Related papers: Weakly-exceptional singularities in higher dimensi…

We use classical invariant theory to construct invariants of complex graded Gorenstein algebras of finite vector space dimension. As a consequence, we obtain a way of extracting certain numerical invariants of quasi-homogeneous isolated…

We study the relationship between singularity categories and relative singularity categories and discuss constructions of differential graded algebras of relative singularity categories. As consequences, we obtain structural results, which…

We discuss a few examples in 2+1 dimensions and 1+1 dimensions supporting a recent conjecture concerning the relation between the Planck scale and the coupling strength of a non-gravitional interaction, unlike those examples in 3+1…

The article contains a survey of our results on weakly commensurable arithmetic and general Zariski-dense subgroups, length-commensurable and isospectral locally symmetric spaces and of related problems in the theory of semi-simple agebraic…

This work is the third part of a series of papers. In the first two we consider curves and varieties in a power of an elliptic curve. Here we deal with subvarieties of an abelian variety in general. Let V be an irreducible variety of…

In this paper it is shown that every non-periodic ergodic system has two topologically weakly mixing, fully supported models: one is non-minimal but has a dense set of minimal points; and the other one is proximal. Also for independent…

We prove the global-in-time existence of nonnegative weak solutions to a class of fourth order partial differential equations on a convex bounded domain in arbitrary spatial dimensions. Our proof relies on the formal gradient flow structure…

We construct a class of spacetimes (without symmetry assumptions) satisfying the vacuum Einstein equations with singular boundaries on two null hypersurfaces intersecting in the future on a 2-sphere. The metric of these spacetimes extends…

We prove the existence of weak solutions for distribution-dependent stochastic Volterra equations under linear growth and continuity conditions on the coefficients and mild regularity assumptions on the kernels, including singular kernels.…

Let $X$ be an algebraic variety with Gorenstein singularities. We define the notion of a wonderful resolution of singularities of $X$ by analogy with the theory of wonderful compactifications of semi-simple linear algebraic groups. We prove…

In this article we prove the following version of the Weak-BAB conjecture for $3$-folds in char $p>5$: Fix a DCC set $I\subset [0, 1)$ and an algebraically closed field $k$ of characteristic $p>5$. Let $\mathfrak{D}$ be a collection of klt…

We study five dimensional(5D) spherically symmetric self-similar perfect fluid space-time with adiabatic equation of state, considering all the families of future directed non-spacelike geodesics. The space-time admits globally strong…

We consider a space-fractional wave equation with a singular mass term depending on the position and prove that it is very weak well-posed. The uniqueness is proved in some appropriate sense. Moreover, we prove the consistency of the very…

We prove some uniqueness results for weak solutions to some classes of parabolic Dirichlet problems.

We derive local boundedness estimates for weak solutions of a large class of second order quasilinear equations. The structural assumptions imposed on an equation in the class allow vanishing of the quadratic form associated with its…

In this paper we prove that any Poisson structure on a sheaf of Lie algebroids admits a weak deformation quantization, and give a sufficient condition for such a Poisson structure to admit an actual deformation quantization. We also answer…

For artinian Gorenstein algebras in codimension four and higher, it is well known that the Weak Lefschetz Property (WLP) does not need to hold. For Gorenstein algebras in codimension three, it is still open whether all artinian Gorenstein…

We compute the Gorenstein weak dimension of a coherent power series rings over a commutative rings and we show that, in general, $\gwd(R) \leq 1$ does not imply that $R$ is an arithmetical ring.

We show that if $X$ has a zero-set diagonal and $X^2$ has countable weak extent, then $X$ is submetrizable. This generalizes earlier results from Martin and Buzyakova. Furthermore we show that if $X$ has a regular $G_\delta$-diagonal and…

We study a boundary value elliptic problem having a lower order nonlinear term with subquadratic growth in the gradient of the solution and possibly singular when the solution vanishes. If the singularity is mild enough (and even in the…