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 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 the usefulness of 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)
Geometric perspectives on categorical braid group actions
Abstract: One of the many intriguing discoveries inspired by Kontsevich's homological mirror symmetry is the concept of spherical twists, introduced by Seidel and Thomas. These are autoequivalences described by a categorification of the classical Picard-Lefschetz formula for monodromy actions on homology. More recently, it was proposed by Kapranov and Schechtman to interpret spherical twists within a (still hypothetical) theory of categorical analogs of perverse sheaves, so-called perverse schobers. In this talk, I will give an introduction to this circle of ideas, outline some recent progress on perverse schobers, and explain how they provide new structural insights on categorical braid group actions relevant for link homology theory.
17.07. Prof. Dr. Amru Hussein (Universität Kassel)
Title: From old make new - coupling of partial differential equations
Abstract: Partial differential equations help us to express physical principals and to describe problems in engineering. Once there is more than a single influence, we have to take care of the possible interactions. From a mathematical point of view one can ask which of these are admissible and therefore allows one to make from an "old" well-understood uncoupled setting a "new" one - now coupled and interconnected. This is exemplified for coupling boundary conditions on networks where information can be transmitted in various ways through the nodes, and for interconnected systems in fluid mechanics. Examples of the latter are geophysical flow equations describing the dynamics of ocean and atmosphere, and models describing liquid crystals which entered our every day life as liquid crystal displays or LCDs.
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