@article{19727, abstract = {By studying some Clausen-like multiple Dirichlet series, we complete the proof of Manin's conjecture for sufficiently split smooth equivariant compactifications of the translation-dilation group over the rationals. Secondary terms remain elusive in general.}, author = {Wang, Victor}, issn = {1090-2082}, journal = {Advances in Mathematics}, publisher = {Elsevier}, title = {{Asymptotic growth of translation-dilation orbits}}, doi = {10.1016/j.aim.2025.110341}, volume = {475}, year = {2025}, } @article{19673, abstract = {We show that almost all primes p =\= ± 4 mod9 are sums of three cubes, assuming a conjecture due to Hooley, Manin, et al. on cubic fourfolds. This conjecture is approachable under standard statistical hypotheses on geometric families of L-functions.}, author = {Wang, Victor}, issn = {2998-4114}, journal = {Journal of the Association for Mathematical Research}, number = {1}, pages = {1--26}, publisher = {Association for Mathematical Research}, title = {{Prime Hasse principles via diophantine second moments}}, doi = {10.56994/JAMR.003.001.001}, volume = {3}, year = {2025}, } @article{19407, abstract = {We discuss, in a non-Archimedean setting, the distribution of the coefficients of L-polynomials of curves of genus g over Fq . Among other results, this allows us to prove that the Q-vector space spanned by such characteristic polynomials has dimension g + 1. We also state a conjecture about the Archimedean distribution of the number of rational points of curves over finite fields.}, author = {Ballini, Francesco and Lombardo, Davide and Verzobio, Matteo}, issn = {1473-7124}, journal = {Proceedings of the Royal Society of Edinburgh Section A: Mathematics}, publisher = {Cambridge University Press}, title = {{On the L-polynomials of curves over finite fields}}, doi = {10.1017/prm.2025.7}, year = {2025}, } @article{19483, abstract = {We prove matching upper and lower bounds for the average of the6-torsionof class groups of quadratic fields. Furthermore, we count the number of integer solutions on an affine quartic threefold.}, author = {Chan, Yik Tung and Koymans, Peter and Pagano, Carlo and Sofos, Efthymios}, issn = {2036-2145}, journal = {Annali della Scuola Normale Superiore di Pisa, Classe di Scienze}, publisher = {Scuola Normale Superiore - Edizioni della Normale}, title = {{6-torision and integral points on quartic threefolds}}, doi = {10.2422/2036-2145.202412_006}, year = {2025}, } @article{20222, abstract = {Let X be a smooth projective hypersurface defined over Q. We provide new bounds for rational points of bounded height on X. In particular, we show that if X is a smooth projective hypersurface in Pn with n 4 and degree d 50, then the set of rational points on X of height bounded by B have cardinality On,d,ε (Bn−2+ε ). If X is smooth and has degree d 6, we improve the dimension growth conjecture bound. We achieve an analogue result for affine hypersurfaces whose projective closure is smooth.}, author = {Verzobio, Matteo}, issn = {1687-0247}, journal = {International Mathematics Research Notices}, number = {16}, publisher = {Oxford University Press}, title = {{Counting rational points on smooth hypersurfaces with high degree}}, doi = {10.1093/imrn/rnaf249}, volume = {2025}, year = {2025}, } @article{20367, abstract = {We prove upper and lower bounds on the number of pairs of commuting n x n matrices with integer entries in [-T, T], as T -> . Our work uses Fourier analysis and leads to an analysis of exponential sums involving matrices over finite fields. These are bounded by combining a stratification result of Fouvry and Katz with a new result about the flatness of the commutator Lie bracket.}, author = {Browning, Timothy D and Sawin, Will and Wang, Victor}, issn = {1432-1807}, journal = {Mathematische Annalen}, pages = {1863–1880}, publisher = {Springer Nature}, title = {{Pairs of commuting integer matrices}}, doi = {10.1007/s00208-025-03285-5}, volume = {393}, year = {2025}, } @article{20423, abstract = {For any d 2, we prove that there exists an integer n0(d) such that there exists an n × n magic square of dth powers for all n n0(d). In particular, we establish the existence of an n × n magic square of squares for all n 4, which settles a conjecture of Várilly-Alvarado. All previous approaches had been based on constructive methods and the existence of n × n magic squares of dth powers had only been known for sparse values of n. We prove our result by the Hardy-Littlewood circle method, which in this setting essentially reduces the problem to finding a sufficient number of disjoint linearly independent subsets of the columns of the coefficient matrix of the equations defining magic squares. We prove an optimal (up to a constant) lower bound for this quantity.}, author = {Rome, Nick and Yamagishi, Shuntaro}, issn = {2363-9555}, journal = {Research in Number Theory}, number = {4}, publisher = {Springer Nature}, title = {{On the existence of magic squares of powers}}, doi = {10.1007/s40993-025-00671-5}, volume = {11}, year = {2025}, } @unpublished{22340, abstract = {We show that Laplace isospectral deformations within a conformal class of generic Liouville metrics on the two-dimensional torus that are linear in the deformation parameter are necessarily trivial. Two of the main ingredients in our proof are a noncancellation result for the wave trace and an analysis of the second order variational formula for the energy functional associated to closed geodesics. Noncancellation allows us to detect parts of the length spectrum from the Laplace spectrum and conclude rational integrability for the deformed geodesic flow (Liouville metrics are folklorically conjectured to be the only Riemannian metrics with integrable geodesic flow on the torus). We then use the second variational formula to show how the preservation of a single rational torus is sufficient to conclude triviality of the deformation, assuming linearity. We also present some evidence that our hypothesis of linearity may indeed be necessary.}, author = {Henheik, Sven Joscha and Kaloshin, Vadim and Li, Yunzhe and Vig, Amir}, booktitle = {arXiv}, keywords = {Differential Geometry (math.DG), Mathematical Physics (math-ph), Dynamical Systems (math.DS), Spectral Theory (math.SP), FOS: Mathematics, FOS: Mathematics, FOS: Physical sciences, FOS: Physical sciences, 58J42, 37J35, 37J35, 35P20, 58J40, 58J50, 37D40}, title = {{Spectral rigidity of Liouville tori}}, doi = {10.48550/ARXIV.2511.10398}, year = {2025}, } @unpublished{22341, abstract = {We construct nontrivial deformations of the standard map which preserve the symplectic actions, respectively the Lyapunov exponents, of infinitely many periodic orbits accumulating to an invariant curve. The proof uses a resonant normal-form construction to obtain a sequence of periodic orbits accumulating on an invariant curve with a Liouville rotation number. Within these normal forms we capture the dependence of these periodic orbits on the resonant Fourier coefficients of the dynamics on the invariant curve and, using the contraction mapping principle, obtain a suitable deformation achieving the prescribed spectral data associated with this sequence of orbits. The result can be viewed as a symplectic twist-map analogue of a length spectral nonrigidity phenomenon for Riemannian manifolds and convex billiards, and it motivates the existence problem for similar 'partially length-isospectral' deformations of strictly convex billiard tables.}, author = {Li, Yunzhe}, booktitle = {arXiv}, keywords = {Dynamical Systems (math.DS), FOS: Mathematics, FOS: Mathematics}, title = {{Deformations of the standard map with prescribed actions and Lyapunov exponents}}, doi = {10.48550/ARXIV.2512.03865}, year = {2025}, } @inproceedings{20844, abstract = {We introduce and construct a new proof system called Non-interactive Arguments of Knowledge or Space (NArKoS), where a space-bounded prover can convince a verifier they know a secret, while having access to sufficient space allows one to forge indistinguishable proofs without the secret. An application of NArKoS are space-deniable proofs, which are proofs of knowledge (say for authentication in access control) that are sound when executed by a lightweight device like a smart-card or an RFID chip that cannot have much storage, but are deniable (in the strong sense of online deniability) as the verifier, like a card reader, can efficiently forge such proofs. We construct NArKoS in the random oracle model using an OR-proof combining a sigma protocol (for the proof of knowledge of the secret) with a new proof system called simulatable Proof of Transient Space (simPoTS). We give two different constructions of simPoTS, one based on labelling graphs with high pebbling complexity, a technique used in the construction of memory-hard functions and proofs of space, and a more practical construction based on the verifiable space-hard functions from TCC’24 where a prover must compute a root of a sparse polynomial. In both cases, the main challenge is making the proofs efficiently simulatable.}, author = {Dujmovic, Jesko and Günther, Christoph Ullrich and Pietrzak, Krzysztof Z}, booktitle = {23rd International Conference on Theory of Cryptography}, isbn = {9783032122896}, issn = {1611-3349}, location = {Aarhus, Denmark}, pages = {171--202}, publisher = {Springer Nature}, title = {{Space-deniable proofs}}, doi = {10.1007/978-3-032-12290-2_6}, volume = {16271}, year = {2025}, } @article{20931, abstract = {Context. Asymmetries in the observed rotational splittings of a multiplet contain information about the star’s rotation profile and internal magnetic field. Moreover, the frequency regularities of multiplets can be used for mode identification. However, to exploit this information, highly accurate theoretical predictions are needed. Aims. We aim to quantify the difference in the predicted mode asymmetries between a 1D perturbative method and a 2D method that includes a 2D stellar structure model, which takes rotation into account. We then place these differences between 1D and 2D methods in the context of asteroseismic measurements of internal magnetic fields. We only focus on the asymmetries and not on possible additional frequency peaks that can arise when the magnetic and rotation axis are misaligned. Methods. We coupled the 1D pulsation codes GYRE and StORM to the 2D stellar structure code ESTER and compared the oscillation predictions with the results from the 2D TOP pulsation code. We focused on zero-age main-sequence models representative of rotating β Cephei pulsators spinning at up to 20 per cent of the critical Keplerian rotation rate. Specifically, we investigated low-radial-order gravity and pressure modes. Results. We find a generally good agreement between the oscillation frequencies resulting from the 1D and 2D pulsation codes. We report differences in predicted mode multiplet asymmetries of mostly below 0.06 d−1. Since the magnetic asymmetries are small compared to the differences in the rotational asymmetries resulting from the 1D and 2D predictions, accurate measurements of the magnetic field are in most cases challenging. Conclusions. Differences in the predicted mode asymmetries of a rotating star between 1D perturbative methods and 2D non-perturbative methods can greatly hinder accurate measurements of internal magnetic fields in main-sequence pulsators with low-order modes. Nevertheless, reasonably accurate measurements could be possible with npg ≥ 2 modes if the internal rotation is roughly below 10 per cent of the Keplerian critical rotation frequency for (aligned) magnetic fields of the order of a few hundred kilogauss. While the differences between the 1D and 2D frequency predictions are mostly too large for internal magnetic field detections, the rotational asymmetries predicted by StORM are in general accurate enough for asteroseismic modelling of the stellar rotation in main-sequence stars with identified low-order modes.}, author = {Mombarg, J. S.G. and Vanlaer, V. and Das, Srijan B and Rieutord, M. and Aerts, C. and Bugnet, Lisa Annabelle and Mathis, S. and Reese, D. R. and Ballot, J.}, issn = {1432-0746}, journal = {Astronomy & Astrophysics}, publisher = {EDP Sciences}, title = {{Is a 1D perturbative method sufficient for asteroseismic modelling of β Cephei pulsators? Implications for measurements of rotation and internal magnetic fields}}, doi = {10.1051/0004-6361/202557247}, volume = {704}, year = {2025}, } @article{20927, abstract = {Cavity-magnon polaritons are hybrid excitations from the interaction between cavity photons and magnons, the quanta of collective spin oscillations. Along with the tunability of the magnon-photon coupling strength, fast information transfer and conversion speed are desired in hybrid devices. This can be achieved utilizing the propagating nature of spin waves with nonzero momentum for their ultrafast time dynamics and reduced ohmic dissipation. Antiferromagnets are particularly interesting as hosts for magnons since stray-field interactions are minimized and they support multiple modes with distinctive magnetic-field behavior across the phase diagram. Chromium trichloride (CrCl3) is a van der Waals layered antiferromagnet having a strong easy-plane anisotropy and a weak in-plane easy-axis anisotropy. Despite some magnetic resonance studies, the impact of magnetic reorientation of spins in CrCl3 on the cavity-magnon-polariton interaction strength as a function of magnetic field remains largely unexplored. In this study, we investigate the coupling between magnons in CrCl3 and photons in a coplanar waveguide resonator as a function of magnetic field. In particular, we find that the magnon-photon coupling strength varies nonmonotonically and distinctly with the magnetic field for the acoustic and the optical magnons, which can be utilized to tune the magnon-photon coupling strength using an external magnetic field as a knob. We find the signature of spin-flop transition in the two harmonics of the cavity due to a stronger dispersive coupling between optical magnons and cavity photons at lower fields. Additionally, we find standing modes formed by spin waves with nonzero momentum associated with the two hybrid magnons when the external field is applied at an angle with the crystal plane. These modes do not undergo substantial coupling with the cavity mode unlike the antiferromagnetic modes and can be used as low-loss propagation channels in hybrid devices.}, author = {Mandal, Supriya and Maji, Krishnendu and Kapoor, Lucky and Sasmal, Souvik and Manni, Soham and Jesudasan, John and Raychaudhuri, Pratap and Thamizhavel, Arumugam and Deshmukh, Mandar M.}, issn = {2469-9969}, journal = {Physical Review B}, number = {21}, publisher = {American Physical Society}, title = {{Cavity based sensing of antiferromagnetic canting and nonzero-momentum spin waves in a van der Waals cavity-magnon-polariton system}}, doi = {10.1103/bdd1-b8ys}, volume = {112}, year = {2025}, } @misc{20936, abstract = {Supplementary material for Mombarg et al. (2025, A&A). Title: "Is a 1D perturbative method sufficient for asteroseismic modelling of ~Cephei pulsators? Implications for measurements of rotation and internal magnetic fields" Content: - Non-rotating ESTER models and associated .GSM models. (Xini = 0.71, Zini = 0.014, vertical/horizonal viscosity 10^7 cm^2/s, vertical chemical diffusion 10^4 cm^2/s for evolution model. More details on the ESTER models can be found in the ESTER manual. - Rotational asymmetries computed with StORM and TOP in 1/d, and the central m=0 frequency from TOP in 1/d. (all_A*_new.pkl) - Magnetic asymmetries in 1/d for different obliquity angles between 0 and 90 deg for ZAMS and MAMS model, for B_0 = 75 kG. *_nu key gives unperturbed mode frequencies, *_npg the radial order (asym_dict.pkl, asym_dict_evol.pkl)}, author = {Mombarg, Joey and Vanlaer, Vincent and Das, Srijan B and Rieutord, Michel and Aerts, Conny and Bugnet, Lisa Annabelle and Mathis, Stephane and Reese, Daniel and Ballot, Jerome}, publisher = {Zenodo}, title = {{Is a 1D perturbative method sufficient for asteroseismic modelling of β Cephei pulsators?}}, doi = {10.5281/ZENODO.17580178}, year = {2025}, } @unpublished{21016, abstract = {Motivated by applications in chemistry, we give a homlogical definition of tunnels, or more generally cobordisms, connecting disjoint parts of a cell complex. For a filtered complex, this defines a persistence module. We give a method for identifying birth and death times using kernel persistence and a matrix reduction algorithm for pairing birth and death times.}, author = {Bleile, Yossi and Fajstrup, Lisbeth and Heiss, Teresa and Svane, Anne Marie and Sørensen, Søren Strandskov}, booktitle = {arXiv}, title = {{Identifying cobordisms using kernel persistence}}, doi = {10.48550/arXiv.2505.17858}, year = {2025}, } @misc{20940, abstract = {These are the raw data files that supplement our study of mode dispersion with magnetic field of a cavity-magnonics system containing chromium trichloride on coplanar waveguide resonator.}, author = {Mandal, Supriya and Maji, Krishnendu and Kapoor, Lucky and Sasmal, Souvik and Manni, Soham and Jesudasan, John and Raychaudhuri, Pratap and Thamizhavel, Arumugam and Deshmukh, Mandar M.}, publisher = {Zenodo}, title = {{Mode dispersion with magnetic field in a cavity-magnonics system}}, doi = {10.5281/ZENODO.15321721}, year = {2025}, } @unpublished{21399, abstract = {We report on the Equational Theories Project (ETP), an online collaborative pilot project to explore new ways to collaborate in mathematics with machine assistance. The project successfully determined all 22 028 942 edges of the implication graph between the 4694 simplest equational laws on magmas, by a combination of human-generated and automated proofs, all validated by the formal proof assistant language Lean. As a result of this project, several new constructions of magmas satisfying specific laws were discovered, and several auxiliary questions were also addressed, such as the effect of restricting attention to finite magmas.}, author = {Bolan, Matthew and Breitner, Joachim and Brox, Jose and Carlini, Nicholas and Carneiro, Mario and Doorn, Floris van and Dvorak, Martin and Goens, Andrés and Hill, Aaron and Husum, Harald and Mejia, Hernán Ibarra and Kocsis, Zoltan A. and Floch, Bruno Le and Bar-on, Amir and Luccioli, Lorenzo and McNeil, Douglas and Meiburg, Alex and Monticone, Pietro and Nielsen, Pace P. and Osazuwa, Emmanuel Osalotioman and Paolini, Giovanni and Petracci, Marco and Reinke, Bernhard and Renshaw, David and Rossel, Marcus and Roux, Cody and Scanvic, Jérémy and Srinivas, Shreyas and Tadipatri, Anand Rao and Tao, Terence and Tsyrklevich, Vlad and Vaquerizo-Villar, Fernando and Weber, Daniel and Zheng, Fan}, booktitle = {arXiv}, title = {{The equational theories project: Advancing collaborative mathematical research at scale}}, doi = {10.48550/arXiv.2512.07087}, year = {2025}, } @unpublished{21207, abstract = {Personalized federated learning has emerged as a popular approach to training on devices holding statistically heterogeneous data, known as clients. However, most existing approaches require a client to have labeled data for training or finetuning in order to obtain their own personalized model. In this paper we address this by proposing FLowDUP, a novel method that is able to generate a personalized model using only a forward pass with unlabeled data. The generated model parameters reside in a low-dimensional subspace, enabling efficient communication and computation. FLowDUP's learning objective is theoretically motivated by our new transductive multi-task PAC-Bayesian generalization bound, that provides performance guarantees for unlabeled clients. The objective is structured in such a way that it allows both clients with labeled data and clients with only unlabeled data to contribute to the training process. To supplement our theoretical results we carry out a thorough experimental evaluation of FLowDUP, demonstrating strong empirical performance on a range of datasets with differing sorts of statistically heterogeneous clients. Through numerous ablation studies, we test the efficacy of the individual components of the method.}, author = {Zakerinia, Hossein and Scott, Jonathan A and Lampert, Christoph}, booktitle = {arXiv}, title = {{Federated learning with unlabeled clients: Personalization can happen in low dimensions}}, doi = {10.48550/ARXIV.2505.15579}, year = {2025}, } @unpublished{21050, abstract = {In 1873, James C. Maxwell conjectured that the electric field generated by $n$ point charges in generic position has at most $(n-1)^2$ isolated zeroes. The first (non-optimal) upper bound was only obtained in 2007 by Gabrielov, Novikov and Shapiro, who also posed two additional interesting conjectures. In this article, we give the best upper bound known to date on the number of zeroes of the electric field, and construct a counterexample to a conjecture of Gabrielov, Novikov and Shapiro that the number of equilibria cannot exceed those of the distance function defined by the unit point charges. Finally, we note that it is quite possible that Maxwell's quadratic upper bound is not tight, so it is prudent to find smaller bounds. Hence, we also explore examples and construct configurations of charges achieving the highest ratios of the number of electric field zeroes by point charges found to this day.}, author = {Edelsbrunner, Herbert and Fillmore, Christopher D and Olivera, Gonçalo}, booktitle = {arXiv}, title = {{Counting equilibria of the electrostatic potential}}, doi = {10.48550/ARXIV.2501.05315}, year = {2025}, } @article{19025, abstract = {A complete understanding of the central stars of planetary nebulae (CSPNe) remains elusive. Over the past several decades, time-series photometry of CSPNe has yielded significant results including, but not limited to, discoveries of nearly 100 binary systems, insights into pulsations and winds in young white dwarfs, and studies of stars undergoing very late thermal pulses. We have undertaken a systematic study of optical photometric variability of cataloged CSPNe, using the light curves from the Zwicky Transient Facility (ZTF). By applying appropriate variability metrics, we arrive at a list of 94 highly variable CSPN candidates. Based on the timescales of the light-curve activity, we classify the variables broadly into short- and long-timescale variables. In this first paper in this series, we focus on the former, which is the majority class comprising 83 objects. We report periods for six sources for the first time, and recover several known periodic variables. Among the aperiodic sources, most exhibit a jitter around a median flux with a stable amplitude, and a few show outbursts. We draw attention to WeSb 1, which shows a different kind of variability: prominent deep and aperiodic dips, resembling transits from a dust/debris disk. We find strong evidence for a binary nature of WeSb 1 (possibly an F-type subgiant companion). The compactness of the emission lines and inferred high electron densities make WeSb 1 a candidate for either an EGB 6-type planetary nucleus, or a symbiotic system inside an evolved planetary nebula, both of which are rare objects. To demonstrate further promise with ZTF, we report three additional newly identified periodic sources that do not appear in the list of highly variable sources. Finally, we also introduce a two-dimensional metric space defined by the von Neumann statistics and Pearson Skew and demonstrate its effectiveness in identifying unique variables of astrophysical interest, like WeSb 1.}, author = {Bhattacharjee, Soumyadeep and Kulkarni, S. R. and Kong, Albert K.H. and Tam, M. S. and Bond, Howard E. and El-Badry, Kareem and Caiazzo, Ilaria and Chornay, Nicholas and Graham, Matthew J. and Rodriguez, Antonio C. and Zeimann, Gregory R. and Fremling, Christoffer and Drake, Andrew J. and Werner, Klaus and Rodriguez, Hector and Prince, Thomas A. and Laher, Russ R. and Chen, Tracy X. and Riddle, Reed}, issn = {0004-6280}, journal = {Publications of the Astronomical Society of the Pacific}, number = {2}, publisher = {IOP Publishing}, title = {{Variability of central stars of planetary nebulae with the zwicky transient facility. I. Methods, short-timescale variables, and the unusual nucleus of WeSb 1}}, doi = {10.1088/1538-3873/ada702}, volume = {137}, year = {2025}, } @article{19639, abstract = {Magnetic interactions are thought to play a key role in the properties of many unconventional superconductors, including cuprates, iron pnictides, and square-planar nickelates. Superconductivity was also recently observed in the bilayer and trilayer Ruddlesden-Popper nickelates, the electronic structure of which is expected to differ from that of cuprates and square-planar nickelates. Here we study how electronic structure and magnetic interactions evolve with the number of layers, 𝑛, in thin film Ruddlesden-Popper nickelates Nd𝑛+1⁢Ni𝑛⁢O3⁢𝑛+1 with 𝑛=1,3, and 5 using resonant inelastic x-ray scattering (RIXS). The RIXS spectra are consistent with a high-spin |3⁢𝑑8⁢ 𝐿̲⟩ electronic configuration, resembling that of La2−𝑥⁢Sr𝑥⁢NiO4 and the parent perovskite, NdNiO3. The magnetic excitations soften to lower energy in the structurally self-doped, higher-𝑛 films. Our observations confirm that structural tuning is an effective route for altering electronic properties, such as magnetic superexchange, in this prominent family of materials.}, author = {Tenhuisen, Sophia F.R. and Pan, Grace A. and Song, Qi and Baykusheva, Denitsa Rangelova and Ferenc Segedin, Dan and Goodge, Berit H. and Paik, Hanjong and Pelliciari, Jonathan and Bisogni, Valentina and Gu, Yanhong and Agrestini, Stefano and Nag, Abhishek and García-Fernández, Mirian and Zhou, Ke Jin and Kourkoutis, Lena F. and Brooks, Charles M. and Mundy, Julia A. and Dean, Mark P.M. and Mitrano, Matteo}, issn = {2469-9969}, journal = {Physical Review B}, number = {16}, publisher = {American Physical Society}, title = {{Magnetic excitations in Ndn+1Nin O3n+1 Ruddlesden-Popper nickelates observed via resonant inelastic x-ray scattering}}, doi = {10.1103/PhysRevB.111.165145}, volume = {111}, year = {2025}, }