**Doktorandprojekt - PhD Projects**

**at the Dept. of Mathematics, Stockholm university**

Our group on Analysis and Mathematical Physics has several research projects for PhD students. In particular we suggest the following two research projects:

**Discrete and Continuous Quantum Graphs**

*Quantum graphs*- differential operators on metric graphs - is a rapidly growing branch of mathematical physics lying on the border between differential equations, spectral geometry and operator theory. Studies of spectral properties of such systems are very important for applications in physics, for example to nano systems.

**Supervisor**: Pavel Kurasov

Project description**Quantum Networks: Random and Regular**

This is another project in the area of*quantum graphs,*more precisely*quantum networks.*The idea is to study infinite periodic, fractal and random networks.

**Supervisor**: Pavel Kurasov

Project description
**Pseudo-Caratheodory functions**

Some classes of analytic functions admit representations via resolvents of operators. Such relations have been useful in many places. The current project aims to find such representations (more precisely the appropriate class of operators) for Pseudo-Caratheodory functions, which appear in electro engineering.

**Supervisor**: Annemarie Luger
Project description

How to apply

** Deadline for application: May 2, 2013**