History of Differential Geometry

Organiser: Gerard Alberts (University of Amsterdam)

Raf Bocklandt (University of Amsterdam)

Italian connections

We investigate how Riemann’s love for Italy influenced whole generations of Italian geometers. We will focus on two specific examples: Betti and the idea of connectedness and Ricci-Curbastro and Levi-Civita and the idea of a connection.

Tilman Sauer (University of Mainz)

Modelling parallel transport

In 1918, the Dutch geometer Jan Arnoldus Schouten used plaster models of standard curved surfaces to illustrate a novel geometric concept of geodesic transport of reference frames in curved spaces. The paper discusses Schouten’s use of material modelling in the context of an emerging abstract geometric concept of parallel transport.

Alberto Cogliati (Università degli Studi di Milano)

Cartan and Schouten: the search for connection

I will provide an analysis, both historical and mathematical, of two joint papers on the theory of connections by Élie Cartan and Jan Arnoldus Schouten that were published in 1926. These papers were the result of a fertile collaboration between the two eminent geometers that flourished in the two-year period 1925–1926. I will describe the birth and the development of their scientific relationship especially in the light of their correspondence that, on the one hand, offers valuable insight into their common research interests and, on the other hand, provides a vivid picture of Cartan’s and Schouten’s different technical choices.

Gerard Alberts (University of Amsterdam)

Brief remark on the Schouten archive

The archive of J.A. Schouten (1883–1971), with its thousands of letters, offers a uniquely close view on the practice of mathematics over a period five decades. It inspires research into the history of differential geometry in particular and the changing practice of mathematics in general.