Related papers: Quantitative singularity theory for random polynom…

The existence of a singularity by definition implies a preferred scale--the affine parameter distance from/to the singularity of a causal geodesic that is used to define it. However, this variable scale is also captured by the expansion…

In this paper, we develop the theory of Perelman's $W$-functional on manifolds with isolated conical singularities. In particular, we show that the infimum of $W$-functional over a certain weighted Sobolev space on manifolds with isolated…

Let $\cP_n$ be the space of homogeneous polynomials of degree $n$ on $\bbR^{m+1}$. We consider the asymptotic behavior of some coefficients relating to the decomposition of $\cP_n$ into the sum of $\SO(m+1)$-irreducible components. Using…

We investigate the evolution of the empirical distribution of the complex roots of high-degree random polynomials, when the polynomial undergoes the heat flow. In one prominent example of Weyl polynomials, the limiting zero distribution…

This paper investigates asymptotic distribution of complex zeros of random polynomials $P_n(z):=\sum_{k=0}^{n}b(k)\xi_k z^k$, as $n\to\infty$, where $b$ is a regularly varying function at infinity with index $\alpha\in \mathbb{R}$ and…

We consider a class of Gaussian random holomorphic functions, whose expected zero set is uniformly distributed over $\C^n $. This class is unique (up to multiplication by a non zero holomorphic function), and is closely related to a…

We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of dense conjugacy classes (the topological Rokhlin property).…

We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…

Let X be a locally compact Abelian group. We consider linear forms of independent random variables with values in X. In doing so, one of the coefficients of the linear forms is a random variable with a Bernoulli distribution. For some…

It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…

The flat, homogeneous, and isotropic universe with a massless scalar field is a paradigmatic model in Loop Quantum Cosmology. In spite of the prominent role that the model has played in the development of this branch of physics, there still…

In this paper we deduce a universal result about the asymptotic distribution of roots of random polynomials, which can be seen as a complement to an old and famous result of Erdos and Turan. More precisely, given a sequence of random…

This paper formulates an elementary algorithm for resolution of singularities in a neighborhood of a singular point over a field of characteristic zero. The algorithm is composed of finite sequences of Newton polyhedra and monomial…

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…

We investigate suitable, physically motivated conditions on spacetimes containing certain submanifolds - the so-called {weakly trapped submanifolds} - that ensure, in a set of neighboring metrics with respect to a convenient topology, that…

This paper provides insights into the role of symmetry in studying polynomial functions vanishing to high order on an algebraic variety. The varieties we study are singular loci of hyperplane arrangements in projective space, with emphasis…

We study the stratification of the space of monic polynomials with real coefficients according to the number and multiplicities of real zeros. In the first part, for each of these strata we provide a purely combinatorial chain complex…

This paper proposes seven combinatorial problems around formulas for the characteristic polynomial and the spectral numbers of a quasihomogeneous singularity. One of them is a new conjecture on the characteristic polynomial. It is an…

We derive for Bohmian mechanics topological factors for quantum systems with a multiply-connected configuration space Q. These include nonabelian factors corresponding to what we call holonomy-twisted representations of the fundamental…

A probability distribution over the Boolean cube is monotone if flipping the value of a coordinate from zero to one can only increase the probability of an element. Given samples of an unknown monotone distribution over the Boolean cube, we…