I am currently a member of staff at Royal Holloway university, paid through a grant I received from the DFG.
My research focuses primarily on quantum graphs and their spectra. Quantum graphs are graphs where all the edges have a length and there is a differential operator acting on them. The key questions are usually of the form:
How can one get information about the graph out of the spectrum?
Which properties of the graph and the operator are encoded in the spectrum?
What types of graphs are characterized by their spectrum?
Can two different graphs have the same spectrum, or almost the same spectrum?
Answering these questions usually involves creating and using tools such as a trace formula or a heat kernel that relate spectral information to topological properties of the graph. Additionally, I sometimes use combinatorial graph theory to translate abstract information about a graph into more concrete properties.
Here is a list of my publications:
2012 joint with Uzy Smilansky, Trace formulae for quantum graphs with edge potentials, in Journal of Physics A, Mathematical and Theoretical, 45 (2012) 475205. http://stacks.iop.org/1751-8121/45/475205
2012 Quasi-isospectrality on quantum graphs, submitted to Journal of Geometric Analysis, http://arxiv.org/abs/1203.3670
2011 Recovering Quantum Graphs from their Bloch Spectrum,
to appear in the Annales de l’Institut Fourier, http://arxiv.org/abs/1101.6002
In my free time, I enjoy playing the Asian board game Go, see for example kiseido for an introduction. My current strength is about 2 kyu.
You can contact me at:
McCray 235, Royal Holloway, University of London
Egham, Surrey TW20 0EX, United Kingdom