Related papers: An update on Weihrauch complexity, and some open q…

We provide a self-contained introduction into Weihrauch complexity and its applications to computable analysis. This includes a survey on some classification results and a discussion of the relation to other approaches.

Weihrauch complexity is now an established and active part of mathematical logic. It can be seen as a computability-theoretic approach to classifying the uniform computational content of mathematical problems. This theory has become an…

This is an overview of recent developments regarding the complexity of matrix multiplication, with an emphasis on the uses of algebraic geometry and representation theory in complexity theory.

We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.

The evolution of complexity has been a central theme for Biology and Artificial Life (Bonner, 1988; Bedau et al., 2000). Complexification has been interpreted in different ways: as a process of diversification between evolving units…

We will review some of the theoretical progresses that have been in the study of complex systems in physics and of their applications to biology.

This paper collects some problems that I have encountered during the years, have puzzled me and which, to the best of my knowledge, are still open. Most of them are well-known and have been first stated by other authors. In this sad season…

We present updates to the problems on Hirzebruch's 1954 problem list focussing on open problems, and on those where substantial progress has been made in recent years. We discuss some purely topological problems, as well as geometric…

This is a survey on Kawaguchi-Silverman conjecture.

In this survey, we give a short overview of the recent progress on the multidimensional L2 conjecture. It can also serve as an introduction to the subject.

This is an extended abstract presenting new results on the topological complexity of omega-powers (which are included in a paper "Classical and effective descriptive complexities of omega-powers" available from arXiv:0708.4176) and…

We survey recent developments on the Restriction conjecture.

Recent developments in Seiberg-Witten theory and relations with Complex Geometry.

This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are…

This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…

This is a brief review of the present status, of some recent developments and of the open challenges in string/M theory.

This survey on flexible Weinstein manifolds is, essentially, an extract from our recent joint book.

We review the current status, and some open issues, of VHE astrophysics.

The 2020s will be the most data-rich decade of astronomy in history. As the scale and complexity of our surveys increase, the problem of scheduling becomes more critical. We must develop high-quality scheduling approaches, implement them as…

In this presentation, I will summarize the present status of the developments with a Universal Theory of Relativity \cite{smw-utr}. Some general challenges to be overcome will also be discussed.