Related papers: A small collection of open problems
The wild McKay correspondence is a form of McKay correspondence in terms of stringy invariants that is generalized to arbitrary characteristics. It gives rise to an interesting connection between the geometry of wild quotient varieties and…
In our comment we show that some of the very difficult problems have been successfully solved. We have to focus on the resolved problems, since the authors claims: Our hope, however, is that the topics we have presented will provide…
Systems are growing into more complex ones for developing and maintaining. Existing systems which do not have much in common on the first look are connected, due to the technical progress, even if it was never intended that way. It is an…
This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some…
Some basic features of confinement are reviewed, in particular the symmetry patterns of the dual dynamics. Open problems and possible directions of progress are discussed.
This article addresses broad trends in interdisciplinary research in physics where interactions with colleagues in fields such as computer science, ecology, or economics can often be derailed by unintentional clashes of methodologies and…
Authorship of scientific articles has profoundly changed from early science until now. If once upon a time a paper was authored by a handful of authors, scientific collaborations are much more prominent on average nowadays. As authorship…
One of the important problems of a modern society - communications. At all readiness of this question both humanitarian, and engineering science, process of transfer and information reception remains in the centre of attention of…
Despite significant research in backscatter communication over the past decade, key technical open problems remain under-explored. Here, we first systematically lay out the design space for backscatter networking and identify applications…
This paper examines the processes involved in attempting to capture the subtlest aspects of nature by the scientific method and argues on this basis that nature is fundamentally elusive and may resist grasping by the methods of science. If…
This paper intends to survey the vast literature devoted to a problem posed by Wilf in 1978 which, despite the attention it attracted, remains unsolved. As it frequently happens with combinatorial problems, many researchers who got involved…
Academic challenges comprise effective means for (i) advancing the state of the art, (ii) putting in the spotlight of a scientific community specific topics and problems, as well as (iii) closing the gap for under represented communities in…
The classical platonist / formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: \emph{Is new mathematics discovered or invented? Using examples from my own mathematical work during the…
In this note we briefly survey and propose some open problems related to isoparametric theory.
The number of research papers written has been growing at least linearly -- if not exponentially -- in recent years. In proportion, the amount of time a reader allocates per paper has been decreasing. While an accessible paper will be…
Researchers and students face an explosion of newly published papers which may be relevant to their work. This led to a trend of sharing human summaries of scientific papers. We analyze the summaries shared in one of these platforms…
Seventy-nine physical problems are listed and explained with whose proposed solutions I do not agree. Such disagreements -- even though some of them may simply reflect our preliminary insight into the laws of nature -- have occasionally…
This paper revisits the conundrum faced when one attempts to understand the dynamics of black hole formation and evaporation without abandoning unitary evolution. Previous efforts to resolve this puzzle assume that information escapes in…
This is an informal survey of progress in Weihrauch complexity (cf arXiv:1707.03202) in the period 2018-2020. Open questions are emphasised.
A number of unsolved problems and open questions about the nature and the properties of supernovae are identified and briefly discussed. Some suggestions and directions toward possible solutions are also considered.