Model theory and functional analysis (3/3)

Date

Feb 17, 2017

Time

3:00 PM - 3:50 PM

Speaker

David Sherman

Affiliation

University of Virginia

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. A. Thom

Description

This series of lectures aims at Master‘s and PhD students in mathematics and offers a first glimpse into topics which are not routinely taught in our MSc/PhD programme. The emphasis is to introduce new concepts and techniques, and not to present full mathematical details. Classical model theory has had little application to functional analysis, notwithstanding the fact that standard objects such as Banach spaces, C*-algebras, and tracial von Neumann algebras carry useful notions of ultraproduct. Recently, building on many years‘ development, it was realized that an elegant model theory for these structures can be based on a logic in which truth values lie in the interval [0,1]. This “continuous model theory“ recovers analogues of many classical logical theorems involving ultraproducts, and it makes a whole arsenal of new tools available to analysts. Work along these lines has answered published questions and raised many new ones. I will try to give a “big picture“ survey of the subject, including history and basic background for both continuous model theory and operator algebras.

Links

• Graduate Lectures in Mathematics

Last modified: Feb 3, 2017, 2:26:04 PM