sgn}(I)$ be its signature ideal. If $I$ is not a principal ideal, we show that the depth of $R/I$ is the depth of $R/{\rm sgn}(I)$, and the regularity of $R/{\rm sgn}(I)$... | https://arxiv.org/abs/2601.03208 | Academic Papers | svg |
59397b3e08664f882a87adec9f00e0b9896e208634a248369f5a30157c96e5cf | 2026-01-07T00:00:00-05:00 | Values of ternary quadratic forms at integers and the Berry-Tabor conjecture for 3-tori | arXiv:2601.03209v1 Announce Type: new Abstract: Berry and Tabor conjectured in 1977 that spectra of generic integrable quantum systems have the same local statistics as a Poisson point process. We verify their conjecture in the case of the two-point spectral density for a quantum particle in a three-dimensional box, su... | https://arxiv.org/abs/2601.03209 | Academic Papers | svg |
96f647382b701a33d871691edadc3032b0e4f3d1956c9d62e0f825675e39deb9 | 2026-01-07T00:00:00-05:00 | Lattice coverings and homogeneous covering congruences | arXiv:2601.03212v1 Announce Type: new Abstract: We consider the problem of covering $\mathbb{Z}^2$ with a finite number of sublattices of finite index, satisfying a simple minimality or non-degeneracy condition. We show how this problem may be viewed as a projective (or homogeneous) version of the well-known problem of... | https://arxiv.org/abs/2601.03212 | Academic Papers | svg |
d69fcda07293951bc40421ba8eff64c0c9a910d71b4aacf92a8955ede00c0c6a | 2026-01-07T00:00:00-05:00 | Generalized affine buildings for semisimple algebraic groups over real closed fields | arXiv:2601.03226v1 Announce Type: new Abstract: We use real algebraic geometry to construct an affine $\Lambda$-building $B$ associated to the $\mathbb{F}$-points of a semisimple algebraic group, where $\mathbb{F}$ is a valued real closed field. We characterize the spherical building at infinity and the local building ... | https://arxiv.org/abs/2601.03226 | Academic Papers | svg |
51f85f1944072d9616feabf0a94d6e6b85b70b02042358e6e12e5017aa4f6fd2 | 2026-01-07T00:00:00-05:00 | Sets of Lengths of Integer-Valued Polynomials on Prime Ideals of Principal Ideal Domains | arXiv:2601.03246v1 Announce Type: new Abstract: Let $D$ be a principal ideal domain with infinite spectrum such that for every nonzero prime ideal $M$ of $D$, the residue field $D/M$ is finite. Let $K$ be the quotient field of $D$. We investigate sets of lengths in the ring of integer-valued polynomials on $M$, $\text{... | https://arxiv.org/abs/2601.03246 | Academic Papers | svg |
41bc3f2a79812b5ef1f29cbb998039828a28d3d729474740fb5c6f6802d4c061 | 2026-01-07T00:00:00-05:00 | Quantum polylogarithms | arXiv:2601.00472v1 Announce Type: cross Abstract: Multiple polylogarithms are periods of variations of mixed Tate motives. Conjecturally, they deliver all such periods. We introduce deformations of multiple polylogarithms depending on a complex parameter h. We call them quantum polylogarithms. Their asymptotic expansio... | https://arxiv.org/abs/2601.00472 | Academic Papers | svg |
a1949bf69d781b884e207d55464a319e0918e2be5962d15b1f2c6bb4e28ae4db | 2026-01-07T00:00:00-05:00 | Color-kinematics duality from an algebra of superforms | arXiv:2601.02478v1 Announce Type: cross Abstract: Color-kinematics duality states that the kinematic numerators of the cubic tree-level Yang-Mills scattering amplitudes obey the same symmetry properties that the color factors obey due to the Jacobi identity. We present a novel strategy for deriving this duality, based ... | https://arxiv.org/abs/2601.02478 | Academic Papers | svg |
6eb596d256c6051a8936258aa6081599ac8697332608958b5c271f79515ec8bf | 2026-01-07T00:00:00-05:00 | Exact critical-temperature bounds for two-dimensional Ising models | arXiv:2601.02502v1 Announce Type: cross Abstract: We derive exact critical-temperature bounds for the classical ferromagnetic Ising model on two-dimensional periodic tessellations of the plane. For any such tessellation or lattice, the critical temperature is bounded from a above by a universal number that is solely de... | https://arxiv.org/abs/2601.02502 | Academic Papers | svg |
80ea66fe2c53a7b12c3ba818ab817ba5bd2804ad2f3fbefe5abcadc545bd911e | 2026-01-07T00:00:00-05:00 | A novel finite-sample testing procedure for composite null hypotheses via pointwise rejection | arXiv:2601.02529v1 Announce Type: cross Abstract: We propose a novel finite-sample procedure for testing composite null hypotheses. Traditional likelihood ratio tests based on asymptotic $\chi^2$ approximations often exhibit substantial bias in small samples. Our procedure rejects the composite null hypothesis $H_0: \t... | https://arxiv.org/abs/2601.02529 | Academic Papers | svg |
19f82e49584f7e32758c560e0724e44a155a461a9ca9c470c919377e763a68a2 | 2026-01-07T00:00:00-05:00 | Higher-Dimensional Anyons via Higher Cohomotopy | arXiv:2601.03150v1 Announce Type: cross Abstract: We highlight that integer Heisenberg groups at level 2 underlie topological quantum phenomena: their group algebras coincide with the algebras of quantum observables of abelian anyons in fractional quantum Hall (FQH) systems on closed surfaces. Decades ago, these groups... | https://arxiv.org/abs/2601.03150 | Academic Papers | svg |
7a4d095037d9a0cb1518a3baa92c7a8107713bae3a6b5314e0029a60d165e457 | 2026-01-07T00:00:00-05:00 | On the Bezrukavnikov-Kaledin quantization of symplectic varieties in characteristic $p$ | arXiv:2011.08259v2 Announce Type: replace Abstract: We prove that after inverting the Planck constant $h$ the Bezrukavnikov-Kaledin quantization $(X, \mathcal{O}_h)$ of symplectic variety $X$ in characteristic $p$ is Morita equivalent to a certain central reduction of the algebra of differential operators on $X$. | https://arxiv.org/abs/2011.08259 | Academic Papers | svg |
a05fd6a30a4b6a4ebf0d6f01621177a2f7b01d609cb2a866995c0f03245fde78 | 2026-01-07T00:00:00-05:00 | Equivariant Chevalley, Giambelli, and Monk Formulae for the Peterson Variety | arXiv:2111.15663v2 Announce Type: replace Abstract: We present a formula for the Poincar\'e dual in the flag manifold of the equivariant fundamental class of any regular nilpotent or regular semisimple Hessenberg variety as a polynomial in terms of certain Chern classes. We then develop a type-independent proof of the ... | https://arxiv.org/abs/2111.15663 | Academic Papers | svg |
604f47d510171ee1b9dc8c009c564544962fa0374c90943d197dc94f90e81ff0 | 2026-01-07T00:00:00-05:00 | Stability of three-dimensional stochastic Navier-Stokes equation with Markov switching | arXiv:2203.15971v2 Announce Type: replace Abstract: A right continuous Markov chain is introduced in the noise terms of the three-dimensional stochastic Navier-Stokes equation, and we call such stochastic system as stochastic Navier-Stokes equation with Markov switching. In the present article, we study the $p$-th mome... | https://arxiv.org/abs/2203.15971 | Academic Papers | svg |
3368d0fc4742a4bee5aa1f7a309e98c1e283aab294affe78889b983cc2636527 | 2026-01-07T00:00:00-05:00 | A Host--Kra ${\mathbf F}_2^\omega$-system of order $5$ that is not Abramov of order $5$, and non-measurability of the inverse theorem for the $U^6({\mathbf F}_2^n)$ norm | arXiv:2303.04853v4 Announce Type: replace Abstract: It was conjectured by Bergelson, Tao, and Ziegler \cite{btz} that every Host--Kra $\F_p^\omega$-system of order $k$ is an Abramov system of order $k$. This conjecture has been verified for $k \leq p+1$. In this paper we show that the conjecture fails when $k=5, p=2$. ... | https://arxiv.org/abs/2303.04853 | Academic Papers | svg |
515e0975fe156c13739723ba07d62d00d22ef44cd19ff34fb5704f7bf3867a79 | 2026-01-07T00:00:00-05:00 | Global Koszul duality | arXiv:2304.08409v4 Announce Type: replace Abstract: We construct a monoidal model structure on the category of all curved coalgebras and show that it is Quillen equivalent, via the extended bar-cobar adjunction, to another model structure we construct on the category of curved algebras. When the coalgebras under consid... | https://arxiv.org/abs/2304.08409 | Academic Papers | svg |
64ee90b201721c8fcfb9709b8ec2f19c0ebc250b9878e9b55a304c7b04b9ebf1 | 2026-01-07T00:00:00-05:00 | An $\mathfrak{sl}_2$ action on link homology of T(2,k) torus links | arXiv:2307.01910v2 Announce Type: replace Abstract: We determine an $\mathfrak{sl}_2$ module structure on the equivariant Khovanov-Rozansky homology of (2,k)-torus links following the framework defined in arXiv:2306.10729. | https://arxiv.org/abs/2307.01910 | Academic Papers | svg |
efa698c17a67703cb41eb19ab09885d0f9fc42564a8d2b25af2eb97153ffb830 | 2026-01-07T00:00:00-05:00 | The Beauville-Voisin conjecture for double EPW sextics | arXiv:2307.15240v2 Announce Type: replace Abstract: We prove that the Beauville-Voisin conjecture is true for any double EPW sextic, i.e. the subalgebra of the Chow ring generated by divisors and Chern classes of the tangent bundle injects into cohomology. | https://arxiv.org/abs/2307.15240 | Academic Papers | svg |
51c42cc72fac9cfb7715b5b604a4ecc1469408293f2467af81e9f6c6917efb22 | 2026-01-07T00:00:00-05:00 | Doubly-weighted zero-sum constants | arXiv:2311.00090v3 Announce Type: replace Abstract: Let $A,B\subseteq\mathbb Z_n$ be given and $S=(x_1,\ldots, x_k)$ be a sequence in $\mathbb Z_n$. We say that $S$ is an $(A,B)$-weighted zero-sum sequence if there exist $a_1,\ldots,a_k\in A$ and $b_1,\ldots,b_k\in B$ such that $a_1x_1+\cdots+a_kx_k=0$ and $b_1a_1+\cdo... | https://arxiv.org/abs/2311.00090 | Academic Papers | svg |
e5d76c6a5851d237da9d1a7422582dfb6230e19d398d664e002d295e54070db5 | 2026-01-07T00:00:00-05:00 | On the kernels of the pro-$p$ outer Galois representations associated to once-punctured CM elliptic curves | arXiv:2312.04196v3 Announce Type: replace Abstract: In this paper, we compare a certain field arising from the pro-$p$ outer Galois representation associated to a once-punctured CM elliptic curve over an imaginary quadratic field $K$ with the maximal pro-$p$ Galois extension of the mod-$p$ ray class field $K(p)$ of $K$... | https://arxiv.org/abs/2312.04196 | Academic Papers | svg |
60b2b4df89741fe96571bf186bca58dbd4bc16b655e9581a0a45f5ff6c76687a | 2026-01-07T00:00:00-05:00 | Decision Making under Costly Sequential Information Acquisition: the Paradigm of Reversible and Irreversible Decisions | arXiv:2401.00569v4 Announce Type: replace Abstract: Decision making in modern stochastic systems, including e-commerce platforms, financial markets and healthcare systems, has evolved into a multifaceted process that combines information acquisition and adaptive information sources. This paper initiates a study on such... | https://arxiv.org/abs/2401.00569 | Academic Papers | svg |
691eff8d500dc21e8d3aa814e9b1d98976e15c9fa7580e0c7008d65fdc8d6033 | 2026-01-07T00:00:00-05:00 | Quasi-ergodic theorems for Feynman-Kac semigroups and large deviation for additive functionals | arXiv:2401.17997v2 Announce Type: replace Abstract: We study the long-time behavior of an additive functional that takes into account the jumps of a symmetric Markov process. This process is assumed to be observed through a biased observation scheme that includes the survival to events of extinction and the Feynman-Kac... | https://arxiv.org/abs/2401.17997 | Academic Papers | svg |
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