Research

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.

Career

• 2021 N.N. Rothschild & Sons Professor and Director, Isaac Newton Institute, University of Cambridge, UK
• 2020 Chern Visiting Professor, Mathematical Sciences Research Institute, Berkeley, USA
• since 2000 Professor of Mathematics, University of Oxford, Oxford, UK
• 1996 Habilitation, University of Bonn, Bonn, Germany
• 1992-2010 Lecturer, Merton College, University of Oxford, Oxford, UK
• 1990-1992 Research Associate, Clare Hall College, University of Cambridge, Cambridge, UK
• 1990 PhD, Stanford University, Stanford, USA
• 1987 Master of Arts, Stanford University, Stanford, USA
• 1985-1990 PhD Student, Stanford University, Stanford, USA
• 1985 Bachelor of Arts, Brandeis University, Waltham, USA
• 1982-1985 Studies in Computer Science and Mathematics, Brandeis University, Waltham, USA

Functions

• since 2023 Member, Einstein Foundation, Berlin, Germany
• since 2023 Vice-President, International Mathematical Union
• 2021-2023 President, London Mathematical Society, London, UK
• 2020-2022 Member, Journal of Foundations of Computational Mathematics
• since 2020 Chair, Advisory Committee on Mathematics Education (RS ACME), Royal Society, UK
• since 2019 Member, Scientific Advisory Board, Austrian Science Fund FWF, Austria
• since 2019 Member, Editorial Boards, Forum of Mathematics, Pi and Sigma
• 2018 Vice-President, Royal Society, UK
• 2018 Member, Programme Committee, International Congress of Mathematicians
• since 2018 Member, Advisory Board, Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany
• 2018-2022 Chair, Advisory Board, Hausdorff Centre of Mathematics, Bonn, Germany
• since 2018 Member, Journal of the American Mathematical Society (JAMS)
• 2018 Member, Programme Committee, International Congress of Mathematicians
• since 2017 Member, Geometry & Topology
• 2017-2020 Member, Council, Royal Society, UK
• 2016-2019 Member, Wolfson Merit Award Committee, Royal Society, UK
• 2016-2019 Deputy Head, Mathematical Institute, University of Oxford, Oxford, UK
• 2016-2017 Chair, Programme Committee, Alan Turing Institute, UK
• 2015-2020 Member, Management Committee of the Isaac Newton Institute, Cambridge, UK
• 2015-2019 Member, Scientific Committee, Barcelona Graduate School of Mathematics, Barcelona, Spain
• 2015-2018 Member, Prizes Committee, London Mathematical Society, London, UK
• 2014 Member, Section Committee “Topology”, International Congress of Mathematicians
• 2013-2021 Vice-Chair, Scientific Advisory Board, Mathematical Research Institute Oberwolfach, Oberwolfach-Walke, Germany
• 2013-2018 Member, Moore Research Article Prize Committee, AMS, UK
• 2012-2014 Vice-President, Merton College, Oxford, UK
• 2011-2014 Chair, Research Meetings Committee, London Mathematical Society, London, UK
• 2011 Chair, International Review Committee, Mathematics in Norway, Norway
• 2010 Member, Section Committee “Topology”, International Congress of Mathematicians
• 2008-2014 Member, Council, London Mathematical Society, London, UK
• 2008-2012 Chair, Scientific Committee, European Mathematical Society/European Women in Mathematics
• 2008-2011 Member, Panel, Section “Mathematics”, Royal Society, UK
• 2007-2012 Member, Publications Committee, London Mathematical Society, London, UK
• 2007-2015 Vice-Chair, Scientific Advisory Board, Courant Research Center, Göttingen, Germany
• 2007-2011 Member and Chair, Panel “International Grants”, Royal Society, UK
• 2005-2017 Member, Programme Committee, International Centre for Mathematical Sciences

Projects

• since 2018 Principal Investigator, Programme “Application Driven Topological Data Analysis”, Engineering and Physical Sciences Research Council (EPSRC), Swindon, UK
• 2003-2006 Senior Scientist, Focused Research Grant, National Science Foundation (NSF), USA
• 2000-2003 Advanced Fellow, “The Topology of the stable mapping class group and applications in quantum field theory”, EPSRC, Swindon, UK

Honours and Memberships

• since 2021 Member, European Academy of Sciences
• since 2017 Member, German National Academy of Sciences Leopoldina, Germany
• since 2016 Fellow, Alan Turing Institute, London, UK
• since 2012 Fellow, American Mathematical Society, USA
• since 2008 Fellow, Royal Society, UK
• 2008 Bessel Research Award, Alexander von Humboldt Foundation, Bonn, Germany
• 2004 Whitehead Prize, London Mathematical Society, London, UK
• 1997-2003 Advanced Fellowship, EPSRC, UK
• 1989-1990 Sloan Research Fellowship, Alfred Sloane Foundation, New York City, USA
• 1982-1985 International Wien Fellowship, Brandeis University, Waltham, USA