Christoph Wockel I left academia, but you can still reach me under christoph (at) wockel.eu.

Fields of Research Interest:

• Cohomology of Lie groups (continuous, smooth, topological, Segal-Mitchison, bounded, measurable, ...) and the related differential geometric structures (flat bundles, symmetric spaces, ...)
• Lie groupoids, Lie algebroids and their relation to infinite-dimensional Lie theory
• String geometry, in particular the string (2-)group, its representations and higher gauge theory in general
• Infinite-dimensional Lie groups (mapping- and gauge groups, diffeomorphism groups) and their cohomological invariants

Publications:

1. Integrating central extensions of Lie algebras via Lie 2-groups (with Chenchang Zhu) 34 pp., J. Eur. Math. Soc. (to appear) (arXiv-version)
2. The Lie group of bisections of a Lie groupoid (with Alexander Schmeding), Ann. Glob. Anal. Geom. 48 (1) (2015) 87-123 (arXiv-version)
3. A Cocycle Model for Topological and Lie Group Cohomology (with Friedrich Wagemann), Trans. Amer. Math. Soc. 367 (2015) 1871-1909 (arXiv-version)
4. Making lifting obstructions explicit, (with Karl-Hermann Neeb and Friedrich Wagemann) Proc. Lond. Math. Soc. (3) 106 (3) (2013) 589-620 (arXiv-version)
5. Universal central extensions of gauge algebras and groups, (with Bas Janssens) J. Reine Angew. Math. 682 (2013) 129-139 (arXiv-version)
6. A Smooth Model for the String Group, (with Thomas Nikolaus and Christoph Sachse) Int. Math. Res. Not. IMRN 16 (2013) 3678-3721 (arXiv-version)
7. Topological Group Cohomology with Loop Contractible Coefficients, (with Martin Fuchssteiner), Topology Appl., 159 (2012) 2627-2634 (arXiv-version)
8. The diffeomorphism supergroup of a finite-dimensional supermanifold (with Christoph Sachse), Adv. Theor. Math. Phys. 15 (2011) 1-39 (arXiv-version)
9. Categorified central extensions, étale Lie 2-groups and Lie's Third Theorem for locally exponential Lie algebras, Adv. Math., 228 (2011) 2218-2257 (arXiv-version)
10. Principal 2-bundles and their gauge 2-groups, Forum Math. 23 (3) (2011) 565-610 (arXiv-version)
11. Non-integral central extensions of loop groups, Contemp. Math. 519 (2010) 203-214 (arXiv-version)
12. Central Extensions of Groups of Section (with Karl-Hermann Neeb), Ann. Glob. Anal. Geom. 36 (4) (2009) 381-418 (arXiv-version)
13. Equivalences of Smooth and Continuous Principal Bundles with Infinite-Dimensional Structure Group (with Christoph Müller), Adv. Geom., 9 (4) (2009) 605-626 (arXiv-version)
14. A Generalisation of Steenrod's Approximation Theorem, Arch. Math. (Brno) 45 (2009) 95-104 (arXiv-version)
15. Lie Group Structures on Symmetry Groups of Principal Bundles, J. Funct. Anal. 251 (2007) 254-288 (arXiv-version)
16. The Samelson Product and Rational Homotopy for Gauge Groups, Abh. Math. Sem. Univ. Hamburg 77 (2007) 219-228 (arXiv-version)
17. Smooth Extensions and Spaces of Smooth and Holomorphic Mappings, J. Geom. Symmetry Phys. 5 (2006) 118-126 (arXiv-version)

Preprints:

1. Functorial aspects of the reconstruction of Lie groupoids from their bisections (with Alexander Schmeding), 16 pp.
2. (Re)constructing Lie groupoids from their bisections and applications to prequantisation (with Alexander Schmeding), 45 pp.
3. Topological group cohomology of Lie groups and Chern-Weil theory for compact symmetric spaces, 25 pp.

Notes and Theses:

1. Higher structures in differential geometry Lecture notes for a lecture given at the University of Hamburg, 2013 (preliminary draft, comments are welcome!)
2. Infinite-dimensional Lie Theory for Gauge Groups, Dissertation, TU Darmstadt, 2006
3. Central Extensions of Gauge Groups, Diploma Thesis, TU Darmstadt 2003
4. Differentialgeometrie, Lecture notes, emerged from a lecture given by J. Wallner, TU Darmstadt, 2001

Teaching:

Third Party Funding:

• Research Network "String Geometry"
• Research Training Group 1670 "Mathematics inspired by String Theory and Quantum Field Theory"
• Collaborative Research Center SFB 676 "Particles, Strings, and the Early Universe"

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

• Infinite-dimensional Structures in Higher Geometry and Representation Theory (2015)
• From Poisson to String Geometry (2012)
• New Perspectives in Topological Field Theories (2012)
• Higher Structures in Topology and Geometry VI (2012)
• Higher Structures in Topology and Geometry V (2011)
• 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)

Notes or slides for some talks that I gave:

• 07.06.2011, A smooth model for the string group, Topology and Analysis in Interaction (Cortona, Italy), sildes
• 08.01.2011, Cohomology Theories for Lie Groups, Seminar Sophus Lie 2011 (Marburg, Germany), sildes
• 24.05.2009, Higher connected covers by categorified principal bundles, Workshop on Topological Field Theories, (Northwestern University, USA), Extended notes by Alex Hoffnung
• 19.05.2008, Gauge groups for lifting gerbes and principal 2-bundles, University of Paderborn (Germany) slides
• 31.05.2007, A bundle-theoretic perspective to Kac-Moody groups and their generalisations, Colloquium of the Graduiertenkolleg Gruppen und Geometrie, (Göttingen, Germany) slides
• 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)
• 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