Related papers: Streamlining resolution of singularities with weig…

For the critical one-dimensional nonlinear Schr\"odinger equation, we construct blow-up solutions that concentrate a soliton at the origin at the conformal blow-up rate, with a non-flat blow-up profile. More precisely, we obtain a blow-up…

We consider a blow-up solution for a strongly perturbed semilinear heat equation with Sobolev subcritical power nonlinearity. Working in the framework of similarity variables, we find a Lyapunov functional for the problem. Using this…

In this work, we consider the singular set in the thin obstacle problem with weight $|x_{n+1}|^a$ for $a\in (-1, 1)$, which arises as the local extension of the obstacle problem for the fractional Laplacian (a non-local problem). We develop…

Two main algorithmic approaches are known for making Hironaka's proof of resolution of singularities in characteristic zero constructive. Their main difference is the use of different notions of transforms during the resolution process and…

Let X be a smooth and tame stack with finite inertia. We prove that there is a functorial sequence of blow-ups with smooth centers after which the stabilizers of X become abelian. Using this result, we can extend the destackification…

Let f: X -> Z be a local, projective, divisorial contraction between normal varieties of dimension n with Q-factorial singularities. Let $Y \subset X$ be a f-ample Cartier divisor and assume that f|Y: Y -> W has a structure of a weighted…

In terms of the gauged nonlinear $\sigma$-models, we describe some results and implications of solving the following problem: Given a smooth symplectic manifold as target space with a quasi-free Hamiltonian group action, perform the…

Let $X$ be a smooth projective toric variety, and let $\widetilde{X}$ denote the blow-up of $X$ at finitely many distinct tours-invariant points. This paper provides an explicit combinatorial formula for the Chow weight of $\widetilde{X}$…

We construct a functor from the category of manifolds with generalized corners to the category of complexes of toric monoids, and for every `refinement' of the complex associated to a manifold, we show there is a unique `blow-up', i.e., a…

This paper explores the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the Fokker-Planck equation. The unified features of the discrete singular convolution algorithm are discussed. It is…

In this article we study the structure of solutions to the one-phase Bernoulli problem that are modeled either infinitesimally or at infinity by one-homogeneous solutions with an isolated singularity. In particular, we prove a uniqueness of…

We give an algorithm for removing stackiness from smooth, tame Artin stacks with abelian stabilisers by repeatedly applying stacky blow-ups. The construction works over a general base and is functorial with respect to base change and…

Recently Corteel and Welsh outlined a technique for finding new sum-product identities by using functional relations between generating functions for cylindric partitions and a theorem of Borodin. Here, we extend this framework to include…

In this paper we consider the blow-up of solutions to a weakly coupled system of semilinear damped wave equations in the scattering case with nonlinearities of mixed type, namely, in one equation a power nonlinearity and in the other a…

This paper presents a new perspective on unifying all fundamental interactions--gravitational, electromagnetic, weak and strong--based on stochastic processes rather than conventional quantum mechanics. Earlier work by Nelson, Kac and…

This paper deals with a class of Boltzmann equations on the real line, extensions of the well-known Kac caricature. A distinguishing feature of the corresponding equations is that therein, the collision gain operators are defined by…

We are concerned with rigid analytic geometry in the general setting of Henselian fields $K$ with separated analytic structure, whose theory was developed by Cluckers--Lipshitz--Robinson. It unifies earlier work and approaches of numerous…

The representation scheme ${\tt rep}_n A$ of the 3-dimensional Sklyanin algebra $A$ associated to a plane elliptic curve and n-torsion point contains singularities over the augmentation ideal $\mathfrak{m}$. We investigate the semi-stable…

Splice type surface singularities were introduced by Neumann and Wahl as a generalization of the class of Pham-Brieskorn-Hamm complete intersections of dimension two. Their construction depends on a weighted tree called a splice diagram. In…

We establish a semi-orthogonal decomposition for the weighted blowup of an algebraic stack along a Koszul-regular weighted centre, generalising the classic result of Orlov. Our approach is based on the work of Bergh-Schn\"urer.