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

Of all the issues discussed at {\em Alife VII: Looking Forward, Looking Backward}, the issue of whether it was possible to create an artificial life system that exhibits {\em open-ended evolution} of novelty is by far the biggest. Of the 14…

I review some recent progress, open puzzles and future opportunities in heavy quarkonium physics in the framework of effective field theories

The paper proposes open problems in classical Kolmogorov complexity. Each problem is presented with background information and thus the article also surveys some recent studies in the area.

The purpose of this article is to survey the developments on the Kakeya problem in recent years, concentrating on the period after the excellent 1999 survey of Wolff, and including some recent work by the authors. We will focus on the…

This document is a brief summary of progress that has been made on the problems posed in the document "Twenty Open Problems in Enumeration of Matchings" (also available from this server as math.CO/9801060). NOTE: This article has now been…

We illustrate the current status of heavy quark physics on the lattice. Special emphasis is paid to the question of systematic uncertainties and to the connection of lattice computations to continuum physics. Latest results are presented…

The Weihrauch degrees are a tool to gauge the computational difficulty of mathematical problems. Often, what makes these problems hard is their discontinuity. We look at discontinuity in its purest form, that is, at otherwise constant…

In the week 3--9, October 2010, the Mathematisches Forschungsinstitut at Oberwolfach hosted a mini workshop Linear Series on Algebraic Varieties. These notes contain a variety of interesting problems which motivated the participants prior…

We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.

Neutrino physics has seen an explosion of activity and new results in the last decade. In this report the current state of the field is summarized, with a particular focus on progress in the last two years. Prospects for the near term…

Recently, there is an explosive growth of activities to understand stringy properties of orbifolds. In this article, we survey some of recent developments.

Reporting on a computer--assisted search for nonpositively curved CW complexes of intermediate rank conducted some years ago. Not intended for publication.

This is a partially survey collection of material on gravity, entropy, and information with some new heuristic results related to the WDW equation.

In this survey we review the progress made in the last ten years in understanding the Black Hole Rigidity problem in the setting of smooth spacetimes. We review both local and global results and discuss the main mathematical ideas behind…

The first three sections of this survey represent an updated and much expanded version of the abstract of my talk at FPSAC'2010: new results are incorporated and several concrete conjectures on the interactions between the three…

This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. The purpose of our…

We report on some recent progress achieved in [arXiv:2111.14811] on the ergodicity of the frame flow of negatively-curved Riemannian manifolds. We explain the new ideas leading to ergodicity for nearly $0.25$-pinched manifolds and give…

Evolutionary complexity is here measured by the number of trials/evaluations needed for evolving a logical gate in a non-linear medium. Behavioural complexity of the gates evolved is characterised in terms of cellular automata behaviour. We…

Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging from dominant ones such as statistical lossless compression…

We are entering an era where the numerical construction of generic spacetimes is becoming a reality. The use of computer simulations, in principle, allows us to solve Einstein equations in their full generality and unravel important…