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This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.

Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite groups into bounded products of subsets of various kinds…

We propose a set of questions on the dynamics of H\'enon maps from the real, complex, algebraic and arithmetic points of view.

The classification of textual data often yields important information. Most classifiers work in a closed world setting where the classifier is trained on a known corpus, and then it is tested on unseen examples that belong to one of the…

While research on scientific claim verification has led to the development of powerful systems that appear to approach human performance, these approaches have yet to be tested in a realistic setting against large corpora of scientific…

This is a survey of the diversity of problems in additive number theory. Equity requires the consideration of less currently popular problems, and suggests their inclusion in the additive canon. Of particular interest are problems about the…

In this contribution we briefly review some of the current issues and promises for the future by asteroseismology. We are entering a new phase in this field driven by the wealth of data that has been collected and data that will soon be…

This is an informal survey of progress in Weihrauch complexity (cf arXiv:1707.03202) in the period 2018-2020. Open questions are emphasised.

Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized.…

The notion of a k-automatic set of integers is well-studied. We develop a new notion - the k-automatic set of rational numbers - and prove basic properties of these sets, including closure properties and decidability.

We extend a recent breakthrough result relating expectation thresholds and actual thresholds to include some rainbow versions.

This talk tries to summarise where we are now, in the "nature and nurture" questions in galaxy formation and evolution, and briefly describe unsolved problems, and perspectives of progress.

In recent years, multi-task learning has turned out to be of great success in various applications. Though single model training has promised great results throughout these years, it ignores valuable information that might help us estimate…

The growing need for trustworthy machine learning has led to the blossom of interpretability research. Numerous explanation methods have been developed to serve this purpose. However, these methods are deficiently and inappropriately…

We prove new general results on sumsets of sets having Szemer\'edi--Trotter type. This family includes convex sets, sets with small multiplicative doubling, images of sets under convex/concave maps and others.

I was asked at the end of this conference to provide a few comments on the present status of the field of cosmic abundances, which I summarize (and extend upon) in this contribution. A discussion of the present ``state of play'' is given,…

Known and new results on free Boolean topological groups are collected. An account of properties which these groups share with free or free Abelian topological groups and properties specific of free Boolean groups is given. Special emphasis…

Learning analytics is a research topic that is gaining increasing popularity in recent time. It analyzes the learning data available in order to make aware or improvise the process itself and/or the outcome such as student performance. In…

We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…

Answer Set Planning refers to the use of Answer Set Programming (ASP) to compute plans, i.e., solutions to planning problems, that transform a given state of the world to another state. The development of efficient and scalable answer set…