arXiv research

Study quotients of curve complex actions by mapping class group.

The paper studies hyperbolic quotients of projection complexes and their actions.

Study shows Poisson boundary matches hyperbolic boundary for certain groups.

We study random walks on groups of isometries of non-proper delta-hyperbolic spaces under the assumption that at least one element in the group satisfies Bestvina-Fujiwara's WPD condition. We show that in this case typical elements are WPD, and the Poisson boundary coincides with the Gromov boundary. Moreover, we show …

Metric WPD for pseudo-Anosov maps shows many unbounded quasi-morphisms.

New group with non-loxodromic Morse element found.

We show that if a f.g. group $G$ has a non-elementary WPD action on a hyperbolic metric space $X$, then the number of $G$-conjugacy classes of $X$-loxodromic elements of $G$ coming from a ball of radius $R$ in the Cayley graph of $G$ grows exponentially in $R$. As an application we prove that for $N\ge 3$ the number of…

The aim of this note is to give the simplest possible proof that Mapping Class Groups of closed hyperbolic surfaces are acylindrically hyperbolic, and more specifically that their curve graphs are hyperbolic and that pseudo-Anosovs act on them as loxodromic WPDs.

Study of groups and their quasi-isometrically embedded subgroups.

We give examples of symplectic actions of a cyclic group, inducing a trivial action on homology, on four-manifolds that admit Hamiltonian circle actions, and show that they do not extend to Hamiltonian circle actions. Our work applies holomorphic methods to extend combinatorial tools developed for circle actions to stu…

Reduces proper actions to simpler core actions for analysis.

Introduces Conditional Action Trees to simplify RL action spaces.

One problem in the application of reinforcement learning to real-world problems is the curse of dimensionality on the action space. Macro actions, a sequence of primitive actions, have been studied to diminish the dimensionality of the action space with regard to the time axis. However, previous studies relied on human…

Study polar actions on Damek-Ricci spaces, proving existence and finding examples.

Reduction principles for proper actions on smooth manifolds.

Totally geodesic sections found in polar actions.

Simplifies large action space bandits by selecting representative actions.

We study isometric actions on Riemannian symmetric spaces of noncompact type which are induced by reductive algebraic subgroups of the isometry group. We show that for such an action there exists a corresponding isometric action on a dual compact symmetric space, which reflects many properties of the original action. F…

Classifies totally geodesic submanifolds and polar actions on Stiefel manifolds.

Conditions for reducing quasi-actions to tree actions and group properties.

We identify action representations from video data, proving their statistical benefits.

Study properties of orbits of Hermann actions without commutability assumptions.

We classify the polar actions on the complex hyperbolic plane up to orbit equivalence. Apart from the trivial and transitive polar actions, there are five polar actions of cohomogeneity one and four polar actions of cohomogeneity two.

A new method learns action representations for reinforcement learning.

The paper studies curvatures and austere properties of orbits in symmetric spaces.

New reinforcement learning framework for adapting to new actions.

Defines and computes a generalized spectral action for Lorentz warped products.

The paper studies acylindrical actions on trees and proves acylindrical hyperbolicity of Baumslag-Solitar groups.

Classifies polar actions on 3D homogeneous spaces.

UTE improves reinforcement learning by measuring action uncertainty, enhancing policy learning efficiency.

Proper actions on bornological spaces are characterized with compatible coarse structures.

Learning how to act when there are many available actions in each state is a challenging task for Reinforcement Learning (RL) agents, especially when many of the actions are redundant or irrelevant. In such cases, it is sometimes easier to learn which actions not to take. In this work, we propose the Action-Elimination…

We analyze polar actions on Hermitian and quaternion-Kähler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries concerning the geometry of these actions. The results are independent of the classificatio…

Reinforcement learning (RL) in discrete action space is ubiquitous in real-world applications, but its complexity grows exponentially with the action-space dimension, making it challenging to apply existing on-policy gradient based deep RL algorithms efficiently. To effectively operate in multidimensional discrete acti…

The study examines how perturbations of lattice actions on group boundaries behave.

Non-proper surface group action on product of trees found.

We consider actions of Z^k, k \ge 2, by Anosov diffeomorphisms which are uniformly quasiconformal on each coarse Lyapunov distribution. These actions generalize Cartan actions for which coarse Lyapunov distributions are one-dimensional. We show that, under certain non-resonance assumptions on the Lyapunov exponents, a …

Study free circle actions on specific 7-manifolds with positive Ricci curvature.

Study of symplectomorphisms on ruled surfaces under circle actions.

In his 1985 paper Sullivan sketched a proof of his structural stability theorem for differentiable group actions satisfying certain expansion-hyperbolicity axioms. In this paper we relax Sullivan's axioms and introduce a notion of "meandering hyperbolicity" for group actions on geodesic metric spaces. This generalizati…

We consider a simple instance of action up to homotopy. More precisely, we consider strict actions of DGLAs in degrees -1 and 0 on degree 1 NQ-manifolds. In a more conventional language this means: strict actions of Lie algebra crossed modules on Lie algebroids. When the action is strict, we show that it integrates to …

The set of equivalence classes of cobounded actions of a group on different hyperbolic metric spaces carries a natural partial order. The resulting poset thus gives rise to a notion of the "best" hyperbolic action of a group as the largest element of this poset, if such an element exists. We call such an action a large…

Recent work has shown that reinforcement learning (RL) is a promising approach to control dynamical systems described by partial differential equations (PDE). This paper shows how to use RL to tackle more general PDE control problems that have continuous high-dimensional action spaces with spatial relationship among ac…

Applying Q-learning to high-dimensional or continuous action spaces can be difficult due to the required maximization over the set of possible actions. Motivated by techniques from amortized inference, we replace the expensive maximization over all actions with a maximization over a small subset of possible actions sam…

We introduce and systematically study the concept of a growth tight action. This generalizes growth tightness for word metrics as initiated by Grigorchuk and de la Harpe. Given a finitely generated, non-elementary group $G$ acting on a $G$--space $\mathcal{X}$, we prove that if $G$ contains a strongly contracting eleme…

A method to generate long-range human actions by leveraging graph convolutional networks and self-attention.

We study isometric Lie group actions on the compact exceptional groups E6, E7, E8, F4 and G2 endowed with a biinvariant metric. We classify polar actions on these groups. We determine all isometric actions of cohomogeneity less than three on E6, E7, F4 and all isometric actions of cohomogeneity less than 20 on E8. More…

Innovates rotation index for matrix pairs, solving group action problems.