Significant research is being carried out in the Department in these areas of Mathematics:
- Graph theory and combinatorics
- Mathematical and computational relativity
- Mathematics of evolutionary biology
- Numerical analysis and uncertainty quantification
- Point patterns and processes
- Quantitative Genetics
- Semiclassical and harmonic analysis
- Stochastic integro-differential equations and their applications
Research group: Semiclassical and harmonic analysis
Semiclassical analysis is the study of parameter dependent pseudo-differential operators. One of the main motivations for this area of research is understanding the behaviour of quantum states at high energy (in this case the energy operates as the parameter). As the energy is increased the quantum state should display behaviour determined by the analogous classical system. A major question in this field is to understand how underlying geometry and dynamics can appear in the properties of the related quantum states. Of particular interest are those systems whose classical analogue displays chaos.
Harmonic analysis is concerned with decomposing functions into basic waves. The underlying strategy is to reduce a general problem to a problem about these more simple building blocks. Semiclassical and harmonic analysis interact very strongly as many results in semiclassical analysis require techniques borrowed from harmonic analysis.
Melissa Tacy works in both semiclassical and harmonic analysis. Her research is mainly concerned with stationary states of quantum systems at high energy. She also works on the behaviour of random combinations of basic waves.