Project at HIAS
Higher Structures in Mathematical Physics
Ralph M. Kaufmann’s research project during his HIAS fellowship comprises linking concrete algebraic structures, categorical constructions and universal spaces. Using categorical input, universal spaces such as moduli spaces or Riemann surfaces will be constructed. As such these spaces give rise to concrete algebraic structures, such as double Poisson algebras. Their super-versions and the relationship to Hopf algebroids and Verdier duality will be special foci.
Ralph Kaufmann’s Tandem Partner is Christoph Schweigert, Professor for Mathematics at the University of Hamburg.
Tandem
Prof. Dr. Christoph Schweigert, Mathematics, University of Hamburg
Biography
Ralph Kaufmann is a professor of mathematics as well as, by courtesy, a professor of physics and astronomy and a professor of philosophy at Purdue University in West Lafayette, Indiana, USA. He studied mathematics, physics and philosophy at the University of Bonn obtaining master’s degrees in physics and philosophy. He did his graduate studies with Yuri Ivanovich Manin at the Max-Planck-Institute for Mathematics and obtained a PhD as well as a Habilitation in mathematics from the University of Bonn. As a post-doc he worked with Maxim Kontesvich at the IHES in Paris. He was twice a member of the Institute for Advanced Studies in Princeton, has held visiting positions at the Max-Planck-Institute for Mathematics in Bonn and the Institut des Hautes Etudes Scientifiques near Paris, France, as well as at the MSRI in Berkeley. He was a fellow of the Studienstiftung des Deutschen Volkes, a fellow for the summer student program at CERN, and a Humboldt fellow. His research has been supported by the NSF, the Simons foundation, and the EU. Kaufmann is Co-Chief Editor and Co-Founder of the Journal “Higher Structures”.
Ralph Kaufmann’s principal research areas are algebraic geometry, algebraic topology and mathematical physics. The main thrust of the research is to understand physical phenomena such as quantum field theory, condensed matter systems and quantum computation via a rigorous mathematical framework. To this end, Kaufmann has been utilizing category theory and introduced the notion of Feynman categories. In philosophy his central recent concentration has been on Hegel’s Philosophy of Nature. He has published over 60 articles in mathematics and physics as well as more than a dozen in philosophy and the liberal arts.
Kaufmann’s HIAS fellowship is provided by the Joachim Herz Stiftung.
Image Information
Photo by Ralph Kaufmann, Musée de Cluny, Paris (6 July, 2014).