Related papers: A stable property of Borel type ideals
We show that there is a stable homotopy theory of profinite spaces and use it for two main applications. On the one hand we construct an \'etale topological realization of the stable motivic homotopy theory of smooth schemes over a base…
We study a large family of products of Borel fixed ideals of maximal minors. We compute their initial ideals and primary decompositions, and show that they have linear free resolutions. The main tools are an extension of straightening law…
Sobolev-type regularity results are proved for solutions to a class of second order elliptic equations with a singular or degenerate weight, under non-homogeneous Neumann conditions. As an application a Pohozaev-type identity for weak…
In this paper, we provide a new PDE proof for the celebrated Borell--Brascamp--Lieb inequality. Our approach reveals a deep connection between the Borell--Brascamp--Lieb inequality and properties of diffusion equations of porous medium type…
We establish homological stability for automorphisms of symmetric bilinear forms over a class of principal ideal domains that includes all fields, the integers, the Gaussian integers, and the Eisenstein integers. In conjunction with…
We summarize results concerning the Bernstein property of differential equations.
Let $X$ be a set of points whose coordinates are known with limited accuracy; our aim is to give a characterization of the vanishing ideal $I(X)$ independent of the data uncertainty. We present a method to compute a polynomial basis $B$ of…
A theorem of Macaulay on colons of ideals in polynomial rings is proved for homogeneous Gorenstein algebras.
In this paper, we show that the regularity of the q-th quasi-symbolic power $I^{((q))}$ and the regularity of the $q$-th bracket power $I^{[q]}$ of a monomial ideal of Borel type $I$, satisfy the relations $reg(I^{((q))})\leq q \cdot…
We give a multivariate generalization of Borell's noise stability theorem for Gaussian vectors. As a consequence we recover two inequalities, also due to Borell, for exit times of the Ornstein-Uhlenbeck process.
This paper is devoted to the study of rigidity properties for special solutions of nonlinear elliptic partial differential equations on smooth, boundaryless Riemannian manifolds. As far as stable solutions are concerned, we derive a new…
We consider the parabolic-parabolic two-dimensional Patlak-Keller-Segel problem. We prove the existence of stable blow-up dynamics in finite time in the radial case. We extend in this article the result of [36] for the parabolic-elliptic…
It is shown that plane wave solutions to the cubic nonlinear Schr\"odinger equation on a torus behave orbitally stable under generic perturbations of the initial data that are small in a high-order Sobolev norm, over long times that extend…
We initiate a study of tensor ideals in linear rigid monoidal categories that are kernels of linear monoidal functors to abelian monoidal categories. We develop general methods and apply them to the category of tilting modules over quantum…
Given a monomial ideal in a polynomial ring over a field, we define the LCM-dual of the given ideal. We show good properties of LCM-duals. Including the isomorphism between the special fiber of LCM-dual and the special fiber of given…
We study global dynamical properties of the isometry group of the Borel randomization of a separable complete structure. In particular, we show that if properties such as the Rohklin property, topometric generics, extreme amenability hold…
We provide a general approach to the classification results of stable solutions of (possibly nonlinear) elliptic problems with Robin conditions. The method is based on a geometric formula of Poincar\'e type, which is inspired by a classical…
The Borell-Brascamp-Lieb inequality is a classical extension of the Pr\'ekopa-Leindler inequality, which in turn is a functional counterpart of the Brunn-Minkowski inequality. The stability of these inequalities has received significant…
An ideal $I$ of a commutative ring $R$ is said to be of linear type when its Rees algebra and symmetric algebra exhibit isomorphism. In this paper, we investigate the conjecture put forth by Jayanthan, Kumar, and Sarkar (2021) that if $G$…
Let $k$ be a field. We determine the ideals $I$ in a finitely generated graded $k$-algebra $A$, whose associated graded rings are isomorphic to $A$. Also we compute the graded local cohomologies of the Rees rings $A[I t]$ and give the…