Fachbereich Mathematik 
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Christoph Wockel

Juniorprofessor
Fachbereich Mathematik
Bereich 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: Tuesday 9.30 - 10.30

Fields of Research Interest:

My field of research are cohomological structures in global analysis in the presence of symmetry. These symmetries are mostly described by Lie groups (which may be infinite-dimensional) or Lie groupoids and their associated Lie algebras and Lie algebroids. More precisely, I often work with the following concepts:
  • 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:

My publications on Google Scholar, arXiv, MathSciNet, Zentralblatt MATH
  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. A Cocycle Model for Topological and Lie Group Cohomology, (with Friedrich Wagemann) 32 pp., Trans. Amer. Math. Soc. (to appear) (arXiv-version)
  3. Making lifting obstructions explicit, (with Karl-Hermann Neeb and Friedrich Wagemann) Proc. Lond. Math. Soc. (3) 106 (3) (2013) 589-620 (arXiv-version)
  4. Universal central extensions of gauge algebras and groups, (with Bas Janssens) J. Reine Angew. Math. 682 (2013) 129-139 (arXiv-version)
  5. A Smooth Model for the String Group, (with Thomas Nikolaus and Christoph Sachse) Int. Math. Res. Not. IMRN 16 (2013) 3678-3721 (arXiv-version)
  6. Topological Group Cohomology with Loop Contractible Coefficients, (with Martin Fuchssteiner), Topology Appl., 159 (2012) 2627-2634 (arXiv-version)
  7. The diffeomorphism supergroup of a finite-dimensional supermanifold (with Christoph Sachse), Adv. Theor. Math. Phys. 15 (2011) 1-39 (arXiv-version)
  8. 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)
  9. Principal 2-bundles and their gauge 2-groups, Forum Math. 23 (3) (2011) 565-610 (arXiv-version)
  10. Non-integral central extensions of loop groups, Contemp. Math. 519 (2010) 203-214 (arXiv-version)
  11. Central Extensions of Groups of Section (with Karl-Hermann Neeb), Ann. Glob. Anal. Geom. 36 (4) (2009) 381-418 (arXiv-version)
  12. Equivalences of Smooth and Continuous Principal Bundles with Infinite-Dimensional Structure Group (with Christoph Müller), Adv. Geom., 9 (4) (2009) 605-626 (arXiv-version)
  13. A Generalisation of Steenrod's Approximation Theorem, Arch. Math. (Brno) 45 (2009) 95-104 (arXiv-version)
  14. Lie Group Structures on Symmetry Groups of Principal Bundles, J. Funct. Anal. 251 (2007) 254-288 (arXiv-version)
  15. The Samelson Product and Rational Homotopy for Gauge Groups, Abh. Math. Sem. Univ. Hamburg 77 (2007) 219-228 (arXiv-version)
  16. Smooth Extensions and Spaces of Smooth and Holomorphic Mappings, J. Geom. Symmetry Phys. 5 (2006) 118-126 (arXiv-version)

Preprints:

  1. The Lie group of bisections of a Lie groupoid (with Alexander Schmeding), 30 pp.
  2. 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:

SS 2014   Analysis III
SS 2014   Lecture: Algebraische und geometrische Strukturen in der Mathematik - Ein Überblick für Lehramtsstudierende
SS 2013   Lecture: Higher Structures in Differential Geometry
WS 12/13   Lecture: Algebra II
SS 2012   Lecture: Algebra
WS 11/12   Seminar: Funktionalanalysis
SS 2011   Lecture: Funktionalanalysis
WS 10/11   Softwarepraktikum
SS 2010   Seminar: Cohomology of Lie Algebras
SS 2010   Übungen zur Analysis 2 (von Ingo Runkel)
WS 09/10   Lecture: Infinite-dimensional Lie groups with a perspective to Mathematical Physics


Third Party Funding:

I am member of the following third party funded research projects:


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

I am part of the organising committee of the Seminar Bremen - Hamburg - Kiel.

Notes or slides for some talks that I gave:


 
  Seitenanfang  Impress 2014-11-26, Christoph Wockel