Journal of the London Mathematical Society-Second Series最新文献

Sunflowers, or $�\Delta$-systems, are a fundamental concept in combinatorics introduced by Erdős and Rado in their paper: [J. London Math. Soc. (1) 35 (1960), 85–90]. A sunflower is a collection of sets where all pairs have the same intersection. This paper explores the wide-ranging applications of sunflowers in computer science and combinatorics. We discuss recent progress toward the sunflower conjecture and present a short elementary proof of the best known bounds for the robust sunflower lemma.

In this note, we highlight the impact of the paper G. H. Hardy, A theorem concerning Fourier transforms, J. Lond. Math. Soc. (1) 8 (1933), 227–231 in the community of harmonic analysis in the last 90 years, reviewing, on one hand, the direct generalizations of the main results and, on the other hand, the different connections to related areas and new perspectives.

That the Journal of the London Mathematical Society came into existence in 1926 can be ascribed to the efforts of one man: G.H. Hardy. As one of the two Secretaries of the Society, Hardy was aware of the increasing demand for publication space in the Society's Proceedings, and the need for an outlet for shorter papers. It was evident that these problems could be solved if the Society could publish a second journal. However, to do so required money, money that the Society did not have; funds would have to be raised. Hardy rose to the challenge. Well-connected and international in outlook, he was the right man for the task. Not only did he secure the funds, he ensured that the Journal was no parochial periodical; of the papers in Volume 1, over 25% came from authors based outside Britain.

This paper surveys the impact of Eremenko and Lyubich's paper “Examples of entire functions with pathological dynamics”, published in 1987 in the Journal of the London Mathematical Society. Through a clever extension and use of classical approximation theorems, the authors constructed examples exhibiting behaviours previously unseen in holomorphic dynamics. Their work laid foundational techniques and posed questions that have since guided a good part of the development of transcendental dynamics.

Throughout the history of 3-manifolds, the fundamental group has played a central role. There is a list of reasons for that, and exactly what that role is has evolved over time, but it has always been a player. The papers under consideration here all written by G. Peter Scott (1944–2023) in a period 1972–1978, highlight and reflect the beginnings of a transitional period for the subject viewed through the prism of fundamental groups.

In this paper, we discuss the first two papers on soluble groups written by Philip Hall and their influence on the study of finite groups. The papers appeared in 1928 and 1937 in the Journal of the London Mathematical Society.

Ledrappier and Walters's article “A Relativised Variational Principle for Continuous Transformations”, J. Lond. Math. Soc. (2) 16 (1977), no. 3, 568–576) is a landmark in the development of thermodynamic formalism. This survey, aimed at newcomers to the field and experts in adjacent fields discusses the background, the Ledrappier–Walters article, and some subsequent developments in the field.

The article gives a brief survey of Murray's notion of bundle gerbes as introduced in his 1996 paper published in the Journal of the London Mathematical Society, together with some of its applications.

In this survey article, we explore a central theme in Diophantine approximation inspired by a celebrated result of Besicovitch on the Hausdorff dimension of well approximable real numbers. We outline some of the key developments stemming from Besicovitch's result, with a focus on the mass transference principle, ubiquity and Diophantine approximation on manifolds and fractals. We highlight the subtle yet profound connections between number theory and fractal geometry, and discuss several open problems at their intersection.