The research of the Algebra, Geometry and Number Theory programme ranges from fundamental mathematical theory to algorithms and applications.

This thesis discusses several questions regarding the double ramification cycle as a Chow class on the moduli space of stable n-pointed genus g curves using tools from so-called logarithmic geometry.

This thesis studies the geometry of representation varieties and character stacks. These are spaces parametrizing the representations of a finitely generated group, typically the fundamental group of a compact manifold, into an algebraic group G.

In this thesis, rational points on K3 surfaces are studied. In the first part of Chapter 1 the Brauer group and the the Brauer-Manin obstruction are introduced.

Promotor: S.J. Edixhoven

In this thesis integral points on affine del Pezzo surfaces are studied.

On 30 September 2013 Ronald Cramer, head of the Cryptology group of Centrum Wiskunde & Informatica (CWI) and a professor of cryptology at the Mathematical Institute of Leiden University, was inaugurated as a member of the Royal Netherlands Academy of Arts and Sciences (KNAW).

Not all problems are easy to solve, but with enough bright minds, you make progress step by step. ‘The kind of problems I am interested in have been occupying mathematicians for over two millennia,’ says theoretical mathematician David Lilienfeldt. In September, he started at the Mathematical Institute…

How can you figure out which points lie on a certain curve? And how many possible curves do you count by a given number of points? These are the kinds of questions Pim Spelier of the Mathematical Institute studied during his PhD research. Spelier received his doctorate with distinction on June 12.

How can you solve equations that define not ‘just’ curves, but also two-dimension surfaces or even higher-dimensional objects? That’s the big question that mathematician Martin Bright and his team will be trying to answer. They’ve received a NWO Science-XL grant of 2.8 million euros.