arXiv subjects

Jianqi Liu

Publications and source records attributed to Jianqi Liu.

At least 19 recordsLinked to original sources

arXiv2026

Vector Bundles of Coinvariants for Admissible Affine Vertex Operator Algebras

Simple affine vertex operator algebras $L_k(\mathfrak{g})$ at non-integral admissible levels $k$ are generally neither $C_2$-cofinite nor rational. Despite the absence of these standard finiteness conditions, we prove that the sheaf of coinvariants (and, dually, of conformal blocks) of ordinary modules in the category $\mathcal{O}_k$ forms a vector bundle over the moduli space $\overline{\mathcal{M}}_{0,n}$ of stable $n$-pointed genus-zero curves. The proof relies on establishing the finite-dimensionality of genus-zero coinvariants, a vanishing theorem that isolates ordinary admissible modules at the boundary, and a smoothing theorem enabled by partial strong identity elements in the mode transition algebra. Consequently, admissible affine vertex operator algebras supply a rich class of non-rational, non-$C_2$-cofinite examples in which vector-bundle behavior is preserved for a well-behaved subcategory of modules.

math.AG↗

arXiv2026

Physical Implications and Updated Observational Constraints of the PAge-like Unified Dark Fluid Model

The standard paradigm of cosmology assumes two distinct dark components, namely dark matter and dark energy. However, the necessity of splitting the dark-side world into two sectors has not been experimentally or theoretically proven. Unified dark fluid models provide an alternative in which a single fluid accounts for both phenomena. It is shown in Wang et al. 2024 that a PAge-like unified dark fluid (PUDF) can explain both the cosmic microwave background (CMB) and late-universe data, with the fitting quality not much worse than the standard Lambda cold dark matter ($Λ$CDM) model. Using the Planck 2018 CMB, baryon acoustic oscillations measurement from the dark energy spectroscopic instrument (DESI) data release 2, dark energy survey 5-year supernova data, and cosmic-chronometer data, we update the constraints on PUDF and clarify its physical implications. We show that PUDF can reproduce the primary CMB anisotropies, the background expansion history, and linear growth that are very close to the $Λ$CDM prediction. Nevertheless, the combined datasets still favor $Λ$CDM, largely due to the significant tension between CMB and DESI + SNe data, which exceeds the $4σ$ level in PUDF and remains non-negligible in the $w$CDM framework. Using mock data generated from the Planck best-fit $Λ$CDM model, we find that PUDF and $Λ$CDM cannot be statistically distinguished, indicating that the precision of current data is insufficient to separate the two models. Overall, the apparent preference for $Λ$CDM may be driven by dataset inconsistencies rather than a genuine physical difference, leaving unified dark fluid models as viable alternatives within current observational limits.

astro-ph.CO↗

arXiv2026

A basis theorem for Genus-One Conformal Blocks and modular invariance of intertwining operators

We prove that trace functions associated to intertwining operators over a strongly rational vertex operator algebra form a global frame of the conformal block bundle $\mathscr{C}_{\mathbb{H}}(W)$ over $\mathbb{H}$. Consequently, for each $τ\in\mathbb{H}$, these trace functions, evaluated at $τ$, form a basis of the fiber $\mathscr{C}(E_τ,\mathsf{p},z,W)$, and the natural $\mathrm{SL}(2,\mathbb{Z})$-action on the fiber is represented in this basis. This result is both a generalization and a refinement of Zhu's and Dong-Li-Mason's modular invariance theorems for trace functions associated to vertex operators and twisted vertex operators, and a specialization and refinement of Huang's and Miyamoto's modular invariance theorems for (logarithmic) intertwining operators for $C_2$-cofinite vertex operator algebras. The proof combines a new construction of a connection on the bundle $\mathscr{C}_{\mathbb{H}}(W)$, Zhu's recursive formulas for trace functions, Frenkel-Zhu's fusion rules theorem, and recent theorems of Damiolini-Gibney-Krashen-Tarasca on the geometry of sheaves of vertex operator algebra conformal blocks over the moduli spaces $\overline{\mathscr{M}}_{g,n}$.

math.QA↗

arXiv2026

On strong identities of almost-canonically seminormed rings

We investigate the strong identity condition (SIC) for almost-canonically seminormed rings, a class of topological graded rings that includes enveloping algebras of vertex operator algebras. This condition was introduced in the algebro-geometric theory of conformal blocks, where it governs the smoothing of nodal curves. To understand the representation-theoretic meaning of SIC, we develop the representation theory of almost-canonically seminormed rings, including Zhu-type algebras, induced modules, rationality conditions, tensor product compatibility, and an end formula for the mode transition algebra. Our main result characterizes the strong identity condition in terms of orthogonal expansions, projectivity of canonical modules, and Morita-type equivalences induced by Zhu-type algebras. As an application, we show that for vertex operator algebras of CFT type, the smoothing property is equivalent to the Zhu algebra inducing a Morita-type equivalence with the category of admissible modules. Consequently, the strong identity condition identifies the precise representation-theoretic obstruction to extending algebraic smoothing beyond the semisimple setting. We further illustrate the theory through explicit examples, including the Weyl algebra and several irrational vertex operator algebras where the strong identity condition fails.

math.QA↗

arXiv2026

Rank-two parabolic-type VOAs and nilpotency of nil ideals

In this paper, we undertake a systematic study of the parabolic-type sub-vertex operator algebras (subVOAs) $V_P$ of rank-two lattice VOAs $V_L$, originally introduced by the first-named author. We first classify all possible types of such subVOAs by analyzing the corresponding submonoids $P \subseteq L$. For each type of $V_P$, we then classify its irreducible modules. Certain Zhu algebras $A(V_P)$ provide new examples of rings with nil ideals that are not nilpotent. Finally, we show that the simple quotient $V_H$ of any parabolic-type subVOA $V_P$ is a $C_1$-cofinite irrational VOA satisfying the strongly unital property recently introduced by Damiolini--Gibney--Krashen.

math.QA↗

arXiv2026

One-Point Restricted Conformal Blocks and the Fusion Tensor Product

We investigate a one-point restriction of conformal blocks on $(\mathbb{P}^1,\infty,1,0)$ associated with modules over a vertex operator algebra. By restricting the module attached to the point $\infty$ to its bottom degree, we obtain a new formula for computing fusion rules in terms of a left $A(V)$-module $M^1\odot M^2$ over the Zhu algebra $A(V)$. As a consequence, for strongly rational VOAs, the construction of $M^1\odot M^2$ induces the fusion tensor product on the module category $\mathsf{Mod}(A(V))$.

math.QA↗

arXiv2025

Finite induction functor for vertex operator algebras

In this paper, we introduce a new induction functor $\mathrm{Ind}^V_U$ between module categories corresponding to an embedding of vertex operator algebras (VOAs) $U \hookrightarrow V$. This induction functor is essentially defined at the level of the finite (Zhu) algebras, which we call the \emph{finite induction functor}. Under suitable conditions on $U$ and $V$, we prove that this functor satisfies the usual properties of induction functors, such as Frobenius reciprocity, functorial property for compositions, and an analogue of Artin's induction theorem for certain associated characters. To better understand the effect of this functor, we explicitly determine the finite induction of irreducible modules for standard subVOAs of the rank-one lattice/affine VOA $V_{A_1}$, as well as the finite induction of irreducible modules over a parabolic-type subVOA $V_P$ of the rank-two lattice/affine VOA $V_{A_2}$.

math.QA↗

arXiv2025

BEV-LIO(LC): BEV Image Assisted LiDAR-Inertial Odometry with Loop Closure

This work introduces BEV-LIO(LC), a novel LiDAR-Inertial Odometry (LIO) framework that combines Bird's Eye View (BEV) image representations of LiDAR data with geometry-based point cloud registration and incorporates loop closure (LC) through BEV image features. By normalizing point density, we project LiDAR point clouds into BEV images, thereby enabling efficient feature extraction and matching. A lightweight convolutional neural network (CNN) based feature extractor is employed to extract distinctive local and global descriptors from the BEV images. Local descriptors are used to match BEV images with FAST keypoints for reprojection error construction, while global descriptors facilitate loop closure detection. Reprojection error minimization is then integrated with point-to-plane registration within an iterated Extended Kalman Filter (iEKF). In the back-end, global descriptors are used to create a KD-tree-indexed keyframe database for accurate loop closure detection. When a loop closure is detected, Random Sample Consensus (RANSAC) computes a coarse transform from BEV image matching, which serves as the initial estimate for Iterative Closest Point (ICP). The refined transform is subsequently incorporated into a factor graph along with odometry factors, improving the global consistency of localization. Extensive experiments conducted in various scenarios with different LiDAR types demonstrate that BEV-LIO(LC) outperforms state-of-the-art methods, achieving competitive localization accuracy. Our code and video can be found at https://github.com/HxCa1/BEV-LIO-LC.

cs.RO↗

arXiv2025

Borel-type subalgebras of the lattice vertex operator algebra

In this paper, we introduce and study new classes of sub-vertex operator algebras of the lattice vertex operator algebras (VOAs), which we call the conic, Borel, and parabolic-type subVOAs. These CFT-type VOAs, which are not necessarily strongly finitely generated, satisfy properties similar to the usual Borel and parabolic subalgebras of a Lie algebra. For the lowest-rank nontrivial example of Borel-type subVOA $V_{B}$ of $V_{\Z\al}$, we explicitly determine its Zhu's algebra $A(V_B)$ in terms of generators and relations.

math.QA↗

arXiv2025

LL-Localizer: A Life-Long Localization System based on Dynamic i-Octree

This paper proposes an incremental voxel-based life-long localization method, LL-Localizer, which enables robots to localize robustly and accurately in multi-session mode using prior maps. Meanwhile, considering that it is difficult to be aware of changes in the environment in the prior map and robots may traverse between mapped and unmapped areas during actual operation, we will update the map when needed according to the established strategies through incremental voxel map. Besides, to ensure high performance in real-time and facilitate our map management, we utilize Dynamic i-Octree, an efficient organization of 3D points based on Dynamic Octree to load local map and update the map during the robot's operation. The experiments show that our system can perform stable and accurate localization comparable to state-of-the-art LIO systems. And even if the environment in the prior map changes or the robots traverse between mapped and unmapped areas, our system can still maintain robust and accurate localization without any distinction. Our demo can be found on Blibili (https://www.bilibili.com/video/BV1faZHYCEkZ) and youtube (https://youtu.be/UWn7RCb9kA8) and the program will be available at https://github.com/M-Evanovic/LL-Localizer.

cs.RO↗

arXiv2025

Key drivers of the preference for dynamic dark energy

Joint analysis of the baryon acoustic oscillations (BAO) measurement by the Dark Energy Spectroscopic Instrument (DESI) first data release, Type Ia supernovae (SNe) of the Dark Energy Survey Year 5 (DES5YR) release and cosmic microwave background (CMB) data favors a quintom-like dynamic dark energy model over the standard Lambda cold dark matter ($Λ$CDM) model at $3.9σ$ level (Adame et al. 2024). We confirm the previous finding in the literature that the preference for dynamic dark energy does not rely on the detailed modeling of CMB physics and remains at a similar significance level ($3.2σ$) when the full CMB likelihood is replaced by a CMB acoustic-oscillation angle ($θ_\star$) prior and a baryon abundance ($Ω_bh^2$) prior. The computationally efficient $θ_\star$ and $Ω_bh^2$ priors allow us to take a frequentist approach by comparing DES5YR SNe and DESI BAO with a large number ($\gtrsim 10^4$) of Planck-constrained $Λ$CDM simulations. We find that $\geq 3.2σ$ preference for dynamic dark energy is very rare (occurrence rate = $0.28\%$) in simulations. When we combine DESI BAO with SN simulations or combine DES5YR SNe with BAO simulations, the occurrence rate of $\geq 3.2σ$ preference for dynamic dark energy increases to $1.2\%$ and $4.8\%$, respectively. These results indicate an internal inconsistency, i.e., a significant tension between DESI BAO + DES5YR SNe and Planck-constrained $Λ$CDM models in both Bayesian and frequentist points of view. Although both DESI BAO and DES5YR SNe contribute to the preference for dynamic dark energy, the contribution from DES5YR SNe is more significant. In the frequentist point of view, even DES5YR SNe alone is in tension with Planck-constrained $Λ$CDM models, though in Bayesian point of view this tension is prior dependent and inconclusive.

astro-ph.CO↗

arXiv2024

Quantifying the tension between cosmological models and JWST red candidate massive galaxies

We develop a Python tool to estimate the tail distribution of the number of dark matter halos beyond a mass threshold and in a given volume in a light-cone. The code is based on the extended Press-Schechter model and is computationally efficient, typically taking a few seconds on a personal laptop for a given set of cosmological parameters. The high efficiency of the code allows a quick estimation of the tension between cosmological models and the red candidate massive galaxies released by the James Webb Space Telescope, as well as scanning the theory space with the Markov Chain Monte Carlo method. As an example application, we use the tool to study the cosmological implication of the candidate galaxies presented in Labbé et al. (2023). The standard $Λ$ cold dark matter ($Λ$CDM) model is well consistent with the data if the star formation efficiency can reach $\sim 0.3$ at high redshift. For a low star formation efficiency $ε\sim 0.1$, $Λ$CDM model is disfavored at $\sim 2σ$-$3σ$ confidence level.

astro-ph.CO↗

arXiv2024

A PAge-like Unified Dark Fluid Model

The unified dark fluid model unifies dark matter and dark energy into a single component, providing an alternative and more concise framework for interpreting cosmological observations. We introduce a PAge-like Unified Dark Fluid (PUDF) model based on the PAge approximation (Huang 2020), which is parameterized by the age of the universe and an $η$ parameter indicating the deviation from Einstein-De Sitter Universe. The PUDF model shares many similar features of the standard Lambda cold dark matter ($Λ$CDM) model and can effectively describe the large-scale structure formation and late-time cosmic acceleration. We constrain the PUDF model with the Planck 2018 cosmic microwave background anisotropies, baryon acoustic oscillation measurements including those from the most recent DESI 2024, the Pantheon+ sample of Type Ia supernovae, and the Cosmic Chronometers compilation. Although the PUDF performs well in fitting all the cosmological datasets, the joint analysis of the data still favors the $Λ$CDM model over the PUDF model, according to the Bayesian evidence of model comparison.

astro-ph.CO↗

arXiv2024

Curvature perturbations from kinetic preheating after $α$-attractor inflation

Preheating at the end of inflation is a violent nonlinear process that efficiently transfers the energy of the inflaton to a second field, the preheat field. When the preheat field is light during inflation and its background value modulates the preheating process, the superhorizon isocurvature perturbations of the preheat field may be converted to curvature perturbations that leave an imprint on the cosmic microwave background and the large-scale structure of the universe. We use high-precision lattice simulations to study kinetic preheating after $α$-attractor inflation, a case where the effective mass of the preheat field is naturally suppressed during inflation. By comparing the expansion e-folds between different Hubble patches, we find that the conversion from isocurvature perturbations to curvature perturbations is very inefficient and can hardly be detected by cosmological observations.

astro-ph.CO↗

arXiv2024

Observational constraints on phenomenological emergent dark energy and barotropic dark matter characterized by a constant equation of state parameter

We propose a new cosmological model that considers dark matter as a barotropic fluid with a constant equation of state parameter and interprets dark energy as the phenomenological emergent dark energy rather than a cosmological constant. This proposal is based on extensive research on the extended properties of dark matter in the context of a cosmological constant and the intriguing findings that have emerged from our exploration of dark matter properties within the context of PEDE in our previous studies. We then place constraints on this model in light of the Planck 2018 Cosmic Microwave Background (CMB) anisotropies, baryon acoustic oscillation (BAO) measurements, the Pantheon compilation of Type Ia supernovae, a prior on $H_0$ that based on the latest local measurement by Riess et al., and the combination of KiDS and the VISTA Kilo-Degree Infrared Galaxy Survey (KiDS+VIKING-450). The results indicate a preference for a positive dark matter equation of state parameter at 68\% confidence level for CMB+BAO, CMB+BAO+Pantheon and CMB+BAO+Pantheon+$H_0$ datasets. Furthermore, the Hubble tension between all of the datasets we used with R22 is very close to those of the PEDE, and the $S_8$ tension between Planck 2018 and KiDS+VIKING-450 is reduced from 2.3$σ$ in the PEDE model to 0.4$σ$ in the new model. However, Bayesian evidence indicates that PEDE favors our new model with very strong evidence from all the datasets considered in this study. Consequently, we conclude that the PEDE+$w_{\rm dm}$ model is not a viable alternative to the PEDE model.

astro-ph.CO↗

arXiv2024

Noetherianity of twisted Zhu algebra and bimodules

In this paper we show that for a large natural class of vertex operator algebras (VOAs) and their modules, the Zhu algebras and bimodules (and their $g$-twisted analogs) are Noetherian. These carry important information about the representation theory of the VOA, and its fusion rules, and the Noetherian property gives the potential for (non-commutative) algebro-geometric methods to be employed in their study.

math.QA↗

arXiv2024

Twisted restricted conformal blocks of vertex operator algebras II: twisted restricted conformal blocks on totally ramified orbicurves

In this paper, we introduce a notion of twisted restricted conformal blocks on totally ramified orbicurves and establish an isomorphism between the space of twisted restricted conformal blocks and the space of twisted conformal blocks. The relationships among twisted (restricted) conformal blocks, $g$-twisted (restricted) correlation functions, and twisted intertwining operators are explored. Furthermore, by introducing a geometric generalization of Zhu's algebra and its modules, we obtain a description of the space of coinvariants by modules over associative algebras and show it is finite-dimensional under some conditions. In particular, a more conceptual proof of the $g$-twisted fusion rules theorem in vertex operator algebra theory is provided.

math.AG↗

arXiv2024

Cosmological constraints on neutrino masses in light of JWST red and massive candidate galaxies

The overabundance of the red and massive candidate galaxies observed by the James Webb Space Telescope (JWST) implies efficient structure formation or large star formation efficiency at high redshift $z\sim 10$. In the scenario of a low or moderate star formation efficiency, because massive neutrinos tend to suppress the growth of structure of the universe, the JWST observation tightens the upper bound of the neutrino masses. Assuming $Λ$ cold dark matter cosmology and a star formation efficiency $ \in [0.05, 0.3]$ (flat prior), we perform joint analyses of Planck+JWST and Planck+BAO+JWST, and obtain improved constraints $\sum m_ν< 0.196\,\mathrm{eV}$ and $\sum m_ν< 0.111\,\mathrm{eV}$ at 95% confidence level, respectively. Based on the above assumptions, the inverted mass ordering, which implies $\sum m_ν\geq 0.1\mathrm{eV}$, is excluded by Planck+BAO+JWST at 92.7% confidence level.

astro-ph.CO↗