Mathematics underpins many of our scientific and technological advances. It allows us to model and analyze phenomena within the physical universe and, more recently, aids us in the creation and understanding of the digital world. At the heart of mathematics are three key pillars: algebra, analysis, and geometry. Together with their many fascinating interrelations, they provide the basic foundations and tools for a large landscape of important subbranches of mathematics. Generally speaking we can say that

*Algebra*studies discrete structures and their relations. It includes for example the study of groups, rings, and graphs. These abstract concepts are key in modelling concrete problems in a conceptual framework.*Analysis*deals with the continuous, and models this by means of the tools of calculus, such as limits and derivatives, as well as more abstract theories such as topology or measure theory. This field is perfectly suited for studying the behavior of natural signals and systems, such as vision or audio and dynamics governed by (partial) differential equations.*Geometry*is, in its simplest form, the study of shape and position of structures such as points, lines and surfaces defined on finite or infinite sets. More recent breakthroughs in mathematics have completely transformed our concept of space, leading to many novel insights and forms of geometry with which physical theories can then be built to understand the universe around us.

To solve problems in the mathematical, physical or digital world, we often create toy models and examples, or collect data to gain insights into the underlying patterns and relationships. Because of the recent advances in hardware, we can now leverage mathematical modelling with data science, using techniques such as deep learning, natural language processing, automated theorem provers and physical (e.g. quantum) computing, to make powerful models and predictions.

More information about our member's research areas.

**Head of the Large Research Group: **Prof. Dr. Ann Dooms