Related papers: To collide, or not to collide, that is the questio…

We study rationality problems for smooth complete intersections of two quadrics. We focus on the three-dimensional case, with a view toward understanding the invariants governing the rationality of a geometrically rational threefold over a…

The paper has a form of a survey and consists of three parts. It is focused on the relationship between the many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on the important model-theoretic concepts.…

We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…

When are two collider events similar? Despite the simplicity and generality of this question, there is no established notion of the distance between two events. To address this question, we develop a metric for the space of collider events…

In this paper we study the intersection theory on surfaces with abelian quotient singularities and we derive properties of quotients of weighted projective planes. We also use this theory to study weighted blow-ups in order to construct…

Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a…

We consider geometric collision-detection problems for modular reconfigurable robots. Assuming the nodes (modules) are connected squares on a grid, we investigate the complexity of deciding whether collisions may occur, or can be avoided,…

We present new algorithms to perform fast probabilistic collision queries between convex as well as non-convex objects. Our approach is applicable to general shapes, where one or more objects are represented using Gaussian probability…

A rough collision law describes the limiting contact dynamics of a pair of rough rigid bodies, as the scale of the rough features (asperities) on the surface of each body goes to zero. The class of rough collision laws is quite large and…

This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…

When a confined system interacts with its walls (treated quantum mechanically), there is an intertwining of degrees of freedom. We show that this need not lead to entanglement, hence decoherence. It will generally lead to error. The wave…

We give an introduction to the study of algebraic hypersurfaces, focusing on the problem of when two hypersurfaces are isomorphic or close to being isomorphic. Working with hypersurfaces and emphasizing examples makes it possible to discuss…

Solutions to the collinear three-body problem which do not end in triple collision pass through an infinite number of binary collisions. Given three masses, we show that four geometric quantities generate a finite description of itineraries…

A procedure for interpolating between specified points of a curve or surface is described. The method guarantees slope continuity at all junctions. A surface panel divided into p x q contiguous patches is completely specified by the…

We study experimentally the collision between a sphere falling through a viscous fluid, and a solid plate below. It is known that there is a well-defined threshold Stokes number above which the sphere rebounds from such a collision. Our…

This is a survey article on classical groups (over arbitrary division rings) and their geometries.

A detailed study of the waiting times for the first (multi)-collision in a drawing process.

By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its…

An interesting recent paper in Nature explores a new method to construct solid bodies rolling along given curves on an inclined plane, based on the Gauss Theorem. The present article complements those examinations with rigorous existence…

We prove a strong concentration result about the natural collision estimator, which counts the number of collisions that occur within an iid sample. This estimator is at the heart of algorithms used for uniformity testing and entropy…