Related papers: Bridgeland walls destabilizing one-dimensional spa…

A hybrid of the critical three dimensional Gross-Neveu and Thirring models deformed by explicit parity breaking operators is studied in the large N expansion and using the renormalization group. The regime of coupling constants where the…

In the rapidly rotating limit, we derive a balanced set of reduced equations governing the strongly nonlinear development of the convective wall-mode instability in the interior of a general container. The model illustrates that wall-mode…

We introduce the notion of Gepner type Bridgeland stability conditions on triangulated categories, which depends on a choice of an autoequivalence and a complex number. We conjecture the existence of Gepner type stability conditions on the…

In this paper, we prove the Bogomolov-Gieseker type inequality conjecture for threefolds with nef tangent bundles. As a corollary, there exist Bridgeland stability conditions on these threefolds.

It is argued that there are three distinct zones in a wall bounded turbulent flow field dominated by three completely different mechanisms: - An outer region where the velocity profile is determined by the pressure distribution - A highly…

Using Langer's construction of Bridgeland stability conditions on normal surfaces, we prove Reider-type theorems generalizing the work done by Arcara-Bertram in the smooth case. Our results still hold in positive characteristic or when…

We explore Seiberg-like dualities, or mutations, for ${\cal N}=4$ quiver quantum mechanics in the context of wall-crossing. In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care. With fixed…

In terms of the number of triangles, it is known that there are more than exponentially many triangulations of surfaces, but only exponentially many triangulations of surfaces with bounded genus. In this paper we provide a first geometric…

The Brill-Noether theory of curves plays a fundamental role in the theory of curves and their moduli and has been intensively studied since the 19th century. In contrast, Brill-Noether theory for higher dimensional varieties is less…

Following the RG flow of an N=1 quiver gauge theory and applying Seiberg duality whenever necessary defines a duality cascade, that in simple cases has been understood holographically. It has been argued that in certain cases, the dualities…

The work addresses 2D and 3D turbulent transonic flows past a wall with an expansion corner. A curved shock wave is formed upstream of a cylinder located above the corner. Numerical solutions of the Reynolds-averaged Navier-Stokes equations…

In this article it is shown that the equilateral triangle maximizes the Cheeger constant and minimizes the torsional rigidity among shapes having a fixed minimal width. The proof techniques use direct comparisons with simpler shapes,…

In this paper, we redefine the theory of walls and chambers due to Qin developing a new tool to study moduli spaces of stable rank 2 vector bundles on algebraic varieties of higher dimension. We apply it to describe components of some…

We introduce an analogue of Bridgeland's stability conditions for polarised varieties. Much as Bridgeland stability is modelled on slope stability of coherent sheaves, our notion of Z-stability is modelled on the notion of K-stability of…

In this article we reconsider high Reynolds number boundary layer flows of fluids with viscoelastic properties. We show that a number of previous studies that have attempted to address this problem are, in fact, incomplete. We correctly…

Here, we investigate the linear spatial stability of a parallel two-dimensional compressible boundary layer on an adiabatic plate by considering 2D and 3D disturbances. We employ the Compound Matrix Method for the first time for…

We give a conjectural construction of Bridgeland stability conditions on the derived category of fibred threefolds. The construction depends on a conjectural Bogomolov-Gieseker type inequality for certain stable complexes. It can be…

We consider the chessboard pebbling problem analyzed by Chung, Graham, Morrison and Odlyzko [3]. We study the number of reachable configurations $G(k)$ and a related double sequence $G(k,m)$. Exact expressions for these are derived, and we…

In a recent paper (math.DG/0701278) we constructed a series of new Moishezon twistor spaces which is a kind of variant of the famous LeBrun twistor spaces. In this paper we explicitly give projective models of another series of Moishezon…

We describe conditions under which higher-dimensional billiard models in bounded, convex regions are fully chaotic, generalizing the Bunimovich stadium to dimensions above two. An example is a three-dimensional stadium bounded by a cylinder…