Related papers: Some open problems on well-filtered spaces and sob…
A review on the classical Plateau problem is presented. Then, the state of the art about the Kirchhoff-Plateau problem is illustrated as well as some possible future directions of research.
The objective of this paper is to explain the principles of the design of a coarse space in a simplified way and by pictures. The focus is on ideas rather than on a more historically complete presentation. Also, space limitation does not…
We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.
We present some recent results on the existence of solutions of the Schr\"odinger flows, and pose some problems for further research.
I survey problems concerning Lindelof spaces which have partial set- theoretic solutions.
We discuss supernear spaces.
The paper contains a survey of the results obtained during the last ten years in the theory of elliptic boundary problems in H\"ormander function spaces, developed by the authors, and other related results of modern analysis. The basics of…
Availability of reliable atomic and molecular opacity tables is essential in a wide variety of astronomical modeling: the solar and stellar interiors, stellar and planetary atmospheres, stellar evolution, pulsating stars, and protoplanetary…
Mass partition problems describe the partitions we can induce on a family of measures or finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this survey we describe recent progress in the area in addition…
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…
Pleated membrane filters, which offer larger surface area to volume ratios than unpleated membrane filters, are used in a wide variety of applications. However, the performance of the pleated filter, as characterized by a flux-throughput…
Problems about attainability in topological spaces are considered. Some nonsequential version of the Warga approximate solutions is investigated: we use filters and ultrafilters of measurable spaces. Attraction sets are constructed.
Spatial filtering is a commonly deployed technique to improve the quality of laser beams by optically filtering the noise. In the "textbook" example, the noise is usually assumed to be high frequency and the laser beam, Gaussian. In this…
In this paper I present an elementary construction to prove that any proper metric space can arise as the asymptotic cone of another proper metric space. Furthermore I answer a question of Drutu and Sapir concerning slow ultrafilters.
This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct…
Several stimulating open questions in high energy spin physics will be described together with the striking progress recently achieved in this field. In view of the new experimental facilities and the new tools, soon available, I will try…
Robots are increasingly tested in public spaces, towards a future where urban environments are not only for humans but for autonomous systems. While robots are promising, for convenience and efficiency, there are challenges associated with…
We review the current state of the homogeneous Banach space problem. We then formulate several questions which arise naturally from this problem, some of which seem to be fundamental but new. We give many examples defining the bounds on the…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
Radio pulsars have been responsible for many astonishing astrophysical and fundamental physics breakthroughs since their discovery 50 years ago. In this review I will discuss many of the highlights, most of which were only possible because…