Related papers: On complex highly regular embeddings and the exten…

We obtain bounds on the least dimension of an affine space that can contain an $n$-dimensional submanifold without any pairs of parallel or intersecting tangent lines at distinct points. This problem is closely related to the generalized…

In [36, Section 8], the present author proposed the hypergraph obstruction for the existence of k-regular embeddings. In this paper, we develop the hypergraph obstruction concretely and give some homological obstructions for the k-regular…

We show that every formal embedding sending a real-analytic strongly pseudoconvex hypersurface in $M\subset \C^N$ into another such hypersurface in $M'\subset \C^{N+1}$ is convergent. More generally, if $M$ and $M'$ are merely…

We formulate a notion of stability for maps between polarised varieties which generalises Kontsevich's definition when the domain is a curve and Tian-Donaldson's definition of K-stability when the target is a point. We give some examples,…

Using techniques from supergravity and dimensional reduction, we study the full isometry algebra of K\"ahler and quaternionic manifolds with special geometry. These two varieties are related by the so-called c-map, which can be understood…

For $E$ a presheaf of spectra on the category of smooth $k$-schemes satisfying Nisnevich excision, we prove that the canonical map from the algebraic singular complex of the theory $E$ with quasi-finite supports to the theory $E$ with…

We design a class of Chudnovsky-type algorithms multiplying k elements of a finite extension of order n a finite field K. We prove that these algorithms give a tensor decomposition of the k-multiplication for which the rank is linear in n…

In this paper we construct and theoretically analyse group equivariant convolutional kernel networks (CKNs) which are useful in understanding the geometry of (equivariant) CNNs through the lens of reproducing kernel Hilbert spaces (RKHSs).…

The embedding theorem arises in several problems from analysis and geometry. The purpose of this paper is to provide a deeper understanding of analysis and geometry with a particular focus on embedding theorems on spaces of homogeneous type…

For an ample groupoid with torsion-free stabilizers, we construct a Chern character map going from the domain of the Baum-Connes assembly map of G to the groupoid homology groups of G with rational coefficients. As a main application,…

Let M be a compact Sasakian manifold. We show that M admits a CR-embedding into a Sasakian manifold diffeomorphic to a sphere, and this embedding is compatible with the respective Reeb fields. We argue that a stronger embedding theorem…

With respect to a $C^{\infty}$ metric which is close to the standard Euclidean metric on $\mathbb{R}^{N+1+\ell}$, where $N\ge 7$ and $\ell\ge 1$ are given, we construct a class of embedded $(N+\ell)$-dimensional hypersurfaces (without…

This paper consists of two related parts. In the first part we give a self-contained proof of homological stability for the spaces C_n(M;X) of configurations of n unordered points in a connected open manifold M with labels in a…

Vershik and Kerov conjectured in 1985 that dimensions of irreducible representations of finite symmetric groups, after appropriate normalization, converge to a constant with respect to the Plancherel family of measures on the space of Young…

We construct a collection of higher Chow cycles on certain surfaces which degenerate to an arrangement of planes in general position. When its degree is 4, this construction gives a new explicit proof of the Hodge-D-Conjecture for a certain…

We study a generalization of a conjecture made by Beauville on the Chow ring of hyper-K\"ahler algebraic varieties. Namely we prove in a number of cases that polynomial cohomological relations involving only CH^1(X) and the Chern classes of…

We prove that harmonic maps into Euclidean buildings, which are not necessarily locally finite, have singular sets of Hausdorff codimension 2, extending the locally finite regularity result of Gromov and Schoen. As an application, we prove…

We prove local measure bounds on the tubular neighbourhood of the singular set of codimension one stationary integral $n$-varifolds $V$ in Riemannian manifolds which have both: (i) finite index on their smoothly embedded part; and (ii)…

We study regularity of the time-delayed coordinate maps \[\phi_{h,k}(x) = (h(x), h(Tx), \ldots, h(T^{k-1}x))\] for a diffeomorphism $T$ of a compact manifold $M$ and smooth observables $h$ on $M$. Takens' embedding theorem shows that if $k…

In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric…