We survey the role of right-angled Artin groups in the theory of diffeomorphism groups of low dimensional manifolds. We first describe some of the subgroup structure of right-angled Artin groups. We then discuss the interplay between algebraic structure, compactness, and regularity for group actions on one–dimensional manifolds. For compact one–manifolds, every right-angled Artin group acts fai...

State-of-the-art industrial-level recommender system applications mostly adopt complicated model structures such as deep neural networks. While this helps with the performance, lack of explainability caused by these nearly blackbox models also raises concerns and potentially weakens users’ trust on system. Existing work explainable recommendation focuses designing interpretable to generate mode...

The Jones–Witten theory gives rise to representations of the (extended) mapping class group of any closed surface Y indexed by a semi-simple Lie group G and a level k . In the case G = SU(2) these representations (denoted VA(Y )) have a particularly simple description in terms of the Kauffman skein modules with parameter A a primitive 4r root of unity (r = k + 2). In each of these representatio...

Relations between the following classes of Galois extensions are given: (1) centrally projective Galois extensions (CP-Galois extensions), (2) faithfully Galois extensions, and (3) H-separable Galois extensions. Moreover, it is shown that the intersection of the class of CP-Galois extensions and the class of faithfully Galois extensions is the class of Azumaya Galois extensions.

The paper seeks a perspective on the reality of Formal Methods in industry today. What has worked; what has not; and what might the future bring? We show that where formality has been adopted it has largely been benefical. We show that formality takes many forms, not all of them obviously