Significant research is being carried out in the Department in these areas of Mathematics:
- Algebraic combinatorics
- 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: Algebraic combinatorics
Algebraic combinatorics concerns the interplay between abstract algebra and combinatorics, where algebraic techniques may be applied to combinatorial problems, or conversely, combinatorial methods used to understand algebraic or geometric problems.
Dominic Searles is interested in questions of positivity, such as when combinatorially or geometrically-inspired bases of polynomials expand in other bases with nonnegative coefficients or have nonnegative structure constants. For example, the structure constants of the basis of Schubert polynomials count intersections of Schubert subvarieties of the complete flag variety, and it is a longstanding open problem to provide a manifestly nonnegative combinatorial rule for these numbers.