Related papers: Normalization of singular contact forms and primit…
A differential form vanishing on the tangent space at smooth points of a reduced embedded analytic germ is called conormal. For proving that a conormal one--form of a hypersurface vanishes at its singularities we state a Bertini--type…
We study conformal symmetry breaking differential operators which map differential forms on $\mathbb{R}^n$ to differential forms on a codimension one subspace $\mathbb{R}^{n-1}$. These operators are equivariant with respect to the conformal…
We compute the cylindrical contact homology of the links of the simple singularities. These manifolds are contactomorphic to $S^3/G$ for finite subgroups $G\subset\text{SU}(2)$. We perturb the degenerate contact form on $S^3/G$ with a Morse…
Given a quadratic form and $M$ linear forms in $N+1$ variables with coefficients in a number field $K$, suppose that there exists a point in $K^{N+1}$ at which the quadratic form vanishes and all the linear forms do not. Then we show that…
We analyze the triviality of inhomogeneous $\gamma$-deformations of the oscillator Lie superalgebra $B(0,n) = \mathfrak{osp}(1|2n)$. As the main theorem, we show that for $n \geq 2$, the $\gamma$-deformation is trivial if and only if all…
Let $W$ be a finite dimensional algebraic structure (e.g. an algebra) over a field $K$ of characteristic zero. We study forms of $W$ by using Deligne's Theory of symmetric monoidal categories. We construct a category $\mathcal{C}_W$, which…
The fundamental invariants for vector ODEs of order $\ge 3$ considered up to point transformations consist of generalized Wilczynski invariants and C-class invariants. An ODE of C-class is characterized by the vanishing of the former. For…
We address the problem of understanding the dynamics around typical singular points of $3D$ piecewise smooth vector fields. A model $Z_0$ in $3D$ presenting a T-singularity is considered and a complete picture of its dynamics is obtained in…
Contact path geometries are curved geometric structures on a contact manifold comprising smooth families of paths modeled on the family of all isotropic lines in the projectivization of a symplectic vector space. Locally such a structure is…
The symplectic cohomology of certain symplectic manifolds $W$ with non-compact ends modelled on the positive symplectization of a compact contact manifold $Y$ is shown to vanish whenever there is a positive loop of contactomorphisms of $Y$…
We study a class of timelike weakly extremal surfaces in flat Minkowski space $\mathbb R^{1+n}$, characterized by the fact that they admit a $C^1$ parametrization (in general not an immersion) of a specific form. We prove that if the…
We consider a commutative family of holomorphic vector fields in an neighbourhood of a common singular point, say $0\in \Bbb C^n$. Let $\lie g$ be a commutative complex Lie algebra of dimension $l$. Let $\lambda_1,...,\lambda_n\in \lie g^*$…
The purpose of this paper is to investigate order of contact on real hypersurfaces in ${\mathbb C}^n$ by using Newton polyhedra which are important notion in the study of singularity theory. To be more precise, an equivalence condition for…
Using the effective potential, we study the one-loop renormalization of a massive self-interacting scalar field at finite temperature in flat manifolds with one or more compactified spatial dimensions. We prove that, owing to the…
We consider Scherk-Schwarz compactifications of M-theory (toroidal compactifications with a non-trivial spin structure) in various dimensions and find isolated critical points of the potential on the moduli space. We demonstrate this by…
This study introduces a new unified structural framework for orbifold sigma models that incorporates twisted sectors, singularities, and smooth regions into a single algebraic object. Traditional approaches to orbifold theories often treat…
In this article, we develop a new approach to the Poincar\'e--Dulac normal form theory for a system of differential equations near a singular point. Using the continuous averaging method, we construct a normalization flow that moves a…
The effects of delayed feedback terms on nonlinear oscillators has been extensively studied, and have important applications in many areas of science and engineering. We study a particular class of second-order delay-differential equations…
In this paper we obtain exact normal forms with functional invariants for local diffeomorphisms, under the action of the symplectomorphism group in the source space. Using these normal forms we obtain exact classification results for the…
The semi-classical study of a 1-dimensional Schr\"odinger operator near a non-degenerate maximum of the potential has lead Colin de Verdi\`ere and Parisse to prove a microlocal normal form theorem for any 1-dimensional pseudo-differential…