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In this note we briefly survey and propose some open problems related to isoparametric theory.

We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…

This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…

Few-body research history, achievements, current development and challenges are presented.

We describe a list of open problems in random matrix theory and the theory of integrable systems that was presented at the conference Asymptotics in Integrable Systems, Random Matrices and Random Processes and Universality, Centre de…

We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…

This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.

We give a selection of major open problems involving selective properties, diagonalizations, and covering properties for sets of real numbers. This is a revision of the version published as a chapter in the book \textbf{Open Problems in…

Over the last couple of decades, there has been a considerable effort devoted to the problem of updating logic programs under the stable model semantics (a.k.a. answer-set programs) or, in other words, the problem of characterising the…

The present paper aims to survey known results and to point out the wealth of rather important open problems that are out there.

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.

We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.

As language and visual understanding by machines progresses rapidly, we are observing an increasing interest in holistic architectures that tightly interlink both modalities in a joint learning and inference process. This trend has allowed…

This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack…

Software engineering research benefited for decades from openly available tools, accessible systems, and problems that could be studied at modest scale. Today, many of the most relevant software systems are large, proprietary, and embedded…

Multiple Object Tracking (MOT) has gained increasing attention due to its academic and commercial potential. Although different approaches have been proposed to tackle this problem, it still remains challenging due to factors like abrupt…

In this final chapter, we consider the state-of-the-art for spreading in social systems and discuss the future of the field. As part of this reflection, we identify a set of key challenges ahead. The challenges include the following…

In real-world scenarios classification models are often required to perform robustly when predicting samples belonging to classes that have not appeared during its training stage. Open Set Recognition addresses this issue by devising models…

A short review of the recent results and models of complex networks.

Open Set Recognition (OSR) is about dealing with unknown situations that were not learned by the models during training. In this paper, we provide a survey of existing works about OSR and distinguish their respective advantages and…