Mathematical Institute Mathematics was one of the first disciplines practiced within Leiden University. Through the years the Mathematical Institute (MI) has specialised in key areas in which the scientists of this institute excel. The main focus of the institute lies with fundamental research. Problems come from the mathematics themselves, rather than from society or industry. Within the mathematical world the institute holds a leading position. Mathematicians from all over the world come to Leiden to work with the scientists from the MI.
Global participation is an important characteristic of the insti-
Arithmetic Geometry
tute. The MI participates in the Erasmus Mundus Master Pro-
Studying geometric properties of sets of solutions of systems
gramme ALGANT, together with institutes in France and Italy,
of polynomial equations is the main topic of this research
which offers first class education and research opportunities.
group. The goal of the research is to understand the relationships between algebraic geometry and number theory. Algebraic
The Mathematical Institute consists of six research groups
geometry has numerous applications within mathematics, but it
divided in two clusters: one is devoted to Number Theory, Alge-
also provides error correcting codes and crypto systems that are
bra and Geometry, the other to Analysis and Stochastics.
intensively used in everyday life.
Number Theory and Algebra
Analysis and Dynamical Systems
The main focus of this group is on number theory, and algebra is
This group focuses on operator-theoretical models to analyze
the dominant method. The algebra part of the research pro-
problems arising from concrete classes of integral, differential
gramme is strongly oriented towards the application of algebra
and difference equations. This research has applications in both
in number theory and arithmetic geometry. Themes of the
chemical engineering and life sciences. The current research
programme include applications of group theory and algebraic
interests of the group include:
number theory, the theory of finite fields, the development of efficient computer algorithms and cryptology.
Graduate School of Science
Graduate School of Science P.O. Box 9502 2300 RA Leiden www.science.leidenuniv.nl/graduateschool Mathematical Institute Snellius Niels Bohrweg 1 2333 CA Leiden www.math.leidenuniv.nl
Algebras associated with dynamical systems, the Ginzburg-
Statistical Science for the Life and Behavioural Sciences
Landau equation and semi-conductor lasers, ordinary and partial
This group, which organizes a master track in cooperation with
differential equations and applications to life sciences and chemi-
several outside partners, concentrates on applying statistical
cal engineering.
skills and methods to problems that arise from the Life and Behavioural Sciences. The life sciences use a lot of biostatistics,
Probability Theory
including quantitative modelling and methods of data analysis
The research of this group focusses on probability theory, ergodic
for clinical and epidemiological research. Most of the empiri-
theory and statistical physics, with excursions into mathematical
cal research in modern social and behavioural sciences relies
Johan Bosman is the first person in the world who has
biology. The aim is to study mathematical models that are capa-
predominantly on statistical analysis.
succeeded to systematically compute polynomials with
ble of describing complex phenomena arising in systems with
rational coefficients that give projectivised residual
a large number of interacting random components, including
Galois representations associated to several modular
phase transitions and associated critical behaviour. Statistical
forms of weight higher than two. The Galois groups
physics and ergodic theory provide the conceptual ideas, while
arising here are non-solvable. Using proven instances
probability theory provides the mathematical language and
of Serre’s conjectures he could prove the correctness
framework.
of these polynomials. One of the consequences is a verification of Lehmer’s conjecture of the non-
Mathematical and Applied Statistics
vanishing of Ramanujan’s Tau(n) up to a bound about
Learning from data and decision making under uncertainty is
1,000 times higher than what was done before. His
the focal point of this group. Mathematical Statistics studies the
presentation of these results at the Dutch Mathemati-
mathematical structure of such problems with an emphasis on
cal Congress earned him the Philips Prize for PhD
stochastic modelling, optimality of statistical inference proce-
students in Mathematics.
dures and approximation.
Graduate School of Science