Related papers: Complexity results for CR mappings between spheres
We investigate the space complexity of certain perfect matching problems over bipartite graphs embedded on surfaces of constant genus (orientable or non-orientable). We show that the problems of deciding whether such graphs have (1) a…
Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a map is called rounding. We introduce a natural equivalence…
We introduce a recursive procedure for computing the number of realizations of a minimally rigid graph on the sphere up to rotations. We accomplish this by combining two ingredients. The first is a framework that allows us to think of such…
Nowhere dense classes of graphs are very general classes of uniformly sparse graphs with several seemingly unrelated characterisations. From an algorithmic perspective, a characterisation of these classes in terms of uniform quasi-wideness,…
The study of Locally Checkable Labelings (LCLs) has led to a remarkably precise characterization of the distributed time complexities that can occur on bounded-degree trees. A central feature of this complexity landscape is the existence of…
We bound the number of incidences between points and spheres in finite vector spaces by bounding the sum of the number of points in the pairwise intersections of the spheres. We obtain new incidence bounds that are interesting when the…
Reidl, S\'anchez Villaamil, and Stravopoulos (2019) characterized graph classes of bounded expansion as follows: A class $\mathcal{C}$ closed under subgraphs has bounded expansion if and only if there exists a function $f:\mathbb{N} \to…
In this paper we show that the number of distinct distances determined by a set of $n$ points on a constant-degree two-dimensional algebraic variety $V$ (i.e., a surface) in $\mathbb R^3$ is at least $\Omega\left(n^{7/9}/{\rm polylog}…
The main result is a wall crossing formula for central projections defined on submanifolds of a real projective space. Our formula gives the jump of the degree of such a projection when the center of the projection varies. The fact that the…
This paper combines two ingredients in order to get a rather surprising result on one of the most studied, elegant and powerful tools for solving convex feasibility problems, the method of alternating projections (MAP). Going back to names…
In this paper, we study degenerate CR embeddings $f$ of a strictly pseudoconvex hypersurface $M\subset \bC^{n+1}$ into a sphere $\bS$ in a higher dimensional complex space $\bC^{N+1}$. The degeneracy of the mapping $f$ will be characterized…
We study a question with connections to linear algebra, real algebraic geometry, combinatorics, and complex analysis. Let $p(x,y)$ be a polynomial of degree $d$ with $N$ positive coefficients and no negative coefficients, such that $p=1$…
Motivated by a sharp eigenvalue estimate for the Kohn Laplacian, we prove a theorem that characterizes the CR sphere in terms of the existence of a non-trivial complex-valued function satisfying a certain overdetermined system.
In part I we reduced the arithmetic (characteristic zero) version of the P \not \subseteq NP conjecture to the problem of showing that a variety associated with the complexity class NP cannot be embedded in the variety associated the…
We consider the curve graph in the cases where it is not a Farey graph, and show that its Gromov boundary is linearly connected. For a fixed center point c and radius r, we define the sphere of radius r to be the induced subgraph on the set…
Many supervised learning problems involve high-dimensional data such as images, text, or graphs. In order to make efficient use of data, it is often useful to leverage certain geometric priors in the problem at hand, such as invariance to…
A realisation of a graph in the plane as a bar-joint framework is rigid if there are finitely many other realisations, up to isometries, with the same edge lengths. Each of these finitely-many realisations can be seen as a solution to a…
We prove tight bounds on the site percolation threshold for $k$-uniform hypergraphs of maximum degree $\Delta$ and for $k$-uniform hypergraphs of maximum degree $\Delta$ in which any pair of edges overlaps in at most $r$ vertices. The…
Despite its long history, there are many fundamental issues concerning random packings of spheres that remain elusive, including a precise definition of random close packing (RCP). We argue that the current picture of RCP cannot be made…
We note that the recent polynomial proofs of the spherical and complex plank covering problems by Zhao and Ortega-Moreno give some general information on zeros of real and complex polynomials restricted to the unit sphere. As a corollary of…