Related papers: Cancellation problem via locally nilpotent derivat…
A new algorithm to determine the position of the crack (discontinuity set) of certain minimizers of Mumford-Shah functional in situations when a crack-tip occurs is introduced. The conformal mapping $w=\sqrt{z}$ in the complex plane is used…
We apply the Nash-Moser theorem for exact sequences of R. Hamilton to the context of deformations of Lie algebras and we discuss some aspects of the scope of this theorem in connection with the polynomial ideal associated to the variety of…
We consider a general class of convolution-type nonlocal wave equations modeling bidirectional propagation of nonlinear waves in a continuous medium. In the limit of vanishing nonlocality we study the behavior of solutions to the Cauchy…
It is shown that the rich algebraic structure of the standard $d$-dimensional Coulomb problem can be extended to its Dunkl counterpart. Replacing standard derivatives by Dunkl ones in the so($d+1$,2) dynamical algebra generators of the…
We prove that termination of lower dimensional flips for generalized klt pairs implies termination of flips for log canonical generalized pairs with a weak Zariski decomposition. Moreover, we prove that the existence of weak Zariski…
This article is the second in a series of two whose aim is to extend a recent result of Guillarmou-Lefeuvre [arXiv:1806.04218] on the local rigidity of the marked length spectrum from the case of compact negatively-curved Riemannian…
We show that any pseudo-effective divisor on a normal surface decomposes uniquely into its "integral positive" part and "integral negative" part, which is an integral analog of Zariski decompositions. By using this decomposition, we give…
An analogue of the Lehmann-Symanzik-Zimmermann reduction formula is obtained for the case of noncommutative space-space theory. Some consequences of the reduction formula and Haag's theorem are discussed.
Let $P_3(\mathbf{C}^{\infty})$ be the space of complex cubic polynomials in infinitely many variables. We show that this space is $\mathbf{GL}_{\infty}$-noetherian, meaning that any $\mathbf{GL}_{\infty}$-stable Zariski closed subset is cut…
We present several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. We first focus on…
We show that non-flatness of a morphism f of complex-analytic spaces with a locally irreducible target Y of dimension n manifests in the existence of vertical components in the n-fold fibred power of the pull-back of f to the…
This paper reviews the essential physics of gravitational instability in a Robertson-Walker background spacetime. Three approaches are presented in a pedagogical manner, based on (1) the Eulerian fluid equations, (2) the Lagrangian…
In the classic Coleman--Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is…
Equations in free groups have become prominent recently in connection with the solution to the well known Tarski Conjecture. Results of Makanin and Rasborov show that solvability of systems of equations is decidable and there is a method…
We offer a groupoid-theoretic approach to computing invariants. We illustrate this approach by describing the Gel'fand-MacPherson correspondence and the Gale transform as well as giving Zariski-local descriptions of the moduli space of…
In this paper we give an algorithm to recognize triangulable locally nilpotent derivations in dimension three. In case the given derivation is triangulable, our method produces a coordinate system in which it exhibits a triangular form.
We carefully review the basic examples of anomaly cancellation in M-theory: the 5-brane anomalies and the anomalies on S^1/Z_2. This involves cancellation between quantum anomalies and classical inflow from topological terms. To correctly…
It is well known that anomaly cancellation {\it almost} determines the hypercharges in the standard model. A related (and somewhat more stronger) phenomenon takes place in Connes' NCG framework: unimodularity (a technical condition on…
The purpose of this paper is to provide a new account of multiplicity for finite morphisms between smooth projective varieties. Traditionally, this has been defined using commutative algebra in terms of the length of integral ring…
We show that 4D gauge theories with Green-Schwarz anomaly cancellation and possible generalized Chern-Simons terms admit a formulation that is manifestly covariant with respect to electric/magnetic duality transformations. This generalizes…