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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
My publications on Google Scholar, arXiv, MathSciNet, Zentralblatt MATH
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Integrating central extensions of Lie algebras via Lie 2-groups (with Chenchang Zhu) 34 pp., J. Eur. Math. Soc. (to appear) (arXiv-version)
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The Lie group of bisections of a Lie groupoid (with Alexander Schmeding),
Ann. Glob. Anal. Geom. 48 (1) (2015) 87-123 (arXiv-version)
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A Cocycle Model for Topological and Lie Group Cohomology
(with Friedrich Wagemann), Trans. Amer. Math. Soc. 367 (2015) 1871-1909
(arXiv-version)
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Making lifting obstructions explicit,
(with Karl-Hermann Neeb and Friedrich Wagemann) Proc. Lond. Math. Soc. (3) 106 (3) (2013) 589-620
(arXiv-version)
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Universal central extensions of gauge algebras and groups,
(with Bas Janssens) J. Reine Angew. Math. 682 (2013) 129-139
(arXiv-version)
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A Smooth Model for the String Group,
(with Thomas Nikolaus and Christoph Sachse) Int. Math. Res. Not. IMRN 16 (2013) 3678-3721
(arXiv-version)
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Topological Group Cohomology with Loop Contractible Coefficients,
(with Martin Fuchssteiner), Topology Appl., 159 (2012) 2627-2634
(arXiv-version)
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The diffeomorphism supergroup of a
finite-dimensional supermanifold
(with Christoph Sachse),
Adv. Theor. Math. Phys. 15 (2011) 1-39
(arXiv-version)
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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)
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Principal 2-bundles and their gauge 2-groups,
Forum Math. 23 (3) (2011) 565-610
(arXiv-version)
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Non-integral central extensions of loop groups,
Contemp. Math. 519 (2010) 203-214
(arXiv-version)
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Central Extensions of Groups of Section
(with Karl-Hermann Neeb),
Ann. Glob. Anal. Geom. 36 (4) (2009) 381-418
(arXiv-version)
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Equivalences of Smooth and Continuous Principal Bundles with
Infinite-Dimensional Structure Group
(with Christoph Müller),
Adv. Geom., 9 (4) (2009) 605-626
(arXiv-version)
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A Generalisation of Steenrod's Approximation Theorem,
Arch. Math. (Brno) 45 (2009) 95-104
(arXiv-version)
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Lie Group Structures on Symmetry Groups of Principal
Bundles,
J. Funct. Anal. 251 (2007) 254-288
(arXiv-version)
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The Samelson Product and Rational Homotopy
for Gauge Groups,
Abh. Math. Sem. Univ. Hamburg 77 (2007) 219-228
(arXiv-version)
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Smooth Extensions and Spaces of Smooth and
Holomorphic Mappings,
J. Geom. Symmetry Phys. 5 (2006) 118-126
(arXiv-version)
Preprints:
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Functorial aspects of the reconstruction of Lie groupoids from their bisections (with Alexander Schmeding),
16 pp.
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(Re)constructing Lie groupoids from their bisections and applications to prequantisation (with Alexander Schmeding),
45 pp.
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Topological group cohomology of Lie groups and Chern-Weil theory for compact
symmetric spaces,
25 pp.
- Higher structures in differential geometry
Lecture notes for a lecture given at the University of Hamburg, 2013 (preliminary draft, comments are welcome!)
- Infinite-dimensional Lie Theory for Gauge Groups,
Dissertation, TU Darmstadt, 2006
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Central Extensions of Gauge Groups,
Diploma Thesis, TU Darmstadt 2003
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Differentialgeometrie,
Lecture notes, emerged from a lecture given by
J. Wallner, TU Darmstadt, 2001
I am member of the following third party funded research projects:
I am part of the organising committee of the Seminar Bremen - Hamburg - Kiel.
- 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
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