相关论文: Higher dimensional conundra

In this paper, we present the results of a computer investigation of asymptotics for maximum dimensions of linear and projective representations of the symmetric group. This problem reduces to the investigation of standard and strict Young…

I propose a few increasingly stronger "superadditivity" conjectures regarding the behavior of Kodaira dimension under morphisms of smooth quasi-projective complex varieties.

The finitistic dimension conjecture is closely connected to the symmetry of the finitistic dimension. Recent work indicates that such connection extends to one of its upper bounds, the delooping level. In this paper, we show that the same…

This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper…

This is a brief discussion of the following features of the Universal Extra Dimension (UED) model: (i) Formulation, (ii) Indirect bounds, (iii) Collider search and the Inverse Problem, (iv) Astrophysical bounds, and (v) UED with two extra…

We examine asymptotic dimension and property A for groups acting on complexes. In particular, we prove that the fundamental group of a finite, developable complex of groups will have finite asymptotic dimension provided the geometric…

We establish the second-order moment asymptotics for a parabolic Anderson model $\partial_{t}u=(\Delta+\xi)u$ in the hyperbolic space with a regular, stationary Gaussian potential $\xi$. It turns out that the growth and fluctuation…

Suppose $(M^{n},g)$ is a Riemannian manifold with nonnegative Ricci curvature, and let $h_{d}(M)$ be the dimension of the space of harmonic functions with polynomial growth of growth order at most $d$. Colding and Minicozzi proved that…

Among the set of hypersurfaces of degree $d$ and dimension $\ell$ defined by the vanishing of a homogeneous polynomial with coefficients $\pm 1$, we investigate the probability that a hypersurface contains a rational point as $d$ and $\ell$…

This brief survey deals with multi-dimensional Diophantine approximations in sense of linear form and with simultaneous Diophantine approximations. We discuss the phenomenon of degenerate dimension of linear subspaces generated by the best…

We show that an $n$-dimensional surface whose entropy is close to that of an $n$-dimensional plane is close in Hausdorff distance to some $n$-dimensional plane at every scale. Moreover we show that self-expanders of low entropy converge in…

We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible estimates for errors of considered approximations in the…

In this paper we investigate complex dynamics in infinite dimensions.

A nonnegative number d_infinity, called asymptotic dimension, is associated with any metric space. Such number detects the asymptotic properties of the space (being zero on bounded metric spaces), fulfills the properties of a dimension, and…

We study analysis over infinite dimensional manifolds consisted by sequences of almost K\"ahler manifolds. In particular we develop moduli theory of pseudo holomorphic curves into the spaces with high symmetry. As applications, we study…

We study the limiting behavior of $r$-maximum distance minimizers and the asymptotics of their $1$-dimensional Hausdorff measures as $r$ tends to zero in several contexts, including situations involving objects of fractal nature.

The asymptotic behaviour of the quantiles in the gamma distribution are investigated as the shape parameter tends to zero. Some remarks about the behaviour at infinity are given.

Here we explore the geometry of the osculating spaces to projective varieties of arbitrary dimension. In particular, we classify varieties having very degenerate higher order osculating spaces and we determine mild conditions for the…

The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in…

Various aspects of Supersymmetry in 1-dimensional systems are analyzed.