Das Institutskolloquium findet während der Vorlesungszeit an jedem Donnerstag um 17:15 Uhr im Raum 05-432 (Hilbertraum) statt. Ab 16:45 Uhr gibt es Kaffee und Kuchen.
18.04.2019, 17 Uhr c.t. NN
25.04.2019, 17 Uhr c.t. Prof. Dr. Peter Stevenhagen (Leiden University, Netherlands)
Primitive roots: multiplicative and elliptic
02.05.2019, 17 Uhr c.t. NN
09.05.2019, 17 Uhr c.t. NN
16.05.2019, 17 Uhr c.t. Prof. Elisenda Feliu (Kopenhagen, Dänemark)
Algebraic methods for biochemical reaction networks
23.05.2019, 17 Uhr c.t. NN
30.05.2019 Christi Himmelfahrt
06.06.2019, 17:00 Uhr im HIM: Dr. Horst Kant (MPI für Wissenschaftsgeschicte, Berlin) trägt vor im Rahmen der Reihe "Meitner - Hahn - Straßmann"
Fritz Straßmann - "Ich dachte schon, den [...] gibt's gar nicht" (N. Bohr)
13.06.2019, 17 Uhr c.t. Dr. Matthias Schlottbom (University of Twente, NL)
On classical approximations for radiative transfer in a unified variational framework
27.06.2019, 17 Uhr c.t. NN
04.07.2019, 17 Uhr c.t. Dr. Annette Bachmayr
Das Umkehrproblem in der Differentialgaloistheorie
11.07.2019, 17 Uhr c.t. Prof. Dr. Roderich Tumulka (Universität Tübingen)
On the present status of quantum mechanics
25.04.19: Primitive roots: multiplicative and elliptic
An unproved conjecture of Artin dating back to 1927 predicts that every non-square integer different from -1 will be a “primitive root” modulo infinitely many primes p, and predicts exactly how many of such p there are. It was first corrected, after more than 25 years, by Artin himself, in view of new nu-merical data, and then“proved" in 1967 by Hooley, under assumption of GRH.
We go into the history and explanation of the conjecture before addressing its analogues in the context of elliptic curves.
16.05.19: Algebraic methods for biochemical reaction networks
Under the law of mass-action, the concentrations of the species of a biochemical reaction network are often modelled by means of a parametrized system of polynomial ordinary differential equations. The polynomial structure of the system allows the use of techniques from algebra to study the steady states of the system and their stability properties for unknown parameter values.
In this talk I will start by presenting the formalism of the modelling approach and proceed to discuss the main research questions in this area, which arise from biology. Afterwards, I will present recent results on the parameter regions where multiple steady states exist and on the stability of the steady states.
13.06.19: On classical approximations for radiative transfer in a unified variational framework
High-frequency electromagnetic radiation is at the heart of several high-tech applications, including medical imaging, tumor treatment, gas and oil reservoir exploration, climate simulations, and in the energy efficient generation of white light. The extremely high complexity of the scattering media in terms of number, geometry and position of scattering objects does not allow to directly simulate Maxwell’s equations in such applications. Instead, the radiative transfer equation (RTE) has been established as a sound physical model by a rigorous derivation from Maxwell’s equations, and important physical observables, such as the electromagnetic energy, can be recovered from the solution of the RTE.
Due to the wide range of applications for the RTE, several techniques for its numerical solution have been developed, and many techniques that are nowadays well-established in various fields can originally be associated to the RTE, such as the Monte-Carlo method or discontinuous Galerkin methods. In this talk we discuss classical deterministic approximations of the RTE, including truncated spherical harmonics approximations and discrete ordinates methods, and give an interpretation in a unified variational framework. We discuss some properties of the resulting linear systems and their numerical solution.
04.07.19: Das Umkehrproblem in der Differentialgaloistheorie
Die Differentialgaloistheorie ordnet linearen Differentialgleichungen Symmetriegruppen zu, welche als Maß der algebraischen Abhängigkeiten zwischen den Lösungen verstanden werden können. Im Vortrag wird eine Einführung in diese Theorie gegeben und es werden Ergebnisse zum Umkehrproblem vorgestellt, d.h. zur Frage welche Gruppen als Symmetriegruppen vorkommen.
11.07.19: On the present status of quantum mechanics
I have borrowed the title from Erwin Schrödinger’s 1935 ``cat’’ paper because I’m addressing the same questions as he did: How can we make sense out of quantum mechanics? How does it work in reality? How does nature do it? While there is consensus about how to predict what observers will see in any quantum mechanical experiment, there is no consensus on these questions. Niels Bohr used to claim that it was impossible to give any coherent explanation of the phenomena of quantum mechanics, but he was wrong: we now even have several such explanations (none of them due to Bohr, unsurprisingly). In my talk, I will describe these explanations, their present status, mathematical development, and future challenges. One of the morals is: It is hard to prove theorems about a physical theory if you don’t have a clear definition of that theory.