Related papers: Singularities of stable varieties

This is a survey article, based on the author's lectures in the 2015 AMS Summer Research Institute in Algebraic Geometry, and to appear in the Proceedings.

We prove in this note a stabilized version of a conjecture on $\A^1$-connectedness. For the stabilized version of this conjecture, we introduce the notion of stable $\A^1$-connectedness, which is can be seen as the stabilization of…

Singularities of the Navier-Stokes equations occur when some derivative of the velocity field is infinite at any point of a field of flow (or, in an evolving flow, becomes infinite at any point within a finite time). Such singularities can…

We study the behavior of Du~Bois singularities under base change and fiber products. For embeddable varieties in characteristic zero, we show that Du~Bois singularities descend from any field extension. We also prove that the product of a…

We survey various approaches to axiomatic stable homotopy theory, with examples including derived categories, categories of (possibly equivariant or localized) spectra, and stable categories of modular representations of finite groups. We…

After a historical discussion of classical uniformisation results for Riemann surfaces, of problems appearing in higher dimensions, and of uniformisation results for projective manifolds with trivial or ample canonical bundle, we introduce…

Singularities of the Poynting vector field at resonant light scattering by nanoparticles are discussed and classified. It is shown that there are two generic types of them, namely (i) the singularities related to the vanishing of the…

The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these pairings,…

In this short note we will explore some recent connections between positivity, singularities, and boundedness in various contexts focusing on birational geometry.

This dissertation deals with singularity formation in spherically symmetric solutions of the hyperbolic Yang Mills equations in (4+1) dimensions and in spherically symmetric solutions of C P^1 wave maps in (2+1) dimensions. These equations…

Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…

A review of the current status of SUSY/SUGRA/String phenomenology is given.

This is the abstract prepared for Workshop on Topology and Geometry (Zhang jiang, China, October 1994), and is a review of my recent works. What kinds of combinations of singularities can appear in small deformation fibers of a fixed…

We observe experimentally higher-order solitons in waveguide arrays with defocusing saturable nonlinearity. Such solitons can comprise several in-phase bright spots and are stable above a critical power threshold. We elucidate the impact of…

The mathematical notion of a spectral singularity admits a physical interpretation as a zero-width resonance. It finds an optical realization as a certain type of lasing effect that occurs at the threshold gain. We explore spectral…

We study the problem of resolving singularities via the blow-up of the module of derivations. Our main results are a positive answer for the case of curves and log-canonical surface singularities, i.e., a finite sequence of blow-ups along…

This note is an introduction to the properties of stable polynomials in several variables with real or complex coefficients. These polynomials are defined in terms of where the polynomial is non-vanishing. We do not cover well-known topics…

Some recent existence, multiplicity, and uniqueness results for singular p-Laplacian systems either in bounded domains or in the whole space are presented, with a special attention to the case of convective reactions. A extensive…

In this paper, we study the uniqueness of coexistence state for multiple species of animals in the same environment.

This is a survey on special metrics. We shall present some results and open questions on special metrics mainly appeared in the last 10 years