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Ruoxi Li

Publications and source records attributed to Ruoxi Li.

8 recordsLinked to original sources
arXiv2026

GIT for root stacks and 3d mirror symmetry

Using window theory, Bodzenta--Donovan showed that the derived category of a root stack $\sqrt[n]{X/D}$ has a $2n$-periodic $2$-term semiorthogonal decomposition. We define a categorical generalization of the root stack construction and interpret this as a pullback on the B-side of the 3d mirror symmetry equivalence of Gammage--Hilburn--Mazel-Gee. We analyze this pullback using categorical representation theoretic results of Ben-Zvi--Francis--Nadler and Ben-Zvi--Nadler--Preygel applied to SODs. We also show that the pullback is equivalent to a pushforward of perverse schobers on the A-side, allowing us to deduce periodicity from a simple decomposition of an A-side Lagrangian skeleton. Additionally, we adapt the construction of Bodzenta--Donovan to a new GIT problem, which yields an embedding of Coh($\sqrt[m]{X/D}$) into Coh($\sqrt[n]{X/D}$) for $m<n$ coprime, and prove $2n$-periodicity of the resulting $2$-term SOD.

math.RT↗
arXiv2026

Minimal Trivializing Isogenies of $\mathbb{G}_m$-gerbes over Abelian Varieties and Period-Index Problem

For an abelian variety $X$ and $\alpha \in Br(X)$, we propose a new invariance $Ind_{SH}(\alpha)$ that refines the known period index relations. It is closely related to the geometry of $\mathcal{X}$, the $\mathbb{G}_m$-gerbe over $X$ that corresponds to $\alpha$: we study the minimal trivializing isogenies for $\mathcal{X}$ via its $\mu_n$-lifts and the $1-$twisted semi-homogeneous vector bundles on $\mathcal{X}$. As an application, we show that the period index conjecture holds true for products of elliptic curves of any dimension.

math.AG↗
arXiv2026

Invariant Algebraic Connections on Connected Reductive Groups

Let $G$ be a connected complex reductive algebraic group. We study finite-rank flat algebraic connections on trivial vector bundles whose connection forms are left invariant, allowing arbitrary algebraic horizontal morphisms. We prove that a flat algebraic connection on $G$ is regular-singular if and only if its pullback to the canonical finite central cover is isomorphic to a left-invariant flat algebraic connection on a trivial vector bundle. Moreover, every regular-singular algebraic connection on $G$ is a direct summand of such a connection. We characterize the essential image of pullback from the abelianization by the vanishing of a derived-monodromy obstruction and show that pullback is an equivalence precisely when $G^{\mathrm{der}}$ is simply connected. For semisimple $G$, regular-singular connections are classified by finite-dimensional representations of the finite central kernel of the simply connected cover. We also classify regular-singular connections on $\mathrm{GL}_r$ by pullback along the determinant, give a $\mathrm{PGL}_2$ counterexample to the abelianization classification of left-invariant trivial-bundle algebraic connections, and compute de Rham and Betti cohomology in the semisimple case.

math.RT↗
arXiv2025

Weyl-invariant subspaces are (usually) not generic

Let $V$ be a linear representation of a connected complex reductive group $G$. Given a choice of character $\theta$ of $G$, Geometric Invariant Theory defines a locus $V^{ss}_\theta(G) \subseteq V$ of semistable points. We give necessary, sufficient, and in some cases equivalent conditions for the existence of $\theta$ such that a maximal torus $T$ of $G$ acts on $V^{ss}_\theta(T)$ with finite stabilizers. In such cases, the stack quotient $[V^{ss}_\theta(G)/G]$ is is known to be Deligne-Mumford. Our proof uses the combinatorial structure of the weights of irreducible representations of semisimple groups. As an application we generalize the Grassmannian flop example of Donovan-Segal.

math.RT↗
arXiv2025

Motivic classes of stacks in finite characteristic and applications to stacks of Higgs bundles

We define a ring of motivic classes of stacks suitable for symmetric powers in finite characteristic. Let $X$ be a smooth projective curve over a field of arbitrary characteristic. We calculate the motivic classes of the moduli stacks of semistable Higgs bundles on $X$. This recovers results of Fedorov, A. Soibelman and Y. Soibelman in characteristic zero, as well as those of Mozgovoy and Schiffmann for finite fields. We also obtain a simpler formula for the motivic classes of the stacks of Higgs bundles in the universal $\lambda$-ring quotient using Mellit's results.

math.AG↗
arXiv2024

Explicit formulas for mixed Hodge polynomials of character varieties of nilpotent groups

Let $Hom^0(\Gamma,G)$ be the path-connected component of the identity representation of the variety of representations of a finitely generated nilpotent group $\Gamma$ into a connected reductive complex affine algebraic group $G$. With the formulas given by Florentino, Lawton and Silva, we provide explicit partition type formulas for the mixed Hodge polynomials of character varieties $Hom^0(\Gamma,G)// G$ when $G=Sp_{2n}$ and $G=SO_{n}$.

math.AG↗
arXiv2024

Automatically Learning HTN Methods from Landmarks

Hierarchical Task Network (HTN) planning usually requires a domain engineer to provide manual input about how to decompose a planning problem. Even HTN-MAKER, a well-known method-learning algorithm, requires a domain engineer to annotate the tasks with information about what to learn. We introduce CURRICULAMA, an HTN method learning algorithm that completely automates the learning process. It uses landmark analysis to compose annotated tasks and leverages curriculum learning to order the learning of methods from simpler to more complex. This eliminates the need for manual input, resolving a core issue with HTN-MAKER. We prove CURRICULAMA's soundness, and show experimentally that it has a substantially similar convergence rate in learning a complete set of methods to HTN-MAKER.

cs.AI↗