Professor Dr Ulrike Tillmann

Research Priorities: Mathematics, algebraic topology and its applications
Ulrike Tillmann is a German-British mathematician. Her focus is on Algebraic Topology, which has the aim to assign structures from algebra to topological spaces to make them viable for mathematical treatment. Ulrike Tillmann is especially interested in the theoretical foundations of quantum field theory and data analysis.
Algebraic Topology connects two foundational pillars of mathematics: algebra and topology. Topology is concerned with the structures of a space that are retained after distortion. A sphere, for example, can be transformed into a cube by stretching and compressing it. Qualities are considered topological qualities if they are retained after the process. Algebra is concerned with the qualities of calculations. Algebraic Topology, on the other hand, searches for possibilities to make topological questions viable for calculation. In the past century, algebraic theory provided a deeper understanding of geometry. Recently, it delivered computational approaches to the topological theory of quantum fields as well as to data science.