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Invariants underlying shape inference are elusive: a variety of shapes can give rise to the same image, and a variety of images can be rendered from the same shape. The occluding contour is a rare exception: it has both image salience, in…

We extend our previous classification of superpotentials of ``scalar curvature type" for the cohomogeneity one Ricci-flat equations. We now consider the case not covered in our previous paper, i.e., when some weight vector of the…

Several novel imaging applications have lead recently to a variety of Radon type transforms, where integration is done over a family of conical surfaces. We call them \emph{cone transforms} (in 2D they are also called \emph{V-line} or…

D3-branes are often a necessary ingredient in global compactifications of F-theory. In minimal realizations of flavor hierarchies in F-theory GUT models, suitable fluxes are turned on, which in turn attract D3-branes to the Yukawa points.…

This paper studies a class of binomial ideals associated to graphs with finite vertex sets. They generalize the binomial edge ideals, and they arise in the study of conditional independence ideals. A Gr\"obner basis can be computed by…

Let G be a real or complex linear algebraic reductive group. Let H and F be reductive subgroups. We study the natural H action on G/F. The main theorem of this note shows that generic H orbits are closed. This theorem is then applied to…

Let $G$ be a connected semisimple simply connected Lie group with a compact Cartan subgroup and let $\Gamma$ be a uniform lattice in $G$. Let $\widehat{G}_d$ denote the set of equivalence classes of unitary discrete series representations…

We study the facial geometry of the homogeneous pseudo-moment cone \(\Sigma_{n,2d}^*\) and its implications for atomic decomposition of moment matrices. For fixed \(d \ge 2\), we show that if a moment matrix is formed by \(O(n^d)\)…

The Tur\'{a}n number of a graph $H$, $\text{ex}(n,H)$, is the maximum number of edges in an $n$-vertex graph that does not contain $H$ as a subgraph. For a vertex $v$ and a multi-set $\mathcal{F}$ of graphs, the suspension $\mathcal{F}+v$…

Previous attempts at explaining the gamma-ray excess near the Galactic Centre have focussed on dark matter annihilation directly into Standard Model particles. This results in a preferred dark matter mass of 30-40 GeV (if the annihilation…

We give a combinatorial description of extremal generators of the supereigenvector cone {x: Ax>=x} in max algebra.

Large-scale accretion shocks around massive clusters of galaxies, generically expected in hierarchical scenarios of cosmological structure formation, are shown to be potential sources of the observed ultrahigh energy cosmic rays (UHECRs) by…

Let K be a finite extension of Qp. We fix a continuous absolutely irreducible representation of the absolute Galois group of K over a finite dimensional vector space with coefficient in a finite field of characteristic p and consider its…

I provide a short review of the current status of indirect dark matter searches with gamma rays, charged cosmic rays and neutrinos. For each case I will focus on various excesses reported in the literature which have been interpreted as…

Let G be a simple complex algebraic group. By using a notion of a G-category we define invariants of tangles with flat G-connections in their complements. We also show that quantized universal enveloping algebras at roots of unity provide…

The Tur\'an type extremal problem asks to maximize the number of edges over all graphs which do not contain fixed subgraphs. Similarly, the spectral Tur\'an type extremal problem asks to maximize spectral radius of all graphs which do not…

We give a characterization of extremal irreducible discrete subfactors $(N\subseteq M, E)$ where $N$ is type ${\rm II}_1$ in terms of connected W*-algebra objects in rigid C*-tensor categories. We prove an equivalence of categories where…

In this paper we find some exponential formulas for the Betti numbers of the De Concini-Procesi minimal wonderful models Y_{G(r,p,n)} associated to the complex reflection groups G(r,p,n). Our formulas are different from the ones already…

We find the exact upper estimate for the upper density of zeros of entire functions of exponential type whose indicator diagram is contained in a given interval.

We present the distributions of geometrical covering factors of active galactic nuclei (AGNs) dusty tori (f2) using an X-ray selected complete sample of 227 AGN drawn from the Bright Ultra-hard XMM-Newton Survey. The AGN have z from 0.05 to…