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We introduce a new notion of a curvature of a superconnection, different from the one obtained by a purely algebraic analogy with the curvature of a linear connection. The naturalness of this new notion of a curvature of a superconnection…
We present a new probabilistic algorithm to find a finite set of points intersecting the closure of each connected component of the realization of every sign condition over a family of real polynomials defining regular hypersurfaces that…
A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F, or, equivalently, from an Euler vector field. This is…
If $X \subset \mathbb P^n$ is a reduced subscheme, we say that $X$ admits an unexpected hypersurface of degree $t$ for multiplicity $m$ if the imposition of having multiplicity $m$ at a general point $P$ fails to impose the expected number…
The first part of this paper considers higher order CR invariants of three dimensional hypersurfaces of finite type. Using a full normal form we give a complete characterization of hypersurfaces with trivial local automorphism group, and…
It is a challenge for the theoretical particle physicists to perform the phenomenology of the Beyond Standard Model (BSM) theories using advanced simulations which can mimic the experimental environment at the colliders as closely as…
We classify the local bifurcations of one dov quantum billiards, showing that only saddle-center bifurcations can occur. We analyze the resulting planar system when there is no coupling in the superposition state. In so doing, we also…
We prove that a complete intersection of $c$ very general hypersurfaces of degree at least two in $N$-dimensional complex projective space is not ruled (and therefore not rational) provided that the sum of the degrees of the hypersurfaces…
Codimension two defects of the $(0,2)$ six dimensional theory $\mathscr{X}[\mathfrak{j}]$ have played an important role in the understanding of dualities for certain $\mathcal{N}=2$ SCFTs in four dimensions. These defects are typically…
Based on the study of saddle points of the potential energy landscapes of generic classical many-particle systems, we present a necessary criterion for the occurrence of a thermodynamic phase transition. Remarkably, this criterion imposes…
The space of degree d single-variable monic and centered complex polynomial vector fields can be decomposed into loci in which the vector fields have the same topological structure. We analyze the geometric structure of these loci and…
We consider the following classification problem: Given a population of individuals characterized by a set of attributes represented as a vector in ${\mathbb R}^N$, the goal is to find a hyperplane in ${\mathbb R}^N$ that separates two sets…
A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. It is intuitively clear that the decomposable polynomials form a small minority among all polynomials over a finite field. The…
In this paper we provide sufficient conditions that ensure the existence of the solution of some vector equilibrium problems in Hausdorff topological vector spaces ordered by a cone. The conditions that we consider are imposed not on the…
We investigate planar piecewise-smooth vector fields with a discontinuity line, focusing on the bifurcation of crossing limit cycles that arise when one of the vector fields is translated along the discontinuity set. We establish…
Searches for dark photons provide serendipitous discovery potential for other types of vector particles. We develop a framework for recasting dark photon searches to obtain constraints on more general theories, which includes a data-driven…
Interrelation between Thom's catastrophes and differential equations revisited. It is shown that versal deformations of critical points for singularities of A,D,E type are described by the systems of Hamilton-Jacobi type equations. For…
We study divisors in the blow-up of $\mathbb{P}^n$ at points in general position that are non-special with respect to the notion of linear speciality introduced in [5]. We describe the cohomology groups of their strict transforms via the…
Vector equilibrium problems are a natural generalization to the context of partially ordered spaces of the Ky Fan inequality, where scalar bifunctions are replaced with vector bifunctions. In the present paper, the local geometry of the…
High dimensional central limit theorems (the CLTs) have been extensively studied in recent years under a variety of sufficient moment conditions connecting the dimension growth rate with the tail decay rate. In this article, we investigate…