Christoph Wockel Juniorprofessor Fachbereich Mathematik Schwerpunkt Algebra und Zahlentheorie Bundesstraße 55 (Geomatikum) 20146 Hamburg Raum 334 Tel.: +49 40 42838-5194 Fax: +49 40 42838-5190 E-Mail: christoph (at) wockel.eu Office hour: Wed. 13-14 and on appointment

Fields of Research Interest:

• dissolving obstructions for integrating central extensions of infinite-dimensional Lie groups by group stacks
• integrating central extensions of Lie 2-algebras
• the relationship between differentiable and locally smooth group cohomology
• higher connected covers of topological groups with a perspective to string group models
• string bundles as principal 2-bundles

Teaching:

Publications:

• Non-integral central extensions of loop groups, 12 pp., to appear in Contemp. Math. (arXiv-version)
• Principal 2-bundles and their gauge 2-groups, 40 pp., to appear in Forum Math. (arXiv-version)
• Central Extensions of Groups of Section (with Karl-Hermann Neeb), Ann. Glob. Anal. Geom., to appear (arXiv-version)
• Equivalences of Smooth and Continuous Principal Bundles with Infinite-Dimensional Structure Group (with Christoph Müller), Adv. Geom., 9 (4) (2009) 605-626 (arXiv-version)
• A Generalisation of Steenrod's Approximation Theorem, Arch. Math. (Brno) 45 (2009) 95-104 (arXiv-version)
• Lie Group Structures on Symmetry Groups of Principal Bundles, J. Funct. Anal. 251 (2007) 254-288 (arXiv-version)
• The Samelson Product and Rational Homotopy for Gauge Groups, Abh. Math. Sem. Univ. Hamburg 77 (2007) 219-228 (arXiv-version)
• Smooth Extensions and Spaces of Smooth and Holomorphic Mappings, J. Geom. Symmetry Phys., 5 (2006) 118-126 (arXiv-version)

Preprints:

• The diffeomorphism supergroup of a finite-dimensional supermanifold, (with Christoph Sachse) 25 pp.
• Categorified central extensions, étale Lie 2-groups and Lie's Third Theorem for locally exponential Lie algebras, 31 pp., submitted
• The Topology of Gauge Groups, 27 pp., available as preprint

Notes and Theses:

• Infinite-Dimensional Lie Theory for Gauge Groups Dissertation, TU Darmstadt, 2006
• Central Extensions of Gauge Groups, Diploma Thesis, TU Darmstadt 2003
• Differentialgeometrie, Lecture notes, emerged from a lecture given by J. Wallner, 2001

Conferences that I (co-)organise(d):

• CRCG Workshop - Higher Structures in Topology and Geometry IV (2010)
• 5th meeting Transformation Groups and Mathematical Physics (2009)
• XXVIII. Session Seminar Sophus Lie (2009)
• CRCG Workshop - Higher Structures in Topology and Geometry III (2009)

Selection of some Talks:

• 24.05.2009, Higher connected covers by categorified principal bundles, Workshop on Topological Field Theories, (Northwestern University, USA), Extended notes by Alex Hoffnung
• 08.04.2009, Non-integral central extensions of loop groups via gerbes, Workshop on Homotopy Theory of Function Spaces and Related Topics, (Oberwolfach, Germany)
• 16.1.2009, Categorical Lie groups and Lie's Third Theorem for locally exponential Lie algebras, Seminar Sophus Lie 2009 (Paderborn, Germany)
• 30.9.2008, Universal group cocycles for simplicial groups, Buildings 2008, (Münster, Germany),
• 19.05.2008, Gauge groups for lifting gerbes and principal 2-bundles, University of Paderborn (Germany), invited by Helge Glöckner, slides
• 22.01.2008, Erweiterungstheorie von Eichtransformationsgruppen, Humbold Universität Berlin (Germany), invited by Ilka Agricola
• 31.05.2007, A bundle-theoretic perspective to Kac-Moody groups and their generalisations, Colloquium of the Graduiertenkolleg Gruppen und Geometrie, (Göttingen, Germany) slides
• 29.01.2007, A bundle-theoretic perspective to Kac-Moody groups and their generalisations, University of Münster (Germany), invited by Linus Kramer
• 02.11.2006, Approximation Theorems for Locally Convex Manifolds, Lie Groups and Principal Bundles, Seminar Sophus Lie 2006 (Vienna, Austria) slides
• 16.06.2006, Equivalences of continuous and smooth principal bundles, 31. Süddeutsches Kolloquium über Differentialgeometrie (Darmstadt, Germany), slides (in German)
• 12.05.2006, Topological properties of Gauge Groups and Applications to thier Infinite-Dimensional Lie Theory, Colloquium of the Graduiertenkolleg Gruppen und Geometrie, (Göttingen, Germany)
• 29.06.2005, Infinte-dimensional Lie theory for Gauge Groups, Workshop "Geometric Methods in Physics" (Bialowieza, Poland), abstract , slides
• 11.06.2005, Infinte-dimensional Lie Theory for Gauge Groups, Seminar Sophus Lie 2005 (Nancy, France), abstract, slides
• 15.09.2004, Zentrale Erweiterungen von Eichgruppen, DMV-Jahrestagung 2004 (Heidelberg, Germany), slides
• 15.11.2003, Zentrale Erweiterungen von Eichgruppen, Workshop "Infinite-dimensional Lie theory" (Darmstadt, Germany)