One of the most difficult but also most fundamental tasks in mathematics is to show that two given objects are different. For example, the shape of a soccer ball cannot be deformed to resemble a donut without tearing it apart or gluing it together. Homological algebra is a branch of mathematics that develops abstract tools to find and work with so-called invariants, which help distinguish between different objects. Recently, a new branch of homological algebra, called higher homological algebra, has been discovered. This branch weakens the assumptions of classical homological algebra and makes it possible to examine new invariants.

In his project, he is doing basic research within this new branch: Carlo compares classical homological algebra with higher homological algebra, generalises results to this new branch and examines applications, for example, in algebraic geometry to study special points on surfaces.

With the EliteForsk travel grant, Carlo can finance a longer stay at the Norwegian University of Science and Technology (NTNU), where he can work with and learn from several of the leading researchers in the field of higher homological algebra. In addition, the scholarship will enable him to attend more conferences and allow him to concentrate on his research.

• EliteForsk portrait of Carlo Klapproth (in Danish)