Mathematics forms the basis of many innovations in technology, the service industry and science, such as data analysis and coding, artificial intelligence, weather or climate change modelling or understanding molecular processes. The researchers from the Mathematical Institute (MI) are constantly developing new mathematics that responds to concrete questions or arises from fundamental mathematical problems.

The researchers from MI work within four research themes:

• Number Theory, Algebra and Geometry
• Analysis and Dynamical Systems
• Probability Theory
• Statistical Science

Pure mathematics

Number theory is an important topic within the Number Theory, Algebra and Geometry group. Number theory largely belongs to ‘pure mathematics,’ which focuses on the logical inference of theorems from axioms. In Leiden, the researchers also focus on algorithms and their use in cryptography, for instance. This forms the basis for computer programmes used to code and decode information, for instance when sending encrypted data through the internet.

Analysis and Dynamical Systems

Differential equations are used within and outside mathematics to describe changes in time and space, for instance when modelling desert formation, population growth or the development of blood vessels. The researchers from Analysis and Dynamical Systems devote a lot of attention to the ensuing patterns and structures. They also work on fundamental mathematical questions, some of which relate to geometry.

Probability Theory

The mathematicians from Leiden within the Probability Theory group work on Markov decision processes, Ergodic theory, population dynamics, statistical physics and complex networks. In their research, they try to describe and optimise the global behaviour of systems with a large number of stochastic components that are in local interaction.

Statistical Science and Data Analysis

The members of the Statistical Science and Data Analysis group focus on all aspects of data analysis, from fundamental theory to computer algorithms and machine learning, with an emphasis on Bayesian statistics. They interpret reality on the basis of prior probability: which state of reality is most probable? The influence of a prior assumption on the final result is of specific relevance to research into big data.

Teaching

MI coordinates the international ALGANT consortium, in which talented international master’s students and PhD candidates are recruited for teaching and research within algebra, geometry and number theory. It also coordinates a master’s programme in applied statistics that is unique in the Netherlands.