Titles and Abstracts

Littlewood--Paley theory was born in a classic paper appearing in J. Lond. Math. Soc. (1), 6 (1931), 230–233. With the benefit of hindsight, this paper gave us an entirely new way to think geometrically about spaces of functions which closely mimics euclidean geometry. This is in spite of there being no obvious notion of orthogonality in these spaces. We discuss this circle of ideas and some of its developments over the last nearly 100 years.

I will discuss the papers of Erdos and Turan (1936) and Roth (1953) about the problem of whether dense sets of integers must contain arithmetic progressions, and their influence on combinatorics and additive number theory 

This talk 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.

Assuming minimal background in topology, I will explain what Wall proved, and give some indication as to how. I will then highlight some of the many ways these two short papers have been influential since then. 

The 1949 Higman-Neumann-Neumann paper "Embedding Theorems for Groups" is a landmark of group theory in the twentieth century. The proof of its main theorem covers less than a page but the construction that it introduced – the HNN extension – quickly became one of the principal tools of combinatorial group theory, widely used to build new groups and to describe enlightening decompositions of existing groups. In this talk, which is based on my article with Carl-Fredrik Nyberg-Brodda, I will sketch the contents of the HNN paper and then discuss some of the important developments that followed in its wake, including the Higman Embedding Theorem and the Bass–Serre theory of groups acting on trees.

"Periodicals are the most important material facts in the mathematical world.” So wrote GH Hardy in his obituary of the Swedish mathematician Gösta Mittag-Leffler, who founded Acta Mathematica in 1882 and served as its editor for the rest of his life. Mittag-Leffler died in 1927, just one year after Hardy had overseen the launch of the JLMS. Although the two journals were established with different aims and at different times, the circumstances of their founding – and the ambitions of their founders – had much in common. In this talk, I will trace the origins of both journals and examine the pivotal roles that Mittag-Leffler and Hardy played in their creation.