Related papers: Gamma positivity, PL homeomorphism types, and orth…
In a previous paper, \cite{Berndtsson}, we have studied a property of subharmonic dependence on a parameter of Bergman kernels for a family of weighted $L^2$-spaces of holomorphic functions. Here we prove a result on the curvature of a…
Let $(X,\mathcal{R})$ be a commutative association scheme and let $\Gamma=(X,R\cup R^\top)$ be a connected undirected graph where $R\in \mathcal{R}$. Godsil (resp., Brouwer) conjectured that the edge connectivity (resp., vertex…
In this paper, we give both positive and negative answers to Gromov's compactness question regarding positive scalar curvature metrics on noncompact manifolds. First we construct examples that give a negative answer to Gromov's compactness…
We study the asymptotics of certain measures on partitions (the so-called z-measures and their relatives) in two different regimes: near the diagonal of the corresponding Young diagram and in the intermediate zone between the diagonal and…
We analyze the single particle states at the edges of disordered graphene quantum dots. We show that generic graphene quantum dots support a number of edge states proportional to circumference of the dot over the lattice constant. Our…
This paper stresses the strong link between the existence of partial holomorphic connections on the normal bundle of a foliation seen as a quotient of the ambient tangent bundle and the extendability of a foliation to an infinitesimal…
A two-dimensional electron gas in a static external magnetic field exhibits two distinct collective excitation modes. The lower frequency mode propagates along the periphery of the domain almost freely with an extended lifetime, which is…
We introduce a notion of singular hermitian metrics (s.h.m.) for holomorphic vector bundles and define positivity in view of $L^2$-estimates. Associated with a suitably positive s.h.m. there is a (coherent) sheaf 0-th kernel of a certain…
Let $G$ be a permutation group on a set $\Omega$. A subset of $\Omega$ is a base for $G$ if its pointwise stabiliser in $G$ is trivial. In this paper we introduce and study an associated graph $\Sigma(G)$, which we call the Saxl graph of…
Suppose that $\gamma$ and $\sigma$ are two continuous bounded variation paths which take values in a finite-dimensional inner product space $V$. Recent papers have introduced the truncated and the untruncated signature kernel of $\gamma$…
Given a principal fibre bundle with structure group $S$, and a fibre transitive Lie group $G$ of automorphisms thereon, Wang's theorem identifies the invariant connections with certain linear maps $\psi\colon \mathfrak{g}\rightarrow…
We show that the set of totally positive unipotent lower-triangular Toeplitz matrices in $GL_n$ form a real semi-algebraic cell of dimension $n-1$. Furthermore we prove a natural cell decomposition for its closure. The proof uses properties…
We prove Barth-type connectedness results for low-codimension smooth subvarieties with good numerical properties inside certain "easy" ambient spaces (such as homogeneous varieties, or spherical varieties). The argument employs some basics…
Using the two-point Edgeworth series up to second order we construct the weakly nonlinear conditional probability distribution function for the density field around an overdense region. This requires calculating the two-point analogues of…
We study the effect of localized modes in lattices of size N with parity-time (PT) symmetry. Such modes are arranged in pairs of quasi-degenerate levels with splitting delta exp{-N/xi}, where \xi is their localization length. The level…
Let $(M,g^{TM})$ be a noncompact (not necessarily complete) enlargeable Riemannian manifold in the sense of Gromov-Lawson and $F$ an integrable subbundle of $T M$ . Let $k^F$ be the leafwise scalar curvature associated to $g^F=g^{TM}|_F$.…
The scattering of a fermion in the background of a sign potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling under the Sturm-Liouville…
We establish several new lower bounds on the $g$-numbers of simplicial spheres without large missing faces. For this class of spheres, we derive bounds on the $g$-numbers in terms of the independence numbers of their graphs, extending a…
We prove generalized Gaffney inequalities and the discrete compactness for finite element differential forms on $s$-regular domains, including general Lipschitz domains. In computational electromagnetism, special cases of these results have…
This paper covers the material of our two talks. We describe a series of projects based upon perturbative expansions to follow the gravitational evolution of the one point probability distribution functions (PDFs) for the density contrast…