Related papers: Topological expanders, coarse geometry and thick e…
Locally finite self-similar graphs with bounded geometry and without bounded geometry as well as non-locally finite self-similar graphs are characterized by the structure of their cell graphs. Geometric properties concerning the volume…
We introduce a spectrum of monotone coarse invariants for metric measure spaces called Poincar\'{e} profiles. The two extremes of this spectrum determine the growth of the space, and the separation profile as defined by…
We consider Hamiltonian diffeomorphisms $\phi$ of the unit cotangent bundle over a closed Riemannian manifold $(M,g)$ which extend to Hamiltonian diffeomorphisms of $T^*M$ equal to the time-1-map of the geodesic flow for $|p| \ge 1$. For…
Hypersurfaces embedded in conformal manifolds appear frequently as boundary data in boundary-value problems in cosmology and string theory. Viewed as the non-null conformal infinity of a spacetime, we consider hypersurfaces embedded in a…
We obtain strong upper bounds for the Betti numbers of compact complex-hyperbolic manifolds. We use the unitary holonomy to improve the results given by the most direct application of the techniques of [DS17]. We also provide effective…
We introduce $k$-robust clique complexes, a family of simplicial complexes that generalizes the traditional clique complex. Here, a subset of vertices forms a simplex provided it does not contain an independent set of size $k$. We…
We consider a subclass of tilings, the tilings obtained by cut and projection. Under somewhat standard assumptions, we show that the natural complexity function has polynomial growth. We compute its exponent \alpha in terms of the ranks of…
The convex dimension of a $k$-uniform hypergraph is the smallest dimension $d$ for which there is an injective mapping of its vertices into $\mathbb{R}^d$ such that the set of $k$-barycenters of all hyperedges is in convex position. We…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
We study the higher expansion properties of locally symmetric spaces, with a particular focus on octonionic hyperbolic manifolds. We show that codimension two minimal submanifolds of compact octonionic locally symmetric spaces must have…
We introduce a new family of closed differential forms naturally associated with minimal graphical submanifolds in Euclidean space, defined in arbitrary codimension. For each minimal graph, we construct an explicit closed form whose…
Given a closed manifold M, we prove the upper bound of (n+d)/2 for the length of a product of systoles that can form a curvature-free lower bound for the total volume of M, in the spirit of M. Gromov's systolic inequalities. Here n is the…
In this article, we compute the topological expansion of all possible mixed-traces in a hermitian two matrix model. In other words we give a recipe to compute the number of discrete surfaces of given genus, carrying an Ising model, and with…
Under certain homological hypotheses on a compact 4-manifold, we prove exactness of the topological surgery sequence at the stably smoothable normal invariants. The main examples are the class of finite connected sums of 4-manifolds with…
We prove sandwich theorems and a Tauberian theorem in the space of compact metric measure spaces, endowed with the Gromov-Hausdorff-Prokhorov (GHP) topology. These results hold with respect to a close relative of Gromov's Lipschitz order.…
For $k \geqslant 0$, we define a simple topological graph $G$ (that is, a graph drawn in the plane such that every pair of edges intersect at most once, including endpoints) to be $k$-matching-planar if for every edge $e \in E(G)$, every…
Treewidth is a parameter that emerged from the study of minor closed classes of graphs (i.e. classes closed under vertex and edge deletion, and edge contraction). It in some sense describes the global structure of a graph. Roughly, a graph…
We adapt algorithms for resolving the singularities of complex algebraic varieties to prove that the natural map of homology theories from complex bordism to the bordism theory of complex derived orbifolds splits. In equivariant stable…
We show that if there exists a topologically expansive homeomorphism on a uniform space, then the space is always a regular space. Through examples we show that in general composition of topologically expansive homeomorphisms need not be…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…