Professor Ulrike Tillmann FRS has been at the University of Oxford since 1992. She is an algebraic topologist, known in particular for her work on Riemann surfaces and the homology of their moduli spaces. She has long standing research interest in homology stability questions. In 2011 she introduced an annual course (with Abramsky) in Computational Algebraic Topology at masters level. In the last year, Tillmann has co-organized four workshops on topological data analysis, as well as an CMI-LMS research school.
She held an EPSRC Advanced Fellowship 1997-2003. She was invited to present at the ICM in 2002 and was a member of the topology subject panel for both the 2010 and 2014 ICMs. In 2008 she was made a Fellow of the Royal Society and received the Bessel Forschungspreis from the Humboldt Gesellschaft. She is an inaugural Fellow of the AMS. Algebraic topology and its applications.
Algebraic topology is a very effective tool to study the global properties of geometric objects. For example, take the surface of a ball and divide it into triangles; now count the number of faces, add the number of vertices and subtract the number of edges; no matter how you choose your triangles, the result will always be 2. Do the same with the surface of a donut and the result is always 0. These numbers were already known by Euler and are foreshadows of homology developed in the 20th century. By now the basic ideas of algebraic topology have permeated nearly every branch of research in mathematics. Her own research has been motivated by questions in quantum physics and string theory. In particular, she has contributed to our understanding of the 'space of surfaces'.