Related papers: Differential topology interacts with isoparametric…
The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…
This article is a continuation of my former article "On Connectivity Spaces". After some brief historical references relating to the subject, separation spaces and then adjoint notions of connective representation and connective foliation…
We prove that a submanifold with parallel focal structure, which is a generalization of isoparametric and equifocal submanifolds, induces a singular Riemannian foliation of the ambient space by its parallel and focal manifolds.
In this paper, we investigate the possibility of constructing isomonodromic deformations of logarithmic connections on curves by using ramified covers. We give new examples and prove a classification result.
We investigate active particles that exhibit long-range interactions only restricted by a field of view, which is characterized by an angle $\beta$. We show that constraining attractive interactions to a field of view leads to the emergence…
In this paper, we study some relationships existing between some particular mathematical structures: discrete surfaces coming from discrete topology and mathematical morphology, poset-based connected manifolds coming from discrete topology,…
We classify the holomorphic parabolic geometries on compact complex manifolds of general type. We accomplish this by bounding the numerical dimension of any smooth projective variety in terms of geometric invariants of the flag variety…
We study the refinement invariance of several intersection (co)homologies existing in the literature. These (co)homologies have been introduced in order to establish the Poincar\'e Duality in variousl contexts. We found the classical…
We study holomorphic foliations with an affine homogeneous transverse structure. We give a friendly characterization of the case of transversely affine foliations in terms of matrix valued pairs of differential forms. This leads naturally…
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
We introduce a new cohomology theory related to deformations of Lie algebra morphisms. This notion involves simultaneous deformations of two Lie algebras and a homomorphism between them.
We explore the connection between tasep-like interacting particle systems and last passage percolation type polymer models, focusing on three models: Geometric, Exponential and Brownian last passage percolation and their associated tasep…
Stochastic growth phenomena on curved interfaces are studied by means of stochastic partial differential equations. These are derived as counterparts of linear planar equations on a curved geometry after a reparametrization invariance…
In this paper, we study the moduli spaces of parabolic connections with a quadratic differential. We endow these moduli spaces with symplectic structures by using the fundamental 2-forms on the moduli spaces of parabolic connections (which…
We investigate the dynamics of forward or backward self-similar systems (iterated function systems) and the topological structure of their invariant sets. We define a new cohomology theory (interaction cohomology) for forward or backward…
The interplay of topology and symmetry in a material's band structure may result in various patterns of topological states of different dimensionality on the boundary of a crystal. The protection of these "higher-order" boundary states…
Let $X$ be a connected non-compact $2$-dimensional manifold possibly with boundary and $\Delta$ be a foliation on $X$ such that each leaf $\omega\in\Delta$ is homeomorphic to $\mathbb{R}$ and has a trivially foliated neighborhood. Such…
This is a review of two-dimensional conformal field theory including some of the relations to integrable models. An effort is made to develop the basic formalism in a way which is as elementary and flexible as possible at the same time.…
There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…
We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algebroid. We also have a closer look at various special cases…