Study G2-metrics from non-integrable special Lagrangian fibrations.
problem Understanding G2-metrics from non-integrable special Lagrangian fibrations. method Decompose SU(3)-structures into solder 1-forms, connection 1-forms, and equivariant matrix-valued functions. result Describe regular parts of G2-manifolds with Lagrangian-type actions. Study Neumann problem for special Lagrangian type equations.
problem Neumann problem for special Lagrangian type equations.
method Uniform a priori estimates, continuity method, direct proof of boundary double normal derivative estimates.
result Existence result for Neumann problem of special Lagrangian type equations.
3-dimensional Harvey Lawson submanifolds were introduced in an earlier paper by Akbulut-Salur, as examples of Lagrangian-type manifolds inside G2 manifold. In this paper, we first show that the space of deformations of a smooth, compact, orientable Harvey-Lawson submanifold HL in a G2 manifold M can be identified with …
In an earlier paper we showed that the space of deformations of a smooth, compact, orientable Harvey-Lawson submanifold HL in a G2 manifold M can be identified with the direct sum of the space of smooth functions and closed 2-forms on HL. In that paper, we also introduced a new class of Lagrangian-type 4-dimensional su…
The paper develops quaternionic toric geometry and classifies local actions.
problem Classifying local quaternionic torus actions on manifolds.
method Develops local Qn-actions, introduces invariants, and studies tetraplectic structures. result Classifies local quaternionic torus actions up to homeomorphism.
As a continuation of previous papers, we study the concept of a Lie algebroid structure on an affine bundle by means of the canonical immersion of the affine bundle into its bidual. We pay particular attention to the prolongation and various lifting procedures, and to the geometrical construction of Lagrangian-type dyn…
We study a fully nonlinear PDE involving a linear combination of symmetric polynomials of the Kähler form on a Kähler manifold. A C0 \emph{a priori} estimate is proven in general and a gradient estimate is proven in certain cases. Independently, we also provide a method-of-continuity proof via a path of Kähler metri…
Maps in Carnot groups are equivalent to solutions of a PDE system.
problem Understanding maps in Carnot groups of step 2.
method Equivalence between intrinsic Lipschitz maps and solutions to a PDE system.
result Intrinsic Lipschitz maps are equivalent to weak solutions of a PDE system.
Let L be a holomorphic line bundle over a compact Kähler manifold X. Motivated by mirror symmetry, we study the deformed Hermitian-Yang-Mills equation on L, which is the line bundle analogue of the special Lagrangian equation in the case that X is Calabi-Yau. We show that this equation is the Euler-Lagrange equ…
Paper solves optimization problems with convex expectation constraints using a new algorithm.
problem Minimizing convex expectation functions with inequality convex expectation constraints.
method Stochastic Augmented Lagrangian-Type Algorithm (Stochastic Linearized Proximal Method of Multipliers).
result Algorithm achieves O(K−1/2) convergence rates for objective reduction and constraint violation. Constructs finite-time singularities in Lagrangian mean curvature flow with precise dynamics.
problem Finite-time singularities in Lagrangian mean curvature flow.
method Modulation analysis around shrinking cohomogeneity-one special Lagrangian desingularizations.
result Explicit curvature blow-up rate and precise dynamics of singularities.
Study of deformed Hermitian Yang-Mills equations with variable Kähler metrics.
problem Solving special Lagrangian type equations with variable metrics.
method Introducing extended gauge group to couple moment maps and scalar curvature.
result Solutions satisfy a mixture of K-stability and Bridgeland-type stability.
Examples show cyclic actions on 4-manifolds can't extend to Hamiltonian circle actions.
problem Cyclic group actions on 4-manifolds that trivialize homology cannot be extended to Hamiltonian circle actions.
method Holomorphic methods applied to combinatorial tools for circle actions.
result Cyclic actions on 4-manifolds that trivialize homology do not extend to Hamiltonian circle actions.
Reduces proper actions to simpler core actions for analysis.
problem Understanding properties of proper actions on manifolds.
method Extending Skjelbred and Straume's construction to non-compact groups, focusing on core of actions.
result Properties of proper actions are determined by simpler core actions.
A new method learns disentangled macro actions from sequences for reinforcement learning.
problem Curse of dimensionality in reinforcement learning action space.
method Autonomously learns disentangled factor representation of actions to generate macro actions.
result Higher scores in complex environments compared to other reinforcement learning algorithms.
Introduces Conditional Action Trees to simplify RL action spaces.
problem Challenges in RL with large, complex action spaces.
method Structures action spaces and reduces complexity through Conditional Action Trees.
result Demonstrates effectiveness in reducing action space and improving decision making.
Study polar actions on Damek-Ricci spaces, proving existence and finding examples.
problem Characterize polar actions on Damek-Ricci spaces.
method Prove criteria for isometric actions to be polar, find examples, and classify actions.
result Non-trivial polar actions exist on all Damek-Ricci spaces.
New RL algorithm tackles complex discrete action spaces.
problem Challenges in applying on-policy RL in high-dimensional discrete action spaces.
method Action-value critic, correlated actions, gradient sparsification.
result Empirically outperforms related on-policy algorithms.
AE-DQN learns to eliminate sub-optimal actions in complex RL environments.
problem Challenges in RL with many actions, especially redundancy.
method Combines DQN with AEN that predicts invalid actions.
result Significant speedup and robustness in games with many actions.
Finite group actions on smooth 3-manifolds can be smoothed.
problem Finite group actions on smooth 3-manifolds.
method Uniform limit of smooth actions.
result Every continuous action of a finite group on a smooth 3-manifold is a uniform limit of smooth actions.
Reduction principles for proper actions on smooth manifolds.
problem Proper actions on smooth manifolds and their properties.
method Exhibit constructions and prove reduction principles for proper actions.
result Reduction principles hold for proper actions, polar actions, and copolarity.
Simplifies large action space bandits by selecting representative actions.
problem Efficiently managing large action spaces with correlated outcomes.
method Random sampling and solving of bandit instances to identify representative actions.
result The algorithm selects a smaller set of representative actions that perform nearly as well as the full action space.
Totally geodesic sections found in polar actions.
problem Understanding sections of polar actions on Riemannian manifolds.
method Elementary proof of a folklore result.
result Sections of polar actions are totally geodesic.
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…
The study proves conditions for symplectic torus actions on manifolds with non-contractible orbits.
problem Conditions for symplectic torus actions with non-contractible orbits.
method Analyzes symplectic torus actions on manifolds, proving conditions for Hamiltonian actions and orbit properties.
result Symplectic Tn−1 actions with non-contractible orbits are not Hamiltonian unless the orbits are contractible. Classifies totally geodesic submanifolds and polar actions on Stiefel manifolds.
problem Classifying totally geodesic submanifolds and polar actions on Stiefel manifolds.
method Classification through polar actions and cohomogeneity-one actions.
result Classification of orbits of polar actions on Stiefel manifolds.
Conditions for reducing quasi-actions to tree actions and group properties.
problem Conditions for reducing quasi-actions to tree actions.
method Reduction to cobounded isometric actions on trees.
result Groups with quasi-orbits quasi-isometric to trees are virtually free.
New stability theorem for non-hyperbolic group actions.
problem Structural stability of non-hyperbolic group actions.
method Introducing 'meandering hyperbolicity' for group actions on geodesic metric spaces.
result Meandering-hyperbolic actions are structurally stable.
We identify action representations from video data, proving their statistical benefits.
problem Identifying latent action policies from video data.
method Entropy-regularized LAPO objective, formalizing desiderata for action representations.
result Entropy-regularized LAPO identifies action representations satisfying desiderata under suitable conditions.
New method learns action representations for better reinforcement learning.
problem Lack of structured action representations in reinforcement learning.
method Decomposes policy into action representation and action transformation components.
result Action representations improve generalization in large action spaces.
Study properties of orbits of Hermann actions without commutability assumptions.
problem Investigate geometric properties of orbits of Hermann actions.
method Compute the second fundamental form and provide conditions for weak reflection and aridity.
result Sufficient conditions for weak reflection and aridity of orbits of Hermann action.
A new method learns action representations for reinforcement learning.
problem Efficient action-value estimation in reinforcement learning.
method Action hypergraph networks framework for learning action representations.
result Hypergraph Q-networks show effectiveness on various domains.
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.
The paper studies curvatures and austere properties of orbits in symmetric spaces.
problem Analyzing curvatures and austere properties of orbits in symmetric spaces.
method Using Hermann actions and hyperpolar properties, the paper derives explicit formulas for principal curvatures and conditions for orbits to be austere.
result The paper provides conditions for orbits to be austere and extends previous results to a larger class of infinite-dimensional submanifolds.
New reinforcement learning framework for adapting to new actions.
problem Making reinforcement learning agents adaptable to new actions without retraining.
method Two-stage framework: infer action representations first, then train a flexible policy.
result Agents can make decisions from new action sets without retraining.
AQL uses amortized inference to handle high-dimensional action spaces in Q-learning.
problem Difficulty in maximizing over large action spaces in Q-learning.
method Replace expensive maximization over all actions with a maximization over a small subset sampled from a learned proposal distribution.
result AQL outperforms existing methods on continuous control tasks with up to 21 dimensional actions.
The paper studies acylindrical actions on trees and proves acylindrical hyperbolicity of Baumslag-Solitar groups.
problem Exploring acylindrical actions on trees and their properties.
method Demonstrates criteria for preserving acylindrical hyperbolicity and analyzes the outer automorphism group of Baumsligar-Solitar groups.
result Proves acylindrical hyperbolicity of non-solvable Baumsligar-Solitar groups.
The study examines largest hyperbolic actions in groups and finds many do not exist.
problem Identifying largest hyperbolic actions in groups.
method Analysis of equivalence classes of cobounded actions on hyperbolic metric spaces.
result Many families of groups, including 3-manifold groups and mapping class groups, do not have largest hyperbolic actions.
Defines and computes a generalized spectral action for Lorentz warped products.
problem Computing spectral actions for Lorentz warped products.
method Defines and computes the bimetric spectral Einstein-Hilbert action for Lorentz warped products.
result Derives a Kastler-Kalau-Walze type theorem for Lorentz warped products.
UTE improves reinforcement learning by measuring action uncertainty, enhancing policy learning efficiency.
problem Degrading performance of action repetition in reinforcement learning, especially with sub-optimal actions.
method UTE uses ensemble methods to measure uncertainty during action extension, allowing strategic exploration or certainty.
result UTE outperforms existing action repetition algorithms, significantly enhancing policy learning efficiency.
Proper actions on bornological spaces are characterized with compatible coarse structures.
problem Characterizing proper actions on bornological spaces.
method Proving the existence of compatible coarse structures for proper actions.
result Bornological spaces admit compatible coarse structures for proper actions.
Classifies polar actions on 3D homogeneous spaces.
problem Classifying polar isometric actions on 3D homogeneous spaces.
method Orbit equivalence classification and study of cohomogeneity one actions.
result Classification of extrinsically homogeneous surfaces and orbit foliations.
Agents learn action spaces from observation alone.
problem Learning an agent's action space from visual observation.
method Stochastic video prediction and composable action representations.
result Learned representations disentangle action structure.
This paper improves RL for PDE control with function-valued actions.
problem Control of PDEs with high-dimensional, spatially related actions.
method Action descriptors and deep deterministic policy gradient.
result Action descriptor approach is more sample efficient.
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…
The study examines how perturbations of lattice actions on group boundaries behave.
problem Understanding how perturbations of lattice actions on group boundaries affect semi-conjugacy.
method Analyzes continuous factorization of perturbed actions onto original actions by semi-conjugacy.
result Perturbations of lattice actions on group boundaries can be C0 semi-conjugate or not. Study shows mean action of periodic orbits in annuli is bounded by their Calabi invariant.
problem Understanding the average distortion of periodic orbits in area-preserving annuli.
method Analyzes action functions and Calabi invariants of diffeomorphisms near annulus boundaries.
result Infimum of mean action of periodic orbits is bounded by their Calabi invariant.
Researchers calculate the action dimension of various group structures.
problem Determining the minimum dimension of contractible manifolds with group actions.
method Computing the action dimension of specific group structures.
result Action dimensions computed for Artin groups, graph products, and aspherical complements.