arXiv research

The sl_3 spider is a diagrammatic category used to study the representation theory of the quantum group U_q(sl_3). The morphisms in this category are generated by a basis of non-elliptic webs. Khovanov- Kuperberg observed that non-elliptic webs are indexed by semistandard Young tableaux. They establish this bijection v…

Analyzes solutions to non-elliptic equations on bounded domains.

Improved indefinite Kasparov modules for non-elliptic operators.

Let G be a simple algebraic group. Labelled trivalent graphs called webs can be used to product invariants in tensor products of minuscule representations. For each web, we construct a configuration space of points in the affine Grassmannian. Via the geometric Satake correspondence, we relate these configuration spaces…

KMRCD detects outliers in non-elliptical data using kernel trick.

The study constructs a Kähler structure on non-elliptic symplectic manifolds.

The paper provides coordinates for ${ m SL}_3$-web diagrams on surfaces.

For a compact Riemannian surface with boundary we study attenuated geodesic transform of functions and differential forms. We generalize several known results on uniqueness and stability of this transform dropping condition of absence of conjugate points.

Study on deformations of Spin(7)-structures on manifolds.

Flexible classifier using Mahalanobis distances for non-elliptical distributions.

We show in this article that Kähler hyperbolic manifolds satisfy a family of optimal Chern number inequalities and the equality cases can be attained by some compact ball quotients. These present restrictions to complex structures on negatively-curved compact Kähler manifolds, thus providing evidence to the rigidity co…

3-manifolds' volumes match stable integral values.

A new vine copula mixture model improves clustering accuracy for non-Gaussian data.

We recall a construction of Mackaay, Pan and Tubbenhauer of the algebras $K^ε$ which allow to understand the $sl_3$ homology for links in a local way (i.e. for tangles). Then, by studying the combinatorics of the Kuperberg bracket, we give a large family of non-elliptic webs whose associated projective $K^ε$-modules ar…

In this paper, we prove a quantitative version of the Tits alternative for negatively pinched manifolds $X$. Precisely, we prove that a nonelementary discrete isometry subgroup of $\mathrm{Isom}(X)$ generated by two non-elliptic isometries $g$, $f$ contains a free subgroup of rank $2$ generated by isometries $f^N , h$ …

Let $x$ denote a diffusion process defined on a closed compact manifold. In an earlier article, the author introduced a new approach to constructing admissible vector fields on the associated space of paths, under the assumption of ellipticity of $x$. In this article, this method is extended to yield similar results fo…

Complex hyperbolic triangle groups are discrete when certain conditions are met.

The abstract manifold cannot have uniformly quasiregular self-maps.

We present a definition of indefinite Kasparov modules, a generalisation of unbounded Kasparov modules modelling non-symmetric and non-elliptic (e.g. hyperbolic) operators. Our main theorem shows that to each indefinite Kasparov module we can associate a pair of (genuine) Kasparov modules, and that this process is reve…

New non-trivial Kaehler-Ricci solitons found in infinite dimensional complex space forms.

Define web algebras for annular SL(2) and SL(3) using foam TQFTs.

Let $M$ be a compact Riemannian manifold, $π:\widetilde{M}\rightarrow M$ be the universal covering and $ω$ be a smooth $2$-form on $M$ with $π^*ω$ cohomologous to zero. Suppose the fundamental group $π_1(M)$ satisfies certain radial quadratic (resp. linear) isoperimetric inequality, we show that there exists a smooth $…

The paper proposes a method to model financial data asynchronously using copulas.

We investigate when the Chevalley-Eilenberg differential of a complex Lie algebroid on a manifold with boundary admits a Hodge decomposition. We introduce the concepts of Cauchy-Riemann structures, elliptic and non-elliptic boundary points and Levi-forms, which we use to define the notion of q-convexity. We show that t…

We study the small-time fluctuations for diffusion processes which are conditioned by their initial and final positions, under the assumptions that the diffusivity has a sub-Riemannian structure and that the drift vector field lies in the span of the sub-Riemannian structure. In the case where the endpoints agree and t…

In this paper we describe a new method for analyzing the Laplacian on asymptotically hyperbolic spaces, which was introduced recently by the author. This new method in particular constructs the analytic continuation of the resolvent for even metrics (in the sense of Guillarmou), and gives high energy estimates in strip…

We describe explicitly the moduli spaces $M^{pst}_g(S,E)$ of polystable holomorphic structures $E$ with $\det E\cong K$ on a rank 2 vector bundle $E$ with $c_1(E)=c_1(K)$ and $c_2(E)=0$ for all minimal class VII surfaces $S$ with $b_2(S)=1$ and with respect to all possible Gauduchon metrics $g$. These surfaces $S$ are …

Study flat connections on hypersurfaces of 4-manifolds with parallel spinors.

This paper is devoted to study the optimal portfolio problem. Harry Markowitz's Ph.D. thesis prepared the ground for the mathematical theory of finance. In modern portfolio theory, we typically find asset returns that are modeled by a random variable with an elliptical distribution and the notion of portfolio risk is d…

In this paper we propose a problem-driven scenario generation approach to the single-period portfolio selection problem which use tail risk measures such as conditional value-at-risk. Tail risk measures are useful for quantifying potential losses in worst cases. However, for scenario-based problems these are problemati…

Flow cytometry is a high-throughput technology used to quantify multiple surface and intracellular markers at the level of a single cell. This enables to identify cell sub-types, and to determine their relative proportions. Improvements of this technology allow to describe millions of individual cells from a blood samp…

Study proves stability of slowly rotating Kerr black holes.

The paper constructs bases for cluster varieties using ${ m SL}_3$-webs and laminations.