Das allgemeine Kolloquium des mathematischen Instituts findet während der Vorlesungszeit donnerstags um 17:15 Uhr im Hilbertraum (Raum 05-432) statt. Ab 16:45 Uhr gibt es Kaffee und Kuchen.
Sommersemester 2025:
15.05. Prof. Dr. Henrik Garde (Aarhus Univ.)
Reconstruction of inclusions and cracks in Calderón's inverse conductivity problem
Abstract:
The inverse conductivity problem (called Calderón's probblem), is to determine the interior electrical conductivity from boundary electrical measurements, in practice using electrodes placed on the surface of an object, or on the skin of a person.
I will talk about the exact reconstruction of general inclusions in Calderón's problem from local boundary measurements. Here "inclusion" means the support of perturbations to a known reference conductivity.
I will briefly outline the cases on open sets, without going into too much analysis. The perturbed coefficient can have finite positive and negative perturbations, can have perfectly conducting parts and have perfectly insulating parts, and may also have parts given as restrictions of Muckenhoupt coefficients with singular and degenerate behavior (enabling continuous growth to infinity or decay to zero).
I will give a more detailed account of newer results, on reconstructing general cracks given as unions of Lipschitz hypersurfaces, including both perfectly conducting and perfectly insulating cracks.
Finally, if time permits it, I will give results on how practical electrode models are rigorously included, and with application to actual measurements from a physics lab.
12.06. Prof.Dr. Laurent Mazliak (Sorbonne)
Émile Borel and the probabilistic turn of a worried Cantorian
Abstract: In this talk, I shall present the singular way in which Émile Borel, from his studies on the structure of real numbers and a certain rejection of Cantor's abstract vision, found in the calculus of probabilities an adequate tool to formulate a new approach to problems. At the same time, he became aware of its usefulness for the approach to the phenomena of physics and society and developed a singular approach to the problem of interpretation of the concept of probability, merging subjectivist and objectivist aspects under an idiosyncratic formulation of the so-called Cournot principle.
03.07. Prof. Dr. Tobias Dyckerhoff (Univ. Hamburg)
title tba
17.07. Prof. Dr. Amru Hussein (Universität Kassel)
title: tba
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