My PhD project

During my years as a PhD student at Aarhus University I was part of the Centre for Quantum Geometry of Moduli Spaces (QGM) and my focus switched towards differential geometry and quantization, under the supervision of Prof. Jørgen Andersen. In a nutshell, I studied star products, which are a way to formalize quantization (in particular, deformation quantization).

Quantization is a mathematical recipe to associate to a classical mechanical system a corresponding quantum system, and it turns out that to formalize this process one has to make a choice of some structure, which is not what one expects from a physical perspective. Each value of the choice gives us a different way to quantize, i.e. a different star product. We can introduce a tool to connect all these products together, and that is called a formal connection (think of what the Hitchin connection does for geometric quantization and bring it to the formal world of deformation quantization). I studied this kind of gadgets and gave a general notion of formal Hitchin connection, which extends the definition given by Andersen. Together with my supervisor and Florian Schätz we gave also an existence result for formal connection and showed that all formal connections are gauge equivalent under certain conditions. These results are written up in a joint paper and in my PhD thesis.