Mathematics
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Department of Mathematics & Statistics

Research

Significant research is being carried out in the Department in these areas of Mathematics:

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.