Related papers: On Visibility and Blockers
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
A potential scattering theory from deterministic and random $\mathcal{PT}$ collections of particles with gain and loss is introduced and the forms of their structure and pair-structure factors are elucidated. An example relating to light…
A systematic exposition of the basic concepts of wakes and impedances is given for relativistic beams in accelerators.
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
This article contains a short and entertaining list of unsolved problems in Plane Geometry. Their statement may seem naive and can be understood at an elementary level. But their solutions have refused to appear for forty years in the best…
In this short expository note, we present a selection of classic and recent ideas in free boundary theory, with a focus on the vectorial case, referred to here as constraint maps. The note includes a brief historical perspective and…
For an irreducible conic $\mathcal C$ in a Desarguesian plane of odd square order, estimating the number of points from a Baer subplane which are external to $\mathcal C$ is a natural problem. In this paper, a complete list of possibilities…
I review the understanding of bulges that emerged from the lively discussions and presentations during the meeting, and emphasize areas for future work. The evidence is for a diversity of `bulges', and of formation mechanisms.
The problem of construction of the surfaces with given sets of the points with horizontal tangential planes is considered. Such considerations are of interest in the problem of computer simulations of the waved ocean surfaces.
We review the literature on the localization transition for the class of polymers with random potentials that goes under the name of copolymers near selective interfaces. We outline the results, sketch some of the proofs and point out the…
In this paper we establish effective lower bounds on the degrees of the Debarre and Kobayashi conjectures. Then we study a more general conjecture proposed by Diverio-Trapani on the ampleness of jet bundles of general complete intersections…
One can imagine a number of mechanisms that could be the cause of brighter/fainter segments of jets. In a sense, jets might be easier to understand if they were featureless. However we observe a wide variety of structures which we call…
Observational evidence and theoretical motivation for dark matter are presented and connections to the CMB and BBN are made. Problems for baryonic and neutrino dark matter are summarized. Emphasis is placed on the prospects for…
We discuss some diverse open problems in the dimer model, motivated by a geometric viewpoint. This is part of a conference proceedings for the OPAC 2022 conference.
A new concept called multilevel contours is introduced through this article by the author. Theorems on contours constructed on a bundle of complex planes are stated and proved. Multilevel contours can transport information from one complex…
We present a concise proof for the supporting hyperplane theorem. We then observe that the proof not only establishes the supporting hyperplane theorem but also extends it to a hyperplane separation theorem for certain non-convex sets. The…
We introduce a conjecture that we call the {\it Two Hyperplane Conjecture}, saying that an isoperimetric surface that divides a convex body in half by volume is trapped between parallel hyperplanes. The conjecture is motivated by an…
In our review of the blazar phenomenon, we discuss blazar models, with a focus on the following issues: sub-parsec jets and their environment; energy dissipation and particle acceleration; and radiative processes.
In this note, the irreducible representations of a lifting of a quantum plane are determined. Both authors thank Hans-J\"urgen Schneider for pointing out a mistake in the published version of the paper, that is corrected here.
As an overview of blazar research, we briefly discuss some of the themes of this conference, including the various types of blazars, blazar samples and selection effects, unified schemes, evolution, and jet physics.