Related papers: Free divisors versus stability and coincidence thr…
A novel concept for the design of nonlinear optical diodes is proposed which uses the multistability of coupled nonlinear microcavities and the dependence of switching thresholds on the direction of incidence. A typical example of such…
This note (which makes no claim to novelty) presents a proof of the separable rational connectedness of smooth cubic hypersurfaces, in any characteristic, by showing how to explicitly construct very free curves (of degree 3) on them. -----…
In this paper, we explore the wall crossing phenomenon for K-stability, and apply it to explain the wall crossing for K-moduli stacks and K-moduli spaces.
We show that the complement of a degree $d$ hypersurface in a projective complete intersection, whose defining equations have degrees strictly larger than $d$, has a rational connectivity higher than expected. The key new feature is that a…
We study a functional defined on the class of piecewise constant functions, combining a jump penalization, which discourages discontinuities, with a fidelity term that penalizes deviations from a given linear function, called the forcing…
Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.
In this paper, we show that general Fano complete intersections over an algebraically closed field of arbitrary characteristics are separably rationally connected. Our proof also implies that general log Fano complete intersections with…
We study properties of stable, strictly stable and locally outermost marginally outer trapped surfaces in spacelike hypersurfaces of spacetimes possessing certain symmetries such as isometries, homotheties and conformal Killings. We first…
We determine non-Hopf hypersurfaces with constant mean curvature in the complex projective plane which attain equality in a basic inequality between the maximum Ricci curvature and the squared mean curvature.
In this paper, we prove the local well-posedness of the free boundary problem in incompressible elastodynamics under a natural stability condition, which ensures that the evolution equation describing the free boundary is strictly…
We consider a driven diffusive system with two types of particles, A and B, coupled at the ends to reservoirs with fixed particle densities. To define stochastic dynamics that correspond to boundary reservoirs we introduce projection…
If supersymmetry is realized with spontaneous breaking of R-parity, there will be important consequences in several different areas which can be tested through different types of experiments. In this talk we review the phenomenological…
We generalise the Vandermonde determinant identity to one which tests whether a family of hypersurfaces in $\mathbf{P}^n$ has an unexpected intersection point.
One deals with arbitrary reduced free divisors in a polynomial ring over a field of characteristic zero, by stressing the ideal theoretic and homological behavior of the corresponding singular locus. A particular emphasis is given to both…
Device independent dimension witnesses provide a lower bound on the dimensionality of classical and quantum systems in a "black box" scenario where only correlations between preparations, measurements and outcomes are considered. We address…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
We study properties of a sample covariance estimate $\widehat \Sigma$ given a finite sample of $n$ i.i.d. centered random elements in $\R^d$ with the covariance matrix $\Sigma$. We derive dimension-free bounds on the squared Frobenius norm…
The geometry of divisors on algebraic curves has been studied extensively over the years. The foundational results of this Brill-Noether theory imply that on a general curve, the spaces parametrizing linear series (of fixed degree and…
This Ph.D. thesis studies the relation between the Harder-Narasimhan filtration and a notion of GIT maximal unstability. When constructing a moduli space by using Geometric Invariant Theory (GIT), a notion of GIT stability appears, which is…
We discuss the structure of threshold corrections to soft supersymmetry-breaking parameters at the mass threshold of heavy chiral superfields. Nontrivial dependence on soft parameters of heavy matter fields originates from the `physical'…