Monday 3rd of April 2023, 15:15-16:15 in HG03.085
Malte Leimbach
How to hear a circle, approximately.
Noncommutative geometry is about formulating geometric information in terms of (C*-)algebras. In this spirit the Gelfand-Naimark theorem can be viewed as the starting point of noncommutative topology. We equip a noncommutative topological space with an extra piece of structure (a special kind of unbounded operator) which allows to measure distances so that one obtains noncommutative metric spaces. However, measuring distances with this operator requires an infinite amount of information (the full spectrum of the operator) which is never available in physical practice. But even with only a finite part of the spectrum one can still make sense of noncommutative metric spaces. It is an open question in general whether the metric spaces arising in this way approximate the original one (in a sense which will be explained). We will see how this works in the case of the circle.