In algebraic geometry, the study objects are curves, surfaces and object of higher dimensions (so-called manifolds) that have in common that they are defined with the help of polynomials. One example is the circle, which can be described as the points in the plane where the polynomial x^2+y^2-1 is zero. Although the circle is easy to understand, manifolds of this kind can be extremely intricate, especially in higher dimensions.

The specific research area for David Witt Nyström, Kähler geometry, focuses on how a manifold’s small-scale form, its curvature, is related to its large-scale form, its topology. In addition to algebraic methods this demands advanced tools from complex analysis.

David Witt Nyström has, among other things, proved a conjecture (proposition) well-known in the area. It describes how, in a specific context, global topological data are determined by local curvature properties.

Another major track in his research is the Hele-Shaw flow, which describes how a viscous liquid moves in a thin layer. There, an unexpected connection to Kähler geometry led to a much discussed counterexample to a well-known conjecture.

– I am incredibly happy and honoured to have been awarded the Göran Gustafsson Prize, and it will clearly be of great importance for my further research, he says.

**Text and photo**: from the page of the Royal Swedish Academy of Sciences, read more about the prize and the prize winners in other subjects (in Swedish) >>