José Luis and I first met at the famous - and hugely enjoyable 1983 El Escorial conference of which he and Ireneo Peral were the chief organisers, but we did not really discuss mathematics together until the spring and summer of 1985. There is an old question - formally posed by Stein in the proceedings of the 1978 Williamstown conference [St] - concerning the disc multiplier and the Bochner-Riesz means.
Around 1923, Élie Cartan introduced affine connections on manifolds and defined the main related concepts: torsion, curvature, holonomy groups. He discussed applications of these concepts in Classical and Relativistic Mechanics; in particular he explained how parallel transport with respect to a connection can be related to the principle of inertia in Galilean Mechanics and, more generally, can be used to model the motion of a particle in a gravitational field. In subsequent papers, Élie Cartan...
1. Introduction. The XVI-th Hilbert problem consists of two parts. The first part concerns the real algebraic geometry and asks about the topological properties of real algebraic curves and surfaces. The second part deals with polynomial planar vector fields and asks for the number and position of limit cycles. The progress in the solution of the first part of the problem is significant. The classification of algebraic curves in the projective plane was solved for degrees less than 8. Among general...
Thomas Harriot (1560?–1621) is known today as an innovative mathematician and a natural philosopher with wide intellectual horizons. This paper will look at his interest in combinations in three contexts: language (anagrams), natural philosophy (the question of atomism) and mathematics (number theory), in order to assess where to situate him in respect of three current historiographical debates: 1) whether there existed in the late Renaissance two opposed mentalities, the occult and the scientific;...
This paper illustrates the themes of the title in terms of: van Kampen type theorems for the fundamental groupoid; holonomy and monodromy groupoids; and higher homotopy groupoids. Interaction with work of the writer is explored.