arXiv research

Study of isometries on hyperbolic 3-manifold cusps.

We study the space of holomorphic discs with boundary on a surface in a real 2-dimensional vector bundle over a compact 2-manifold. We prove that, if the ambient 4-manifold admits a fibre-preserving transitive holomorphic action, then a section with a single complex point has $C^{2,α}$-close sections such that any (non…

Classifies multiply-transitive (2,3,5)-distributions using modern Cartan geometry.

We classify multiply transitive homogeneous real (2,3,5) distributions up to local diffeomorphism equivalence.

New unoriented versions of Schur and Bogomolov multipliers for finite groups.

The study extends group actions from surfaces to 3-manifolds using $G$-cobordisms.

Following the spirit of a previous work of ours, we investigate the group of those General Coordinate Transformations (GCTs) which preserve manifest spatial homogeneity. In contrast to the case of Bianchi Type Models we, here, permit an isometry group of motions $G_{4}=SO(3)\otimes T_{r}$, where $T_{r}$ is the translat…

Study non-transitive pseudo-Anosov flows using group actions.

New method constructs relative invariants for group actions on extended manifolds.

We study the action of conformal transformations of the ambient space on the Dirac operator coming into the Weierstrass (or spinor) representation of a torus in the Euclidean four-space. It is showed that such an action generates a flow acting on the potential of the operator, that this flow is described by a nonlinear…

Study groups acting on trees with specific local actions, proving cohomology vanishing or infinite.

New classification of conformal structures with maximal $G_2$ symmetry.

This paper studies actions of solvable Lie groups on nilpotent Lie groups.

A transitive smooth action of a connected Lie group G on a manifold M is called almost primitive (resp. primitive) if G doesn't contain any proper subgroup (resp. any proper normal subgroup) whose induced action on M is transitive as well. The aim of the present work is to investigate some combinatory properties of sym…

To any connected and simply connected nilpotent Lie group N, one can associate its group of affine transformations Aff(N). In this paper, we study simply transitive actions of a given nilpotent Lie group G on another nilpotent Lie group N, via such affine transformations. We succeed in translating the existence questio…

Semisimple Lie groups act transitively on pseudo-Riemannian manifolds, making them flat.

PQR estimates reward functions from actions and states without assuming state-only rewards.

This paper shows how post-Lie algebra structures can be induced by simply transitive NIL-affine actions.

New algorithm reduces regret and constraint violation in adversarial CMDP learning.

A new RL paradigm reduces state-action-value function approximation inefficiency.

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.

Study of pseudo-Riemannian manifolds with M{ö}bius group actions.

Compact complex manifolds with specific group actions are conformally flat.

A homogeneous space is a manifold on which a Lie group acts transitively. Super generalization of this concept is also studied in [2] and [4]. In this paper we explicitly show that super Lie group GL(m|n) acts transitively on supergrassmannian G_{k|l}(m|n). In this regard, by using functor of point approach, this actio…

Study of transitivity in partially hyperbolic maps with expanding linear part.

We introduce Dynamic Planning Networks (DPN), a novel architecture for deep reinforcement learning, that combines model-based and model-free aspects for online planning. Our architecture learns to dynamically construct plans using a learned state-transition model by selecting and traversing between simulated states and…

This work uses action equivariance to learn structured latent spaces for reinforcement learning.

Identifies latent actions and dynamics from offline data with diverse demonstrators.

It is shown that the Euler-Lagrange equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of reduction and the relation with Lagrange multiplier method are also studied.

The paper studies Einstein-Hilbert action on complex manifolds.

Study shows optimal RL with transition look-ahead is NP-hard for $\ell \geq 2$.

We study higher rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by $\R ^k$ with $k \geq 3$ whose one-parameter groups act transitively as well as nondegenerate totally nonsymplectic $\Zk$-actions for $k \geq 3$.

New proof shows almost all surface group actions are dense.

Classifies special homogeneous curves with polynomial equations.

Study shows how certain spaces can be mapped to R^n with specific properties.

Quasi-vertex-transitive maps are the homogeneous maps on the plane with finitely many vertex orbits under the action of their automorphism groups. We show that there exist quasi-vertex-transitive maps of types $[p^3, 3]$ for $p \equiv 1$ (mod $6$), but there doesn't exist vertex-transitive map of such types. In particu…

Paper introduces a new value function for state transitions and optimal policy learning.

Due to a result by Mackenzie, extensions of transitive Lie groupoids are equivalent to certain Lie groupoids which admit an action of a Lie group. This paper is a treatment of the equivariant connection theory and holonomy of such groupoids, and shows that such connections give rise to the transition data necessary for…

We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial $d$-manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a vertex-transitive automorphism group on $n\leq 13$ vertices. With the exception of act…

We classify the transitive, effective, holomorphic actions of connected complex Lie groups on complex surfaces.

We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply our classification to polar actions on compact symmetric spaces.

Deep reinforcement learning method finds rare events in complex systems.

Classifies special homogeneous surfaces with unique properties.

The equivalence of principal bundles with transitive Lie groupoids due to Ehresmann is a well known result. A remarkable generalisation of this equivalence, due to Mackenzie, is the equivalence of principal bundle extensions with those transitive Lie groupoids over the total space of a principal bundle, which also admi…

A critical and challenging problem in reinforcement learning is how to learn the state-action value function from the experience replay buffer and simultaneously keep sample efficiency and faster convergence to a high quality solution. In prior works, transitions are uniformly sampled at random from the replay buffer o…

New findings reveal discount regularization can be seen as a strong prior, leading to poor performance in unevenly sampled data.

4-manifolds show every flat 3-manifold as cusp sections.

We study the construction of quasimorphisms on groups acting on trees introduced by Monod and Shalom, that we call median quasimorphisms, and in particular we fully characterise actions on trees that give rise to non-trivial median quasimorphisms. Roughly speaking, either the action is highly transitive on geodesics, i…