arXiv research

Generalizes Dolbeault cohomology computation to Levi-flat CR structures on compact Lie groups.

An almost para-CR structure on a manifold $M$ is given by a distribution $HM \subset TM$ together with a field $K \in Γ({\rm End}(HM))$ of involutive endomorphisms of $HM$. If $K$ satisfies an integrability condition, then $(HM,K)$ is called a para-CR structure. The notion of maximally homogeneous para-CR structure of …

Boundary properties of hyperbolic groups are invariant under a maximization procedure.

Study on almost complex structures with maximal Nijenhuis tensor rank and cohomological properties.

A characterization of maximal domains of existence of adapted complex structures for Riemannian homogeneous manifolds under certain extensibility assumptions on their geodesic flow is given. This is applied to generalized Heisenberg groups and naturally reductive Riemannian homogeneous spaces. As an application it is s…

Researchers found a maximal antipodal set of three elements in a 7x7 sphere space.

Study shows almost complex structures with certain tensor properties are prevalent.

We describe moduli spaces of invariant generalized complex structures and moduli spaces of invariant generalized Kähler structures on maximal flag manifolds under $B$-transformations. We give an alternative description of the moduli space of generalized complex structures using pure spinors, and describe a cell decompo…

We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called weakly maximal representations. They are defined in terms of invariants in bounded cohomology and extend considerably the scope of maximal representations. We prove that weakly maximal representations are d…

Study on invariant anti-quasi-Sasakian structures on compact manifolds.

The paper explores maximal nilpotent complex structures on Lie algebras.

We consider complex projective structures on Riemann surfaces and their groups of projective automorphisms. We show that the structures achieving the maximal possible number of projective automorphisms allowed by their genus are precisely the Fuchsian uniformizations of Hurwitz surfaces by hyperbolic metrics. More gene…

Study finds maximal symmetry groups for CR structures with specific properties.

Let $S$ be a closed oriented surface of genus at least $2$. Using the parameterisation of the deformation space of globally hyperbolic maximal anti-de Sitter structures on $S \times \mathbb{R}$ by the cotangent bundle over the Teichmüller space of $S$, we study the behaviour of these geometric structures along pinching…

Study classifies twist knots with maximal self-linking number in S^3.

Study fibrations of projective spaces for maximal representations.

Finite groups can be automorphism groups of translation surfaces with poles.

New superintegrable systems derived from Frobenius structures.

We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called {\em weakly maximal} representations. We prove that weakly maximal representations are discrete and injective and we describe the structure of the Zariski closure of their image. Furthermore we prove that t…

New maximal families of compatible Poisson structures derived from geodesically equivalent metrics.

The paper proposes a method to learn structured representations from unlabeled data using mutual information maximization.

We classify $R$-spaces that admit a certain natural $Γ$-symmetric structure. We further determine the maximal antipodal sets of these structures.

In this paper we combine our recent work on regular globally hyperbolic maximal anti-de Sitter structures with the classical theory of globally hyperbolic maximal Cauchy-compact anti-de Sitter manifolds in order to define an augmented moduli space. Moreover, we introduce a coordinate system in this space that resembles…

For a 4-manifold represented by a framed knot in $S^3$, it has been well known that the 4-manifold admits a Stein structure if the framing is less than the maximal Thurston-Bennequin number of the knot. In this paper, we prove either the converse of this fact is false or there exists a compact contractible oriented smo…

Compactifies maximal component of surface group representations into a closed ball.

The study characterizes real flag manifolds with invariant generalized almost complex structures.

Study on CR structures in 7D, proving maximal symmetry dimension.

Proposes a value-based method for continuous control without an actor.

We study area-stationary, or maximal, surfaces in the space ${\mathbb L}({\mathbb H}^3)$ of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral Kähler structure. We prove that every holomorphic curve in ${\mathbb L}({\mathbb H}^3)$ is a maximal surface. We then classify Lagrangian maximal surfa…

Proposes a new method to enhance neural learning by maximizing information gain.

Let $\mathbb F$ be a real closed field. We define the notion of a maximal framing for a representation of the fundamental group of a surface with values in ${\rm Sp}(2n,\mathbb F)$. We show that ultralimits of maximal representations in ${\rm Sp}(2n,\mathbb R)$ admit such a framing, and that all maximal framed represen…

Maximizes coding rate difference for robust, discriminative features.

Classifies homogeneous CR hypersurfaces in low dimensions with maximal symmetry.

Study h-principles for non-integrable distributions on manifolds.

Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for the existence of a complete uniform differential structure on a given differenti…

The aim of this work is to prove the nonexistence of complex structures over nilpotent Lie algebras of maximal class (also called filiform).

Minimal energy local systems on curves are compact components of character varieties.

New algorithm for maximizing submodular functions in real-time data changes.

Bayesian scores improve structure learning in probabilistic circuits.

We study some properties of transverse contact structures on small Seifert manifolds, and we apply them to the classification of tight contact structures on a family of small Seifert manifolds.

This is the written version of a talk given in Bonn on September 11th, 2001 during a workshop on "Special structures in string theory". We report on joint work in progress with George Papadopoulos aimed at classifying the maximally supersymmetric solutions of the ten- and eleven-dimensional supergravity theories with 3…

We consider a volume maximization program to construct hyperbolic structures on triangulated 3-manifolds, for which previous progress has lead to consider angle assignments which do not correspond to a hyperbolic metric on each simplex. We show that critical points of the generalized volume are associated to geometric …

The paper studies connections in superintegrable systems, revealing geometric insights.

It was shown by Samelson and Wang that each compact Lie group K of even dimension admits left-invariant complex structures. When K has odd dimension it admits a left-invariant CR-structure of maximal dimension. This has been proved recently by Charbonnel and Khalgui who have also given a complete algebraic description …

We construct a partial order relation which acts on the set of 3-cliques of a maximal planar graph G and defines a unique hierarchy. We demonstrate that G is the union of a set of special subgraphs, named `bubbles', that are themselves maximal planar graphs. The graph G is retrieved by connecting these bubbles in a tre…

Investigates sequential problems on graph structures and large action spaces.

Study on a metric for disk automorphisms with maximal modulus.

Maximal cusps are not dense on Teichmüller space for infinite-type surfaces.