Kloosterman lecture by Garth Dales: ``Algebras of continuous functions and set theory''

Datum 12 October 2017, 16:00-17:00hr.
Lokatie Snellius building (Niels Bohrweg 1, Leiden), room 174

Garth Dales (Lancaster University) has been appointed Kloosterman professor at the Mathematical Institute of Leiden University during the month of October 2017, as a guest of Marcel de Jeu. His research interests include Banach algebras, abstract harmonic analysis, and fundamental mathematics. It is a tradition that these distinguished researchers give a general lecture. His lecture ``Algebras of continuous functions and set theory'' is on the interface of Banach algebras and set theory. The abstract is as follows:

``We begin by considering some properties of an apparently-innocent-looking algebra, that of all continuous functions on, say, the closed unit interval. This is a Banach algebra with respect to the uniform norm. Is it a normed algebra for any other norm? An investigation of this leads us to consider the size of the real line, the Continuum Hypothesis, and the role of independence in set theory, and even to muse a little on the philosophy of mathematics; foundations have an impact on what we do in `real mathematics'.
We are also led to Hausdorff's theory of the order-properties of totally ordered sets, to Hahn's construction of large ordered felds, to ultraproducts, to the existence of something similar to a modulus on the finite elements of non-standard models of the real line, and to consideration of a `grown-up version' of the real numbers.''

Organisator Marcel de Jeu (URL, email)
Geplaatst door Marcel de Jeu