

1996  Dr. math., University of Bielefeld  1996  Postdoc, University of Chicago, IL, USA  1997  1998  Postdoc, Massachusetts Institute of Technology, Cambridge, MA, USA  1998  2001  Assistant Professor (C1), University of Bielefeld  2001  Habilitation, University of Bielefeld  2002  2003  Head of Junior Research Group, DFG Collaborative Research Center SFB 478 “Geometric structures in mathematics”, University of Münster  Since 2003  Professor (C4), University of Bonn 


My main area of expertise is algebraic topology, specifically stable homotopy theory. I contributed to the foundations of stable homotopy theory (comparison of models for the stable homotopy category, rigidity theorem for the stable homotopy category, foundations of the theory of symmetric spectra). Further research concerned basic questions about triangulated categories, in particular the existence and uniqueness of models for triangulated categories, the distinction of algebraic and topological triangulated categories and examples of exotic triangulated categories.
Much of my current and future research is in equivariant stable homotopy theory, in particular ''global'' phenomena, i.e., spaces or spectra with simultaneous and compatible actions of all compact Lie groups, up to deformations that preserve all symmetries. I introduced a framework for global equivariant homotopy theory based on orthogonal spectra which opens the door for a rigorous study of global stable homotopy types. The global perspective reveals systematic patterns and facilitates equivariant calculations, for example in the rank filtrations of equivariant infinite symmetric products or global equivariant Ktheory.
Future goals include a better understanding of the universal properties of global Ktheory (both algebraic and topological) and global equivariant bordism. Alongside, we want to further exploit naturally occuring global structures for new computations.


DFG Research Training Group GRK 1150 “Homotopy and Cohomology”
Scientific Member
DFG Priority Program SPP 1786 “Homotopy Theory and Algebraic Geometry”
Initiator
Series of Oberwolfach Workshops on “Homotopy theory” (2007, 2011, 2015)
Organizer
Abel Symposion, 2007
Organizer
HIMTrimester, 2015
Organizer
Semester program “Homotopy Harnessing Higher Structures” at Isaac Newton Institute, 2018
Organizer
“Bonn International Graduate School of Mathematics”
Director, 2013  2017
DFG Cluster of Excellence “Hausdorff Center for Mathematics”
ViceCoordinator (2017  2019) and Principal Investigator





• Documenta Mathematica (2003  2016)
• Mathematische Zeitschrift (2006  2012)
• Geometry & Topology (since 2016)


2019  Fellow of the American Mathematical Society 


2007  Plenary talk, Joint International Meeting UMI  DMV, Perugia, Italy  2008  Plenary talk, European Mathematical Society  Joint Mathematical Weekend, Copenhagen, Denmark 


Christian Ausoni (2008), now Professor, University of Paris 13, France
Gerald Gaudens (2010)
Steffen Sagave (2013), now Assistant Professor, Radboud University Nijmegen, Netherlands


Steffen Sagave (2006): “Universal Toda Brackets of Ring Spectra”,
now Assistant Professor, Radboud University Nijmegen, Netherlands
Constanze Roitzheim (2007): “Rigidity and Exotic Models for the Klocal Stable Homotopy Category”,
now Senior Lecturer, University of Kent, England, UK
Morith Rahn (née Groth) (2011): "On the theory of derivators",
now Akademischer Rat, University of Mainz
Lennart Meier (2012): “United elliptic homology”,
now Assistant Professor, Utrecht University, Netherlands
Irakli Patchkoria (2013): “Rigidity in equivariant stable homotopy theory”,
now Lecturer, University of Aberdeen
Karol Szumilo (2014): “Two models for the homotopy theory of cocomplete homotopy theories”,
now Postdoc, University of Leeds
Markus Hausmann (2016): “Symmetric products, subgroup lattices and filtrations of global Ktheory”,
now Postdoc, University of Bonn


 Master theses: 19, currently 1
 Diplom theses: 15
 PhD theses: 14, currently 2


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