Related papers: Mumford's Degree of Contact and Diophantine Approx…

There has been great interest in developing a theory of "Khintchine types" for manifolds embedded in Euclidean space, and considerable progress has been made for curved manifolds. We treat the case of translates of coordinate hyperplanes,…

The method of the fundamental solutions (MFS) is used to construct an approximate solution for a partial differential equation in a bounded domain. It is demonstrated by combining the fundamental solutions shifted to the points outside the…

In this paper, we give a definition of Diophantine points of type $\gamma$ for $\gamma\geq0$ in a homogeneous space $G/\Gamma$, and compute the Hausdorff dimension of the subset of points which are not Diophantine of type $\gamma$ when $G$…

We study K-theoretic Gromov--Witten invariants of projective hypersurfaces using a virtual localization formula under finite group actions. In particular, it provides all K-theoretic Gromov--Witten invariants of the quintic threefold modulo…

We propose a consistent polynomial-time method for the unseeded node matching problem for networks with smooth underlying structures. Despite widely conjectured by the research community that the structured graph matching problem to be…

We establish a connection between gaps problems in Diophantine approximation and the frequency spectrum of patches in cut and project sets with special windows. Our theorems provide bounds for the number of distinct frequencies of patches…

In this paper, we prove a generalization of the Schmidt's subspace theorem for polynomials of higher degree in subgeneral position with respect to a projective variety over a number field. Our result improves and generalizes the previous…

We describe the equivariant Chow ring of the wonderful compactification $X$ of a symmetric space of minimal rank, via restriction to the associated toric variety $Y$. Also, we show that the restrictions to $Y$ of the tangent bundle $T_X$…

Let X_1, X_2 be symplectic 4-manifolds containing symplectic surfaces F_1,F_2 of identical positive genus and opposite squares. Let Z denote the symplectic sum of X_1 and X_2 along the F_k. Using relative Gromov--Witten theory, we determine…

This work assesses a classical density functional theory (DFT) model for predicting macroscopic static contact angles of pure substances and mixtures by comparison to own experimental data. We employ a DFT with a Helmholtz energy functional…

In Diophantine approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of Diophantine approximation. We prove that…

We engineer U(1)^n Chern-Simons type theories describing fractional quantum Hall solitons (QHS) in 1+2 dimensions from M-theory compactified on eight dimensional hyper-K\"{a}hler manifolds as target space of N=4 sigma model. Based on…

Let $X$ be a smooth projective variety acted on by a reductive group $G$. Let $L$ be a positive $G$-equivariant line bundle over $X$. We use the Witten deformation of the Dolbeault complex of $L$ to show, that the cohomology of the sheaf of…

Let $X$ be a quasi projective scheme over a noetherian affine scheme $Spec(A)$, $U\subseteq X$ be an open subset, and $Z=X-U$.Assume that $Z$ is complete intersection, with $k=codim Z$. Consider the map $$ q:{\mathbb K}\left({\mathscr…

This is an updated version of a paper which appeared in the proceedings of the 1979 Berlin Colloquium on Global Differential Geometry. This paper contains the original exposition together with some notes by the authors made in 2025 (as…

We introduce the concept of parametrized homotopic distance, extending the classical notion of homotopic distance to the fibrewise setting. We establish its correspondence with the fibrewise sectional category of a specific fibrewise…

In these Notes, a comprehensive description of the universal fractal geometry of conformally-invariant scaling curves or interfaces, in the plane or half-plane, is given. The present approach focuses on deriving critical exponents…

Let $H$ be an infinite-dimensional complex Hilbert space. Denote by ${\mathcal G}_{\infty}(H)$ the Grassmannian formed by closed subspaces of $H$ whose dimension and codimension both are infinite. We say that $X,Y\in {\mathcal…

We establish the relation between the Wigner-Weisskopf theory for the description of an unstable system and the theory of coupling to an environment. According to the Wigner-Weisskopf general approach, even within the pole approximation…

Suppose $g_t$ is a $1$-parameter $\mathrm{Ad}$-diagonalizable subgroup of a Lie group $G$ and $\Gamma < G$ is a lattice. We study the dimension of bounded and divergent orbits of $g_t$ emanating from a class of curves lying on leaves of the…