Information for Students
Information for Students
If you are interested in pursuing a graduate degree (Masters or PhD) under my supervision, you should apply to the School of Graduate Studies through the Department of Mathematics. Information about the program and the application process is available at the Graduate Student page for the Department of Mathematics.
If you are accepted into the program we can discuss your interests, see how well they align with my current research and decide at that time if there is a good fit.
Presently I am working in the following areas:
- Quantum Field Theory
Consider a quantum system, such as a hydrogen atom, which is originally in an excited state. We expect such a system to emit photons and descend into its ground state. This is the process of radiation, which in particular produces the light we see. We would like to develop mathematical understanding of the dynamics of this and similar processes.
- Nonlinear Partial Differential Equations of Quantum Physics
Consider (non-integrable) evolution equations which have soliton solutions. Examples of such equations are the nonlinear Schrödinger, Ginzburg-Landau, Landau-Lifshitz and Heisenberg ferromagnet equations, to name just a few. One would like to understand solutions of such equations in the presence of inhomogeneities and/or describing several (interacting) solitons.
- Mathematical Biology
Here we are interested in aggregation phenomena for living organisms, such as cells and bacteria (e.g. chemotaxis), and for proteins.
- Non-equilibrium Statistical Mechanics
Quantum systems are never isolated but interact with their environments. The latter can be assumed to be near their states of (local) equilibrium. The problem here is to describe the dynamics of such a coupled system -- to see, in a mathematically rigorous way, how the dynamics of isolated quantum systems is affected by interaction with its environment.