Related papers: Real intersection theory (I)
This is an expository note to give a brief review of classical elastica theory, mainly prepared for giving a more detailed proof of the author's Li--Yau type inequality for self-intersecting curves in Euclidean space. We also discuss some…
We propose a model for the intersection of two urban streets. The traffic status of the crossroads is controlled by a set of traffic lights which periodically switch to red and green with a total period of T. Two different types of…
In this article we establish bounds for the Castelnuovo-Mumford regularity of projective schemes in terms of the degrees of their defining equations. The main new ingredient in our proof is to show that generic residual intersections of…
In this review I discuss intersection numbers of twisted cocycles and their relation to physics. After defining what these intersection number are, I will first discuss a method for computing them. This is followed by three examples where…
Nonlocal currents, in devices where two normal metal terminals are contacted to a superconductor, are determined using the circuit theory of mesoscopic superconductivity. We calculate the conductance associated with crossed Andreev…
A wide and natural class of closed currents - which are differences of positive closed currents - can be constructed by pulling back smooth closed forms using rational maps. These currents are very singular in general, and hence defining…
A theory is offered for the ballistic 4-terminal Josephson junction. The studied system consists of a mesoscopic two-dimensional normal rectangular layer which is attached in each side to the bulk superconducting banks (terminals). The…
In this short note, we expose some of the works on Serre intersection multiplicity conjecture. I provide a proof of the vanishing of Serre intersection multiplicity in non-proper intersection over a regular ring based on the intersection…
The aim of this note is to describe how to compute the intersection multiplicity defined by Jean Pierre Serre.
This paper contains a new elementary proof of the Fundamental Theorem of Calculus for the Lebesgue integral. The hardest part of our proof simply concerns the convergence in ${\rm L}^1$ of a certain sequence of step functions, and we prove…
In this paper, we present a general principle for the Lebesgue measure theory of limsup sets defined by rectangles under the hypothesis of ubiquity for rectangles.
The purpose of this article is to define and study the notion of absolute intersection motive.
We study the relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension, via its (birational) cycle map, going to the relative symmetric product. We show the cycle map is the blowing up of the…
We study the spectral measures of conservative mixing flows on the 2-torus having one degenerate singularity. We show that, for a sufficiently strong singularity, the spectrum of these flows is typically Lebesgue with infinite multiplicity.…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Summer term 2001, to undergraduate Mathematics and Physics students. It covers a few selected topics from perturbation theory at an introductory…
There are several centrality measures that have been introduced and studied for real world networks. They account for the different vertex characteristics that permit them to be ranked in order of importance in the network. Betweenness…
Traffic safety at intersections is studied quantitatively using methods from Statistical Mechanics on the basis of simple microscopic traffic flow models. In order to determine a relationship between traffic flow and the number of crashes,…
We give a brief introduction to Luttinger liquids and to the phenomena of electronic transport or conductance in quantum wires. We explain why the subject of transport in Luttinger liquids is relevant and fascinating and review some…
The evoluted set is the set of configurations reached from an initial set via a fixed flow for all times in a fixed interval. We find conditions on the initial set and on the flow ensuring that the evoluted set has negligible boundary (i.e.…
For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.