Are you thinking about joining my group?
I am open to working with students of mathematics and physics. The following projects are just a small selection to give you an idea what kind of research I am interested in. Get in touch with me if you want to know more.
Dieses Projekt richtet sich an Lehramtsstudierende mit den Fächerkombinationen Mathematik/Sport bzw. Physik/Sport und kann entweder als Bachelor- oder Master-Arbeit gestaltet werden. Die Arbeit wird gemeinsam von Max Lein, der Didaktik und dem Institut für Sportwissenschaften betreut werden.
Die Inspiration für dieses Projekt stammt aus meiner Erfahrung als Radsportler. Strukturiertes Training im Ausdauersport basiert auf Prinzipien wie Periodisierung, progressive overload, Spezifizität und Individualisierung. So wird beispielsweise das Training in Makro-, Meso- und Mikrozyklen unterteilt, die unter anderem dafür sorgen, dass Athleten regelmäßig Ruhephasen haben, in denen Superkompensation stattfinden kann.
Lernen (z. B. an einer Hochschule) kann man als “strukturiertes Training für das Gehirn” auffassen. Das legt die Vermutung nahe, dass Prinzipien strukturierent Trainings auch auf Lehre angewandt werden können. Ziel dieses Bachelor- oder Master-Projekts ist es,
This project is suitable for Master students of mathematics and physics.
Classical hamiltonian systems are described in the formalism of symplectic geometry. These classical equations can be quantized and a semiclassical limit explains under what circumstances the quantum dynamics can be approximated by the classical dynamics.
The dynamics of open and dissipative quantum systems are described by Lindblad operators, i. e. those operators that generate a continuous semigroup and map density operators (quantum mechanical states) onto density operators. Lindblad identifies the form of the generators in a seminal work.
In contrast, there is no universally accepted form of classical dissipative and open systems. Hence, the task would be to give an overview of the various proposed formalisms, including sub-Riemannian geometry and contact geometry, and to contrast and compare them.
This project is inspired by my experience in the semiconductor industry. Wafers are patterned by a series of litho-etch steps. These patterns are microscopic, but still change fundamental properties such as mechanical properties of the wafer. The goal is to derive the mechanical properties for periodically patterned beams (1 + 1d) and thin plates (2 + 1d) from the fundamental equations of continuum mechanics, which are typically given in terms of functionals. There are many similarities to the mathematics involved in General Relativity, and it fundamentally involves General Relativity. The aim is to answer the following question:
This is important for e. g. wafer bonding where two wafers are (pre-)bonded by pushing the center of the top wafer onto the bottom wafer with a piston (the so-called bond pin). Because the periodic patterns can fundamentally change the mechanical properties of the wafers, the propagation of the so-called bond wave (the boundary line where the two wafers start to touch) is impacted.
This project is suitable for people with a Master degree in mathematics or physics. The content of this work is in mathematical physics, i. e. these results will need to be proven.
Quantum systems can be driven out of equilibrium by applying electric and magnetic fields and changing external parameters such as temperature. Linear Response Theory then allows one to consider the effect of one of these parameters on quantities like the current (expectation value) and “Taylor expand” the current to first order in one of the external parameters. In 2017, together with Giuseppe De Nittis, I have developed an algebraic-analytic linear response formalism, which applies to a broad class of systems. It can handle e. g. disorder, discrete systems and those on the continuum.
The price for such generality are technical assumptions, which need to be verified for each model. Many of these assumptions are necessary to ensure that certain products or (generalized) commutators exist.
The purpose of this thesis project is to apply this linear response framework to magnetic pseudodifferential operators. Mantoiu, Purice and Richard have developed a C*-algebraic point of view of magnetic pseudodifferential operators in terms of twisted crossed product C*-algebras. Hence, products and commutators of magnetic pseudodifferential operators are again magnetic pseudodifferential operators. Consequently, we expect that many of these technical conditions simplify or are lifted altogether.
This project involves
