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Jie Xiao

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math.AP math.QA math.RT math.CV math.DG math.FA hep-ph Artificial Intelligence Machine Learning astro-ph.HE Computer Vision cond-mat.mtrl-sci hep-ex math.CT math.MG math.RA physics.chem-ph

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preprint2026arXiv

Prospects for studying the $WHγ$ process in $pp$ collisions at the LHC

The Standard Model of particle physics, though remarkably successful, leaves open several major questions that continue to motivate searches for new phenomena. Multiboson interactions involving the Higgs boson are of special interest as probes of the electroweak Lagrangian where potential new physics may be hiding. In this work, we present a study of the simultaneous production of a W boson, a Higgs bosons and a photon in proton-proton collisions at the Large Hadron Collider. Monte Carlo simulation is performed to model both the signal and the background processes, and detector effects are included according to CMS specifications. Boosted decision trees are employed to optimize the event selection and enhance signal-background discrimination. We estimate that with an integrated luminosity of 440~ $\rm fb^{-1}$ , the expected significance for the $WHγ$ process is 0.63 $σ$ , projected to reach 1.64 $σ$ at the High-Luminosity LHC (HL-LHC).

preprint2026arXiv

TwinRouterBench: Fast Static and Live Dynamic Evaluation for Realistic Agentic LLM Routing

LLM routing matters most in long-horizon applications such as coding agents, deep research systems, and computer-use agents, where a single user request triggers many model calls. Routing each call to the cheapest sufficient model can cut costs without sacrificing quality, yet existing router benchmarks evaluate routers only on one-shot prompts. They never expose the router-visible prefix at an intermediate agent step, never test whether a cheaper replacement preserves downstream task success, and often rely on online LLM judges at evaluation time. We introduce TwinRouterBench, a step-level routing benchmark with two tracks. The static track provides 970 router-visible prefixes from 520 instances across SWE-bench, BFCL, mtRAG, QMSum, and PinchBench, each paired with an execution-verified target tier estimated under a released downgrade-and-cascade protocol; scoring is deterministic arithmetic over tier labels, trajectory membership, and token costs, with no online evaluator-side LLM judge. The dynamic track supplies a harness that runs routers on the full 500-case SWE-bench Verified suite; in this paper we report a 100-case held-out evaluation disjoint from the static SWE supervision split. At each LLM call the router selects a concrete model from a locked pool, and success is measured by official task resolution and realized API spend. The two tracks support fast offline iteration followed by end-to-end validation under live agent execution. Code and data are available at https://github.com/CommonstackAI/TwinRouterBench.

preprint2024arXiv

RHOBIN Challenge: Reconstruction of Human Object Interaction

Modeling the interaction between humans and objects has been an emerging research direction in recent years. Capturing human-object interaction is however a very challenging task due to heavy occlusion and complex dynamics, which requires understanding not only 3D human pose, and object pose but also the interaction between them. Reconstruction of 3D humans and objects has been two separate research fields in computer vision for a long time. We hence proposed the first RHOBIN challenge: reconstruction of human-object interactions in conjunction with the RHOBIN workshop. It was aimed at bringing the research communities of human and object reconstruction as well as interaction modeling together to discuss techniques and exchange ideas. Our challenge consists of three tracks of 3D reconstruction from monocular RGB images with a focus on dealing with challenging interaction scenarios. Our challenge attracted more than 100 participants with more than 300 submissions, indicating the broad interest in the research communities. This paper describes the settings of our challenge and discusses the winning methods of each track in more detail. We observe that the human reconstruction task is becoming mature even under heavy occlusion settings while object pose estimation and joint reconstruction remain challenging tasks. With the growing interest in interaction modeling, we hope this report can provide useful insights and foster future research in this direction. Our workshop website can be found at \href{https://rhobin-challenge.github.io/}{https://rhobin-challenge.github.io/}.

preprint2022arXiv

A sensitivity study of VBS and diboson WW to dimension-6 EFT operators at the LHC

We present a parton-level study of electro-weak production of vector-boson pairs at the Large Hadron Collider, establishing the sensitivity to a set of dimension-six operators in the Standard Model Effective Field Theory (SMEFT). Different final states are statistically combined, and we discuss how the orthogonality and interdependence of different analyses must be considered to obtain the most stringent constraints. The main novelties of our study are the inclusion of SMEFT effects in non-resonant diagrams and in irreducible QCD backgrounds, and an exhaustive template analysis of optimal observables for each operator and process considered. We also assess for the first time the sensitivity of vector-boson-scattering searches in semileptonic final states.

preprint2022arXiv

Boosted tau lepton as a microscope and macroscope

Anomalies from the LHCb lepton flavour universality and Fermilab muon anomalous magnetic momentum, show tantalizing hints of possible new physics from the lepton sectors. Due to its large mass and shorter lifetime than muon, the tau lepton is believed to couple more to possible new physics beyond the standard model. Traditionally, tau leptons are probed through the decay products due to tau's short life time. On the other hand, at a high energy scale, a large fraction of tau leptons could be boosted to a much longer life time and fly a visible distance from several centimetres up to kilometer length scale, yet very informative to new physics beyond the standard model or high energy cosmic rays. In this article, we show unique yet promising tau physics by exploiting long-lived taus as a microscope or macroscope, to measure tau's anomalous magnetic momentum to an unprecedented level of accuracy and detect high energy cosmic neutrinos at the 1 TeV to 1 PeV scale, respectively.

preprint2022arXiv

Principled Knowledge Extrapolation with GANs

Human can extrapolate well, generalize daily knowledge into unseen scenarios, raise and answer counterfactual questions. To imitate this ability via generative models, previous works have extensively studied explicitly encoding Structural Causal Models (SCMs) into architectures of generator networks. This methodology, however, limits the flexibility of the generator as they must be carefully crafted to follow the causal graph, and demands a ground truth SCM with strong ignorability assumption as prior, which is a nontrivial assumption in many real scenarios. Thus, many current causal GAN methods fail to generate high fidelity counterfactual results as they cannot easily leverage state-of-the-art generative models. In this paper, we propose to study counterfactual synthesis from a new perspective of knowledge extrapolation, where a given knowledge dimension of the data distribution is extrapolated, but the remaining knowledge is kept indistinguishable from the original distribution. We show that an adversarial game with a closed-form discriminator can be used to address the knowledge extrapolation problem, and a novel principal knowledge descent method can efficiently estimate the extrapolated distribution through the adversarial game. Our method enjoys both elegant theoretical guarantees and superior performance in many scenarios.

preprint2022arXiv

Stabilization of Co oxide during oxygen evolution in alkaline media by the introduction of Mn oxide

Improving the stability of electrocatalysts for the oxygen evolution reaction (OER) through materials design has received less attention than improving their catalytic activity. We explored the effect of Mn addition to a cobalt oxide for stabilizing the catalyst by comparing Na-containing CoOx and (Co0.7Mn0.3)Ox films electrodeposited in alkaline solution. The obtained disordered films were classified as layered oxides using X-ray absorption spectroscopy (XAS). The CoOx films showed a constant decrease in the catalytic activity during cycling, confirmed by oxygen detection, while that of (Co0.7Mn0.3)Ox slightly increased as measured by electrochemical metrics. These trends were rationalized based on XAS analysis of the metal oxidation states, which were Co2.8+ and Mn3.7+ near the surface after cycling. Thus, adding Mn to CoOx successfully stabilized the catalyst material and its activity during OER cycling. The development of stabilization approaches is essential to extend the durability of OER catalysts.

preprint2021arXiv

Searching for heavy leptoquarks at a muon collider

The LHCb Collaboration recently gave an update on testing lepton flavour universality with $B^+ \rightarrow K^+ \ell^+ \ell^-$ , in which a 3.1 standard deviations from the standard model prediction was observed. The g-2 experiment also reports a 3.3 standard deviations from the standard model on muon anomalous magnetic moment measurement. These deviations could be explained by introducing new particles including leptoquarks. In this paper, we show the possibility to search for heavy spin-1 leptoquarks at a future TeV scale muon collider by performing studies from three channels: 1) same flavour final states with either two bottom or two light quarks, 2) different flavour quark final states, and 3) a so-called "VXS" process representing the scattering between a vector boson and a leptoquark to probe the coupling between leptoquark and tau lepton. We conclude that a 3 TeV muon collider with $3~{ab^{-1}}$ of integrated luminosity is already sufficient to cover the leptoquark parameter space in order to explain the LHCb lepton flavour universality anomaly.

preprint2016arXiv

A Maximum Problem of S.-T. Yau for Variational p-Capacity

Through using the semidiameter (in connection to: the mean radius and surface radius) of a convex closed hypersurface in $\mathbb R^{n\ge 2}$ as an sharp upper bound of the variational $(1,n)\ni p$ -capacity radius, this paper settles a restriction/variant of S.-T. Yau's \cite[Problem 59]{Yau} from the surface area to the variational $p$ -capacity whose limit as $p\to 1$ actually induces the surface area.

preprint2016arXiv

A quasiconformal composition problem for the Q-spaces

Given a quasiconformal mapping $f:\mathbb R^n\to\mathbb R^n$ with $n\ge2$ , we show that (un-)boundedness of the composition operator ${\bf C}_f$ on the spaces $Q_α(\mathbb R^n)$ depends on the index $α$ and the degeneracy set of the Jacobian $J_f$ . We establish sharp results in terms of the index $α$ and the local/global self-similar Minkowski dimension of the degeneracy set of $J_f$ . This gives a solution to [Problem 8.4, 3] and also reveals a completely new phenomenon, which is totally different from the known results for Sobolev, BMO, Triebel-Lizorkin and Besov spaces. Consequently, Tukia-Väisälä's quasiconformal extension $f:\mathbb R^n\to\mathbb R^n$ of an arbitrary quasisymmetric mapping $g:\mathbb R^{n-p}\to \mathbb R^{n-p}$ is shown to preserve $Q_α (\mathbb R^n)$ for any $(α,p)\in (0,1)\times[2,n)\cup(0,1/2)\times\{1\}$ . Moreover, $Q_α(\mathbb R^n)$ is shown to be invariant under inversions for all $0<α<1$ .

preprint2015arXiv

Geometric realizations of Lusztig's symmetries

In this paper, we give geometric realizations of Lusztig's symmetries. We also give projective resolutions of a kind of standard modules. By using the geometric realizations and the projective resolutions, we obtain the categorification of the formulas of Lusztig's symmetries.

preprint2015arXiv

Hall algebras of cyclic quivers and $q$ -deformed Fock spaces

Based on the work of Ringel and Green, one can define the (Drinfeld) double Ringel--Hall algebra ${\mathscr D}(Q)$ of a quiver $Q$ as well as its highest weight modules. The main purpose of the present paper is to show that the basic representation $L(Λ_0)$ of ${\mathscr D}(Δ_n)$ of the cyclic quiver $Δ_n$ provides a realization of the $q$ -deformed Fock space $\bigwedge^\infty$ defined by Hayashi. This is worked out by extending a construction of Varagnolo and Vasserot. By analysing the structure of nilpotent representations of $Δ_n$ , we obtain a decomposition of the basic representation $L(Λ_0)$ which induces the Kashiwara--Miwa--Stern decomposition of $\bigwedge^\infty$ and a construction of the canonical basis of $\bigwedge^\infty$ defined by Leclerc and Thibon in terms of certain monomial basis elements in ${\mathscr D}(Δ_n)$ .

preprint2015arXiv

p-capacity vs surface-area

This paper is devoted to exploring the relationship between the $[1,n)\ni p$ -capacity and the surface-area in $\mathbb R^{n\ge 2}$ which especially shows: if $Ω\subset\mathbb R^n$ is a convex, compact, smooth set with its interior $Ω^\circ\not=\emptyset$ and the mean curvature $H(\partialΩ,\cdot)>0$ of its boundary $\partialΩ$ then $\left(\frac{n(p-1)}{p(n-1)}\right)^{p-1}\le\frac{\left(\frac{\hbox{cap}_p(Ω)}{\big(\frac{p-1}{n-p}\big)^{1-p}σ_{n-1}}\right)}{\left(\frac{\hbox{area}(\partialΩ)}{σ_{n-1}}\right)^\frac{n-p}{n-1}}\le\left(\sqrt[n-1]{\int_{\partialΩ}\big(H(\partialΩ,\cdot)\big)^{n-1}\frac{dσ(\cdot)}{σ_{n-1}}}\right)^{p-1}\quad\forall\quad p\in (1,n)$ whose limits $1\leftarrow p\ \&\ p\rightarrow n$ imply $1=\frac{cap_1(Ω)}{\hbox{area}(\partialΩ)}\ \ \& \ \int_{\partialΩ}\big(H(\partialΩ,\cdot)\big)^{n-1}\frac{dσ(\cdot)}{σ_{n-1}}\ge 1,$ thereby not only discovering that the new best known constant is roughly half as far from the one conjectured by Pólya-Szegö in \cite[(2)]{P} but also extending the Pólya-Szegö inequality in \cite[(5)]{P}, with both the conjecture and the inequality being stated for the electrostatic capacity of a convex solid in $\mathbb R^3$ .

preprint2015arXiv

Uniqueness of nonnegative weak solution to $u^p\le(-Δ)^\fracα{2}u$ on $\mathbb R^N$

This note shows that under $(p,α, N)\in (1,\infty)\times(0,2)\times\mathbb Z_+$ the fractional order differential inequality $(\dagger)\quad u^p \le (-Δ)^{\fracα{2}} u\quad\hbox{in}\quad\mathbb R^{N}$ has the property that if $N\leα$ then a nonnegative solution to $(\dagger)$ is unique, and if $N>α$ then the uniqueness of a nonnegative weak solution to $(\dagger)$ occurs when and only when $p\le N/(N-α)$ , thereby innovatively generalizing Gidas-Spruck's result for $u^p+Δu\le 0$ in $\R^N$ discovered in \cite{GS}.

preprint2014arXiv

Analytic Campanato Spaces and Their Compositions

This paper is devoted to characterizing the analytic Campanato spaces $\mathcal{AL}_{p,η}$ (including the analytic Morrey spaces, the analytic John-Nirenberg space, and the analytic Lipschitz/Hölder spaces) on the complex unit disk $\mathbb D$ in terms of the Möbius mapping and the Littlewood-Paley form, and consequently their compositions with the analytic self-maps of $\mathbb D$ .

preprint2014arXiv

Gaussian integral means of entire functions: logarithmic convexity and concavity

For $0<p<\infty$ and $α\in (-\infty,\infty)$ we determine when the $L^p$ integral mean on $\{z\in\mathbb C: |z|\le r\}$ of an entire function with respect to the Gaussian area measure $e^{-α|z|^2}\,dA(z)$ is logarithmic convex or logarithmic concave.

preprint2014arXiv

Geometric Capacity Potentials on Convex Plane Rings

Under $1<p\le 2$ , this paper presents some old and new convexity/isoperimetry based inequalities for the variational $p$ -capacity potentials on convex plane rings.

preprint2014arXiv

Global Mild Solutions of Fractional Naiver-Stokes Equations with Small Initial Data in Critical Besov-Q Spaces

In this paper, we establish the global existence and uniqueness of a mild solution of the so-called fractional Navier-Stokes equations with a small initial data in the critical Besov-Q space covering many already known function spaces.

preprint2014arXiv

Holomorphic Campanato Spaces on the Unit Ball

As outlined below, this paper is devoted to a Carleson-type-measure-based study of the holomorphic Campanato $2$ -space on the open unit ball $\mathbb B_n$ of $\mathbb C^n$ , comprising all Hardy $2$ -functions whose oscillations in non-isotropic metric balls on the compact unit sphere $\mathbb S_n$ are proportional to some power of the radius other than the dimension $n\ge 1$ .

preprint2014arXiv

Isocapacity Estimates for Hessian Operators

Through a new powerful potential-theoretic analysis, this paper is devoted to discovering the geometrically equivalent isocapacity forms of Chou-Wang's Sobolev type inequality and Tian-Wang's Moser-Trudinger type inequality for the fully nonlinear $1\leq k\leq n/2$ Hessian operators.

preprint2014arXiv

Optimal geometric estimates for fractional Sobolev capacities

This note develops certain sharp inequalities relating the fractional Sobolev capacity of a set to its standard volume and fractional perimeter.

preprint2014arXiv

Preduals of quadratic Campanato spaces associated to operators with heat kernel bounds

Let $L$ be a nonnegative, self-adjoint operator on $L^2(\mathbb{R}^n)$ with the Gaussian upper bound on its heat kernel. As a generalization of the square Campanato space $\mathcal{L}^{2,λ}_{-Δ}(\mathbb R^n)$ , in \cite{DXY} the quadratic Campanato space $\mathcal{L}_L^{2,λ}(\mathbb{R}^n)$ is defined by a variant of the maximal function associated with the semigroup $\{e^{-tL}\}_{t\geq 0}$ . On the basis of \cite{DX} and \cite{YY} this paper addresses the preduality of $\mathcal{L}_L^{2,λ}(\mathbb{R}^n)$ through an induced atom (or molecular) decomposition. Even in the case $L=-Δ$ the discovered predual result is new and natural.

preprint2014arXiv

Towards spaces of harmonic functions with traces in square Campanato space and its scaling invariant

For $n\ge 1$ and $α\in (-1,1)$ , let $H^{α,2}$ be the space of harmonic functions $u$ on the upper half space $\mathbb{R}^{n+1}_+$ satisfying $\displaystyle\sup_{(x_0,r)\in \mathbb R^{n+1}_+}r^{-(2α+n)}\int_{B(x_0,r)}\int_0^r|\nabla_{x,t} u(x,t)|^2t\,dt\,dx<\infty,$ and $\mathcal{L}_{2,n+2α}$ be the Campanato space on $\mathbb R^n$ . We show that $H^{α,2}$ coincide with $e^{-t\sqrt{-Δ}}\mathcal{L}_{2,n+2α}$ for all $α\in (-1,1)$ , where the case $α\in [0,1)$ was originally discovered by Fabes, Johnson and Neri [Indiana Univ. Math. J. 25 (1976), 159-170] and yet the case $α\in (-1,0)$ was left open. Moreover, for the scaling invariant version of $H^{α,2}$ , $\mathcal{H}^{α,2}$ , which comprises all harmonic functions $u$ on $\mathbb R^{n+1}_+$ satisfying $\sup_{(x_0,r)\in\mathbb R^{n+1}_+}r^{-(2α+n)}\int_{B(x_0,r)} \int_0^r|\nabla_{x,t} u(x,t)|^2\,t^{1+2α} \,dt\,dx<\infty,$ we show that $\mathcal{H}^{α,2}=e^{-t\sqrt{-Δ}}(-Δ)^\fracα{2}\mathcal{L}_{2,n+2α}$ , where $(-Δ)^{\fracα{2}}\mathcal{L}_{2,n+2α}$ is the collection of all functions $f$ such that $(-Δ)^{-\fracα{2}}f$ are in $\mathcal{L}_{2,n+2α}$ . Analogues for solutions to the heat equation are also established. As an application, we show that the spaces $\big((-Δ)^{\fracα{2}}\mathcal{L}_{2,n+2α}\big)^{-1}$ unify $Q_α^{-1}$ , ${\mathrm{BMO}}^{-1}$ and $\dot{B}^{-1,\infty}_\infty$ naturally.

preprint2014arXiv

Two Predualities and Three Operators over Analytic Campanato Spaces

This article is devoted to not only characterizing the first and second preduals of the analytic Campanato spaces ( $\mathcal{CA}_p)$ on the unit disk, but also investigating boundedness of three operators: superposition ( $\mathsf{S}^ϕ$ ); backward shift ( $\mathsf{S_b}$ ); Schwarzian derivative ( $\mathsf{S}$ ), acting on $\mathcal{CA}_p$ .

preprint2013arXiv

Gaussian Integral Means of Entire Functions

For an entire mapping $f:\mathbb C\mapsto\mathbb C$ and a triple $(p,α, r)\in (0,\infty)\times(-\infty,\infty)\times(0,\infty]$ , the Gaussian integral means of $f$ (with respect to the area measure $dA$ ) is defined by ${\mathsf M}_{p,α}(f,r)=\Big({\int_{|z|<r}e^{-α|z|^2}dA(z)}\Big)^{-1}{\int_{|z|<r}|f(z)|^p{e^{-α|z|^2}}dA(z)}.$ Via deriving a maximum principle for ${\mathsf M}_{p,α}(f,r)$ , we establish not only Fock-Sobolev trace inequalities associated with ${\mathsf M}_{p,p/2}(z^m f(z),\infty)$ (as $m=0,1,2,...$ ), but also convexities of $r\mapsto\ln {\mathsf M}_{p,α}(z^m,r)$ and $r\mapsto {\mathsf M}_{2,α<0}(f,r)$ in $\ln r$ with $0<r<\infty$ .

preprint2013arXiv

Homothetic variant of fractional Sobolev space with application to Navier-Stokes system revisited

This note provides a deeper understanding of the main results obtained in the author's 2007 DPDE paper \cite{Xiao}.

preprint2013arXiv

Regularity and Capacity for the Fractional Dissipative Operator

This note is devoted to exploring some analytic-geometric properties of the regularity and capacity associated to the so-called fractional dissipative operator $\partial_t+(-Δ)^α$ , naturally establishing a diagonally sharp Hausdorff dimension estimate for the blow-up set of a weak solution to the fractional dissipative equation $(\partial_t+(-Δ)^α)u(t,x)=F(t,x)$ subject to $u(0,x)=0$ .

preprint2013arXiv

Remarks on Hall algebras of triangulated categories

We introduce the notion of the Drinfeld dual of an algebra and show that Hall algebras defined by Kontsevich-Soibelman in \cite{KS} are the Drinfeld duals of derived Hall algebras defined in \cite{Toen2005} and \cite{XX2006}. Moreover, we construct the motivic analogue of a derived Hall algebra and prove that it is isomorphic to the motivic Hall algebra constructed in \cite{KS}.

preprint2013arXiv

Towards Conformal Capacities in Euclidean Spaces

This paper addresses the so-called conformal capacities in $\mathbb R^n$ , $n\ge 3$ , through comparing three existing definitions (due to Betsakos, Colesanti-Cuoghi, Anderson-Vamananmurthy-Fuglede respectively) and studying their associated iso-capacitary inequalities with connection to half-diameter, mean-width, mean-curvature and ADM-mass, Hadamard type variational formula, Minkowski type problem, and Yau type problem.

preprint2012arXiv

A parameterization of the canonical bases of affine modified quantized enveloping algebras

For symmetrizable Kac-Moody Lie algebra $\textbf{g}$ , Lusztig introduced the modified quantized enveloping algebra $\dot{\textbf{U}}(\textbf{g})$ and its canonical basis in [12]. In this paper, for finite and affine type symmetric Lie algebra $\textbf{g}$ we define a set which depend only on the root category and prove that there is a bijection between the set and the canonical basis of $\dot{\textbf{U}}(\textbf{g})$ , where the root category is the $T^2$ -orbit category of the derived category of Dynkin or tame quiver. Our method bases on one theorem of Lin, Xiao and Zhang in [9], which gave the PBW-basis of $\textbf{U}^+(\textbf{g})$ .

preprint2012arXiv

BGP-Reflection Functors and Lusztig's Symmetries of Modified Quantized Enveloping Algebras

Let $\mathbf{U}$ be the quantized enveloping algebra and $\dot{\mathbf{U}}$ its modified form. Lusztig gives some symmetries on $\mathbf{U}$ and $\dot{\mathbf{U}}$ . Since the realization of $\mathbf{U}$ by the reduced Drinfeld double of the Ringel-Hall algebra, one can apply the BGP-reflection functors to the double Ringel-Hall algebra to obtain Lusztig's symmetries on $\mathbf{U}$ and their important properties, for instance, the braid relations. In this paper, we define a modified form $\dot{\mathcal{H}}$ of the Ringel-Hall algebra and realize the Lusztig's symmetries on $\dot{\mathbf{U}}$ by applying the BGP-reflection functors to $\dot{\mathcal{H}}$ .

preprint2012arXiv

Composition Operators between Analytic Campanato Spaces

This note characterizes both boundedness and compactness of a composition operator between any two analytic Campanato spaces on the unit complex disk.

preprint2012arXiv

Hall algebra approach to Drinfeld's presentation of quantum loop algebras

The quantum loop algebra $U_{v}(\mathcal{L}\mathfrak{g})$ was defined as a generalization of the Drinfeld's new realization of the quantum affine algebra to the loop algebra of any Kac-Moody algebra $\mathfrak{g}$ . It has been shown by Schiffmann that the Hall algebra of the category of coherent sheaves on a weighted projective line is closely related to the quantum loop algebra $U_{v}(\mathcal{L}\mathfrak{g})$ , for some $\mathfrak{g}$ with a star-shaped Dynkin diagram. In this paper we study Drinfeld's presentation of $U_{v}(\mathcal{L}\mathfrak{g})$ in the double Hall algebra setting, based on Schiffmann's work. We explicitly find out a collection of generators of the double composition algebra $\mathbf{DC}(\Coh(\mathbb{X}))$ and verify that they satisfy all the Drinfeld relations.

preprint2012arXiv

Limiting Weak Type Estimate for Capacitary Maximal Function

A capacitary analogue of the limiting weak type estimate of P. Janakiraman for the Hardy-Littlewood maximal function of an L1-function is discovered.

preprint2011arXiv

The Semi-linear Torsional Rigidity on a Complete Riemannian Two-Manifold

This note is concerned with some essential properties (optimal isoperimetry, first variation, and monotonicity formula) of the so-called $[0,1)\niγ$ -torsional rigidity $\mathcal{T}_{γ,\mathsf{g}}$ on a complete Riemannian two-manifold $(\mathbb M^2,\mathsf{g})$ . Even in the special case of $\mathbb R^2$ , major results are new.

preprint2011arXiv

Weighted Integral Means of Mixed Areas and Lengths under Holomorphic Mappings

This note addresses monotonic growths and logarithmic convexities of the weighted ( $(1-t^2)^αdt^2$ , $-\infty<α<\infty$ , $0<t<1$ ) integral means $\mathsf{A}_{α,β}(f,\cdot)$ and $\mathsf{L}_{α,β}(f,\cdot)$ of the mixed area $(πr^2)^{-β}A(f,r)$ and the mixed length $(2πr)^{-β}L(f,r)$ ( $0\leβ\le 1$ and $0<r<1$ ) of $f(r\mathbb D)$ and $\partial f(r\mathbb D)$ under a holomorphic map $f$ from the unit disk $\mathbb D$ into the finite complex plane $\mathbb C$ .

preprint2010arXiv

Complex Lie algebras corresponding to weighted projective lines

The aim of this paper is to give an alternative proof of Kac's theorem for weighted projective lines (\cite{W}) over the complex field. The geometric realization of complex Lie algebras arising from derived categories (\cite{XXZ}) is essentially used.

preprint2010arXiv

Derived Categories and Lie Algebras

Let $\md^b(A)$ be the derived category of a finite dimensional basic algebra $A$ with finite global dimension. We construct the Lie algebra arising from the 2-periodic version $\mk_2(\mp(A))$ of $\mk^b(\mp(A))$ in term of constructible functions on varieties attached to $\mk_2(\mp(A))$.

preprint2010arXiv

Integral bases of cluster algebras and representations of tame quivers

In \cite{CK2005} and \cite{SZ}, the authors constructed the bases of cluster algebras of finite types and of type $\widetilde{A}_{1,1}$ , respectively. In this paper, we will deduce $\mathbb{Z}$ -bases for cluster algebras of affine types.

preprint2009arXiv

Coarse and Precise $L^p$ -Green Potential Estimates on Noncompact Riemannian Manifolds

We are concerned about the coarse and precise aspects of a priori estimates for Green's function of a regular domain for the Laplacian-Betrami operator on any $3\le n$ -dimensional complete non-compact boundary-free Riemannian manifold through the square Sobolev/Nash/logarithmic-Sobolev inequalities plus the rough and sharp Euclidean isoperimetric inequalities. Consequently, we are led to evaluate the critical limit of an induced monotone Green's functional using the asymptotic behavior of the Lorentz norm deficit of Green's function at the infinity, as well as the harmonic radius of a regular domain in the Riemannian manifold with nonnegative Ricci curvature.

preprint2009arXiv

The double Ringel-Hall algebra on a hereditary abelian finitary length category

In this paper, we study the category $\mathscr{H}^{(ρ)}$ of semi-stable coherent sheaves of a fixed slope $ρ$ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category. We will define the Ringel-Hall algebra of $\mathscr{H}^{(ρ)}$ and relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type theorem to describe the indecomposable objects in this category, i.e. the indecomposable semi-stable sheaves.

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math.AP math.QA math.RT math.CV math.DG math.FA hep-ph Artificial Intelligence Machine Learning astro-ph.HE Computer Vision cond-mat.mtrl-sci hep-ex math.CT math.MG math.RA physics.chem-ph

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arxivconfidence 95%

external id: arxiv:2601.00191:author:2:jie-xiao

Imported May 21, 2026Synced May 21, 2026

arxivconfidence 95%

external id: arxiv:2605.18859:author:12:jie-xiao

Imported May 20, 2026Synced May 21, 2026

Fan Xu3 works Minghui Zhao3 works Rujing Dou3 works Chunjie Wang2 works

Jie Xiao

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41 publications

Prospects for studying the WHγWHγWHγ process in pppppp collisions at the LHC

TwinRouterBench: Fast Static and Live Dynamic Evaluation for Realistic Agentic LLM Routing

RHOBIN Challenge: Reconstruction of Human Object Interaction

A sensitivity study of VBS and diboson WW to dimension-6 EFT operators at the LHC

Boosted tau lepton as a microscope and macroscope

Principled Knowledge Extrapolation with GANs

Stabilization of Co oxide during oxygen evolution in alkaline media by the introduction of Mn oxide

Searching for heavy leptoquarks at a muon collider

A Maximum Problem of S.-T. Yau for Variational p-Capacity

A quasiconformal composition problem for the Q-spaces

Geometric realizations of Lusztig's symmetries

Hall algebras of cyclic quivers and qqq-deformed Fock spaces

p-capacity vs surface-area

Uniqueness of nonnegative weak solution to up≤(−Δ)α2uu^p\le(-Δ)^\fracα{2}uup≤(−Δ)2α​u on RN\mathbb R^NRN

Analytic Campanato Spaces and Their Compositions

Gaussian integral means of entire functions: logarithmic convexity and concavity

Geometric Capacity Potentials on Convex Plane Rings

Global Mild Solutions of Fractional Naiver-Stokes Equations with Small Initial Data in Critical Besov-Q Spaces

Holomorphic Campanato Spaces on the Unit Ball

Isocapacity Estimates for Hessian Operators

Optimal geometric estimates for fractional Sobolev capacities

Preduals of quadratic Campanato spaces associated to operators with heat kernel bounds

Towards spaces of harmonic functions with traces in square Campanato space and its scaling invariant

Two Predualities and Three Operators over Analytic Campanato Spaces

Gaussian Integral Means of Entire Functions

Homothetic variant of fractional Sobolev space with application to Navier-Stokes system revisited

Regularity and Capacity for the Fractional Dissipative Operator

Remarks on Hall algebras of triangulated categories

Towards Conformal Capacities in Euclidean Spaces

A parameterization of the canonical bases of affine modified quantized enveloping algebras

BGP-Reflection Functors and Lusztig's Symmetries of Modified Quantized Enveloping Algebras

Composition Operators between Analytic Campanato Spaces

Hall algebra approach to Drinfeld's presentation of quantum loop algebras

Limiting Weak Type Estimate for Capacitary Maximal Function

The Semi-linear Torsional Rigidity on a Complete Riemannian Two-Manifold

Weighted Integral Means of Mixed Areas and Lengths under Holomorphic Mappings

Complex Lie algebras corresponding to weighted projective lines

Derived Categories and Lie Algebras

Integral bases of cluster algebras and representations of tame quivers

Coarse and Precise LpL^pLp-Green Potential Estimates on Noncompact Riemannian Manifolds

The double Ringel-Hall algebra on a hereditary abelian finitary length category

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Prospects for studying the $WHγ$ process in $pp$ collisions at the LHC

Hall algebras of cyclic quivers and $q$ -deformed Fock spaces

Uniqueness of nonnegative weak solution to $u^p\le(-Δ)^\fracα{2}u$ on $\mathbb R^N$

Coarse and Precise $L^p$ -Green Potential Estimates on Noncompact Riemannian Manifolds