Dr. Detta Dickinson

Lecturer

Room: 1 Top Logic
Phone: +353 1 708 4635
Fax: +353 1 708 3913
Email: Detta.Dickinson@nuim.ie

Research Interests

Detta Dickinson's research interests lie in the areas of measure theory and metric Diophantine approximation. In particular, Diophantine approximation on manifolds.

Classically, Diophantine approximation is the study of how well real numbers can be approximated by rationals. This can be extended to higher dimensions by asking how well real points in n-dimensional Euclidean space can be approximated by rational points or by rational hyperplanes. Results in this area are very delicate as shown in Khintchine's theorem, where the set of well approximable points has either zero or full measure depending on the convergence or divergence of a certain volume sum. This leads to further questions - those of Hausdorff dimension in the case of measure zero and those of asymptotic number of solutions in the case of full measure.

Both of the above questions become more difficult when the set under investigation is restricted to a manifold embedded in Euclidean space and this is Detta's current area of interest.