San Francisco, California
London, United Kingdom
On Thu 19th December, ICMS is delighted to host the Scottish Topology Seminar
Topology is the study of shapes and spaces.
The programme for the afternoon is shown below. The four lectures on ‘From the History of Topology’ will have broad appeal. Accordingly, the organisers have suggested that we open up the afternoon to a wider audience.
Attendees are welcome to attend for the entire afternoon or individual talks.
Scottish Topology Seminar, Thu 19th December
13.00-13.55 Jeremy Gray (Open University and University of Warwick)
Poincaré and the study of surfaces
The study of surfaces was one of Henri Poincaré’s lifelong interests. He began in the early 1880s with the study of flows on surfaces, which he partly regarded as a preliminary to the study of celestial mechanics, and then switched to the study of complex differential equations and their connection to the study of complex (Riemann) surfaces. His discovery of the role of non-Euclidean geometry in the theory of Riemann surfaces led to a competition with the German mathematician Felix Klein, and to the conjecture of the uniformisation theorem, which was to resist proof for a further 25 years.
14.05-15.00 Jeremy Gray (Open University and University of Warwick)
Poincaré and the creation of the theory of 3-manifolds
In the opening years of the 20th century Poincaré was led to create a theory of three-dimensional manifolds, and to try to impose some order on a new subject in mathematics. How can three-dimensional manifolds be defined, and how can they be classified? Poincaré’s attempts to answer these questions led him to deepen the tools of algebraic topology and to pose – but, famously, not to answer – what became known as the Poincaré conjecture.
15:30-16:30 June Barrow-Green (Open University)
GD Birkhoff and the development of dynamical systems theory
In October 1912, the young American mathematician GD Birkhoff 'astonished the mathematical world' by providing a proof of Poincaré's last geometric theorem. The theorem, which was connected to Poincaré's longstanding interest in the periodic solutions of the three-body problem, had been proposed by Poincaré only months before he died. Birkhoff continued to work on aspects of dynamical systems throughout his career, his aim being to create a general theory. Many of his ideas are contained in his book Dynamical Systems (1927), the first book to develop the qualitative theory of systems defined by differential equations and where he effectively 'created a new branch of mathematics separate from its roots in celestial mechanics and making broad use of topology'.
16.40-17.40 Julia Collins (University of Edinburgh)
A Knot's Tale: the story of Peter Guthrie Tait
Peter Guthrie Tait (1831 - 1901) was significantly less famous than his friends Maxwell and Kelvin, but unfairly so because he was an important and prolific mathematical physicist. He was Professor of Natural Philosophy at the University of Edinburgh from 1859, narrowly beating Maxwell to the post, and worked on a variety of topics including thermodynamics and the kinetic theory of gases. In a fantastic experiment involving smoke rings, Tait and Kelvin came up with a new atomic theory based around the idea of knots and links. This took on a mathematical life on its own, with Tait becoming one of the world's first topologists and inventing conjectures which remained unproven for over a hundred years.
The Scottish Topology Seminar is supported by the Glasgow Mathematical Journal Trust.