Anyone can be a "maths person". Check out my discussion with the Education Hub about what mathematics is, and when we know we are using it.

Melissa Tacy

Department of Mathematics,

University of Auckland.

I work in the intersection of microlocal, semiclassical and harmonic analysis. Key problems I am interested in are:

How do high energy solutions to PDE and pseudodifferential equations behave? What kind of concentration properties do they display? Typically these kinds of problems involved proving a growth bound for a function norm.
How do these concentration properties fit in with the theories and hypothesis of Quantum Chaos?
How can we use growth bounds for solutions to obtain mapping norm estimates for classical harmonic analysis operators (such as Bochner-Riesz means)?
How can we use Fourier integral operators to produce effective analysis/synthesis systems?
How do random waves behave, what can we expect at a small scale?