Fratrædelsesforelæsninger ved Durhuus & Lützen
Retirement lectures by Professor Emeritus Bergfinnur Durhuus and Professor Emeritus Jesper Lützen. Afterwards, they are honoured at a reception.
13:15 Bergfinnur Durhuus: "Path Integrals"
14:00 Jesper Lützen: "The History of Impossibility Theorems and Arrow’s Impossibility Theorem in particular"
14:45 After the lectures, bubbles and snacks will be served in Vandrehallen
Bergfinnur Durhuus: Path Integrals
Abstract: The path integral concept plays an important role in Quantum Mechanics and in Probability Theory, both from a technical and a fundamental viewpoint. I will discuss this concept in elementary terms in various situations and from various angles, including some illustrative examples involving random geometric structures, such as trees and surfaces.
Jesper Lützen: The History of Impossibility Theorems and Arrow’s Impossibility Theorem in particular
Abstract: In modern mathematics, impossibility results occupy a prominent place. Famous examples include Fermat’s last theorem, Gödel’s theorem, the impossibility of squaring the circle with ruler and compass and the impossibility of solving the general quintic equation by radicals. I shall begin my talk by giving a survey of the historical development of such theorems. In particular, I shall argue that such theorems were at first considered as unimportant compared with positive theorems and that they only gradually obtained the status of real mathematical results within mathematics having earlier been considered a kind of meta results about mathematics. The last part of my talk will deal with the history of Arrow’s surprising impossibility theorem stating that in an election with three or more candidates, it is impossible to design an election procedure satisfying a few desirable and innocent-looking requirements. Arrow’s proof (1950) of his impossibility theorem initiated the so-called theory of social choice.