Related papers: General real-valued theories with the Schr\"oder-B…

We prove homological stability for standard unitary groups over R, C and H and for general linear groups over skew-fields with infinite centre. We focus on the similarities and differences of these proofs. Both proofs are due to Chih-Han…

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.

We prove the following result: if a $\mathbb{Q}$-Fano variety is uniformly K-stable, then it admits a K\"{a}hler-Einstein metric. We achieve this by modifying Berman-Boucksom-Jonsson's strategy with appropriate perturbative arguments and…

We present a summarizing account of a series of investigations whose central topic is to address the question whether atomic stabilization exists in an analytical way. We provide new aspects on several issues of the matter in the…

In [19] and [26], the authors proved the stability of multi-solitons for derivative nonlinear Schr{\"o}dinger equations. Roughly speaking, sum of finite stable solitons is stable. We predict that if there is one unstable solition then…

We consider the existence of a dynamically stable soliton in the one-dimensional cubic-quintic nonlinear Schr\"odinger model with strong cubic nonlinearity management for periodic and random modulations. We show that the predictions of the…

In this paper we study a mixed problem for the nonlinear Schr\"odinger equation globally that have a nonlinear adding, in which the coefficient is a generalized function. Here is proved a global solvability theorem of the considered problem…

We study the relation (and differences) between stability and Property (S) in the simple and stably finite framework. This leads us to characterize stable elements in terms of its support, and study these concepts from different sides :…

In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…

Under Gromov--Hausdorff convergence, and equivariant Gromov--Hausdorff convergence, we prove stability results of Wasserstein spaces over certain classes of singular and non-singular spaces. For example, we obtain an analogue of Perelman's…

In this short note we provide a relatively simple proof of the Erd\H{o}s-Hajnal conjecture for families of finite (hyper-)graphs without the $k$-order property. It was originally proved by M. Malliaris and S. Shelah in "Regularity lemmas…

We prove global existence for Einstein's equations with a charged scalar field for initial conditions sufficiently close to the Minkowski spacetime without matter. The proof relies on generalized wave coordinates adapted to the outgoing…

In recent years, a number of alternative theories of gravity have been proposed as possible resolutions of certain cosmological problems or as toy models for possible but heretofore unobserved effects. However, the implications of such…

In 1987, the $\alpha$-invariant theorem gave a fundamental criterion for existence of Kahler-Einstein metrics on smooth Fano manifolds. In 2012, Odaka-Sano extended the framework to $\mathbb{Q}$-Fano varieties in terms of K-stability, and…

In the first edition of Classification Theory, the second author characterized the stable theories in terms of saturation of ultrapowers. Prior to this theorem, stability had already been defined in terms of counting types, and the unstable…

We review recent developments in structural stability as applied to key topics in general relativity. For a nonlinear dynamical system arising from the Einstein equations by a symmetry reduction, bifurcation theory fully characterizes the…

We perform canonical quantization of General Relativity, as an effective quantum field theory below the Planck scale, within the BRST-invariant framework. We show that the promotion of constraints to dynamical equations of motion for…

We develop the General Theory of Relativity in a formalism with extended causality that describes physical interaction through discrete, transversal and localized pointlike fields. The homogeneous field equations are then solved for a…

We use Renormalization Group ideas to study stability of moving fronts in the Ginzburg-Landau equation in one spatial dimension. In particular, we prove stability of the real fronts under complex perturbations. This extends the results of…

The Darmois-Skitovich theorem is a simple characterization of the normal distribution in terms of the independence of linear forms. We present here a non-commutative version of this theorem in the context of Gaussian bosonic states and show…