**With a European Consolidator Grant of nearly two million euros, Martijn Kool, a mathematician at Utrecht University, will investigate a completely unexplored area in algebraic geometry: counting surfaces on Calabi-Yau fourfolds. It is very fundamental research that is valuable for the development of mathematics, but also for other areas, such as string theory.**

The research of Associate Professor Martijn Kool is part of enumerative geometry. This is a subfield of mathematics which essentially involves the description of shapes: algebraic geometry. Enumerative geometry was already practiced by the Ancient Greeks, and revolves around counting solutions to geometric questions. A well-known example of such a geometric question is Apollonius’s Problem: If you draw three random circles in a plane, how many circles can you then draw that touch all three circles? Apollonius’s Problem may seem abstract, but it plays an important role in current GPS techniques.

## Logical sequel

Kool will work on such geometric issues for Calabi-Yau fourfolds. These are special, four-dimensional objects. It is a logical sequel to research on counting curves on Calabi-Yau threefolds, which is ongoing but has already borne fruit. "It is a truly successful story," Kool says. "It contributed to the breakthrough of string theory and the discovery of mirror symmetry."I find it fascinating to do research at the edge of what we know

Martijn Kool, Associate Professor