Related papers: The unreasonable effectiveness of wall-crossing in…
For a smooth projective complex variety whose Albanese morphism is finite, we show that every Bridgeland stability condition on its bounded derived category of coherent sheaves is geometric, in the sense that all skyscraper sheaves are…
In this paper we introduce a new property for normed algebras. This property which we call it stability, plays a key role in the studying of the theory of almost multiplier maps. In this note we study some of the basic properties of this…
We utilize a geometric argument to determine the effects of boundary scattering on the carrier mean-free path in samples of various cross sections. Analytic expressions for samples with rectangular and circular cross sections are obtained.…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
Survey article on representation stability and examples in algebraic geometry and topology, written for the Notices of the AMS.
We give further counterexamples to the conjectural construction of Bridgeland stability on threefolds due to Bayer, Macr\`i, and Toda. This includes smooth projective threefolds containing a divisor that contracts to a point, and…
We discuss the model robustness of the infinite two-dimensional square grid with respect to symmetry breakings due to the presence of defects, that is, lacks of finitely or infinitely many edges. Precisely, we study how these topological…
Let $X$ be a smooth compact complex surface with the canonical divisor $K_X$ ample and let $\Theta_X$ be its holomorphic tangent bundle. Bridgeland stability conditions are used to study the space $H^1 (\Theta_X)$ of infinitesimal…
In this paper, we give a definition of weak stability condition on a triangulated category. The difference between our definition and existing definitions is that we allow objects in the kernel to have non-maximal phases. We then construct…
We relate Hilbert schemes of points and Fulton-MacPherson compactifications by an interpolating stability condition. We then derive wall-crossings formulas and some applications for the enumerative geometry of Hilbert schemes.
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
This is a survey paper on Alegbraic Geometry over Lie Algebras
We study conformally invariant boundary conditions that break part of the bulk symmetries. A general theory is developped for those boundary conditions for which the preserved subalgebra is the fixed algebra under an abelian orbifold group.…
: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…
In this paper we discuss some physical applications of topological *-algebras of unbounded operators. Our first example is a simple system of free bosons. Then we analyze different models which are related to this one. We also discuss the…
Stabilization schemes in wall-bounded flows often invoke fluid transpiration through porous boundaries. While these have been extensively validated for external flows, their efficacy in channels, particularly from the standpoint of…
The key result in the theory of Bridgeland stability conditions is the property that they form a complex manifold. This comes from the fact that given any small deformation of the central charge, there is a unique way to correspondingly…
We generalize the natural cross ratio on the ideal boundary of a rank one symmetric spaces, or even $\mathrm{CAT}(-1)$ space, to higher rank symmetric spaces and (non-locally compact) Euclidean buildings - we obtain vector valued cross…
We prove that the Gieseker moduli space of stable sheaves on a smooth projective threefold $X$ of Picard rank 1 is separated from the moduli space of PT stable objects by a single wall in the space of Bridgeland stability conditions on $X$,…
In this paper, we investigate the effect of boundary surface roughness on numerical simulations of incompressible fluid flow past a cylinder in two and three spatial dimensions furnished with slip boundary conditions. The governing…