Since I have moved to The
University of Adelaide, this
web page is no longer maintained!
Thomas
Leistner
Juniorprofessor
am
Bereich Analysis
und Differentialgeometrie (AD)
Fachbereich Mathematik der Universität
Hamburg
Bundesstrasse 55, 20146 Hamburg, Germany
Phone: +49 (0)40 428385147, Fax: +49 40 42838 5190, Room:
Geomatikum 222
Mitglied im Zentrum
für Mathematische Physik und im SFB 676 "Particles, Strings and
the Early Universe: the Structure of Matter and Space-Time" im
Teilprojekt A6: "Mathematical
Aspects
of String Compactification".
Teaching
Sommersemester
2009:
Wintersemester 2008/09:
Teaching
in
previous years
Research
Preprints,
Publications
and Theses:
- Half
flat
structures and special holonomy (with V. V. Cortés, L.
Schäfer, and F. Schulte-Hengesbach), arxiv:0907.122 , 40
pages.
- Conformal
structures
with $G_{2(2)}$-ambient metrics (with P. Nurowski), preprint
at arxiv:0904.0186 ,
13 pages.
- Ambient
metrics
for n-dimensional pp-waves (with P. Nurowski), preprint at arXiv:0810.2903, 17
pages.
- Connected
subgroups
of SO(2,n) acting irreducibly on $\R^{2,n}$ (with A. J. Di
Scala), to appear in Israel Journal
of Mathematics, preprint available as ESI preprint no. 2033,
22
pages.
- Cones
over
pseudo-Riemannian manifolds and
their holonomy (with D. V. Alekseevsky, V. Cortés, and A.
Galaev), to appear in Crelle's
Journal, preprint available as ESI preprint no. 1939,
47
pages.
- Holonomy
groups
of Lorentzian manifolds:
classification, examples and applications. (with Anton Galaev), in Recent
Developments in Pseudo-Riemannian Geometry, ESI-Series on
Mathematics and Physics, European Mathematical
Society, 2008.
- Recent
development
in pseudo-Riemannian
holonomy theory (with Anton
Galaev), 2006, to appear in Handbook
of Pseudo-Riemannian Geometry,
IRMA Lectures in Mathematics and Theoretical Physics.
- Irreducibly
acting
subgroups of $Gl(n,\rr)$ (with Antonio J. Di Scala and
Thomas Neukirchner), 2005, to
appear in the Handbook of
Pseudo-Riemannian Geometry, IRMA Lectures in
Mathematics and Theoretical Physics, math.DG/0507047.
- Higher
symmetries
of the square of the
Laplacian (with Michael Eastwood), in: Symmetries and Overdetermined Systems of
Partial Differential Equations, Vol. 144 of IMA
Volumes in Mathematics and Its Applications, 2008: 319-338, link to toc,
also at math.DG/0610610
.
- Ambient
connections
realising conformal
Tractor holonomy (with Stuart Armstrong), Monatshefte
fuer Mathematik, 152
(2007), no. 4: 265-282, journal
link.
- On
the
classification of Lorentzian holonomy groups, Journal of Differential Geometry, 76, no. 3: 423-484, journal
link.
- Screen
bundles
of Lorentzian manifolds and some generalisations of pp-waves, Journal of Geometry
and Physics, 56 (2006),
no. 10: 2117 -- 2134, journal
link (also as math.DG/0507048).
- Conformal
holonomy
of C-spaces, Ricci-flat, and Lorentzian manifolds, Differential Geometry and
its Applications, 24
(2006), no. 5: 458 -- 478, journal
link, also at math.DG/0501239).
- Holonomy and Parallel Spinors in
Lorentzian Geometry, Dissertation, Humboldt-Universität zu
Berlin, 2003, published in Logos-Verlag
Berlin, 2004.
- Towards
a
classification of Lorentzian holonomy groups. Part II: Semismple,
non-simple weak-Berger algebras,
2003, math.DG/0309274.
- Towards
a
classification of Lorentzian
holonomy groups, 2003, math.DG/0305139.
- Berger
algebras,
weak-Berger algebras and Lorentzian holonomy, Sfb
288-preprint no. 567, 2002: ftp://ftp-sfb288.math.tu-berlin.de/pub/Preprints/preprint567.ps.gz.
- Lorentzian
manifolds
with special holonomy and parallel spinors, in: The
proceedings of the 21st winter school "Geometry and Physics",
Srni, January 13-20, 2001, Supplemento ai Rendiconti del Circolo
Matematico di Palermo, Nr. 69, pp. 131-159, 2002 (This
is an extended version of the SFB 288 preprint
no.
468 wit h some additional results.)
- Das Huygenssche Prinzip fuer den
Diracoperator auf Lorentzmannigfaltigkeiten (The Huygens
priciple for the Dirac operator on Lorentzian manifolds), diploma
thesis, Humboldt University Berlin, 1999,
zipped ps-file.
Recent
talks:
- Cones over pseudo-Riemannian
manifolds and their holonomy, talk given at: Seminario de Xeometria e
Topoloxıa, Universidade de Santiago de Compostela, July 18, 2007,
at
Forschungsseminar
Differentialgeometrie, Potsdam University, July 19, 2007, at the Pure
Mathematics Colloquium of the Department of Mathematics, Hamurg
University, February 5, 2008, and at the Seminar for Differential
Geometry, Mathematics Institute, Humboldt University, February 13,
2008.
- Recent developments in
pseudo-Riemannian holonomy theory: classification, examples, and applications, invited talk at
the Symposium
on Differential Geometry, Annual conference of the Deutsche
Mathematiker Vereinigung (Association
of German Mathematicians), Berlin, March 25 – March 30, 2007.
- Holonomy groups of Lorentzian
manifolds, invited lecture
at the IVth
International
Meeting on Lorentzian Geometry, Santiago de
Compostela, February 5 – 8, 2007.
- Some results about
conformal Tractor holonomy, Humboldt University Berlin,
Seminar
on
Differential Geometry, abstract.
- Ambient connections
realising conformal Tractor holonomy,
Poster
at the IMA 2006 Summer
programm Symmetries and
Overdetermined Systems of Partial Differential Equations, July
15
- August 4, 2006, University of Minnesota.
- Conformal holonomy of
Lorentzian manifolds, 08/04/2005, IGA,
University of Adelaide, pdf-file
of
the slides.
- Transitivity of
Lorentzian holonomy systems and some generalisations of pp-waves, Workshop
on
Differential Geometry and Mathematical Physics, Humboldt
University of Berlin,
July 14 - 16, 2004.
- Lorentzian holonomy
groups (with application to parallel spinors). Different
versions of this talk I gave at several occasions: at the <>Black
Sea EDGE-Workshop on Differential Geometry,
Albena, Bulgaria,
July 7 - 13, 2003 , at
the Workshop
on
Differential Geometry:
Transformation Groups, Holonomy and
Spinors in
Pseudo-Riemannian Geometry, Humboldt University of
Berlin,
September 23 - 25, 2003, at the IGA
seminar<>, at the Colloquium
of the Priority programm Global
Differential Geometry, Leipzig 23.-25. Juli 2004, and at the
48th Annual Meeting of
the Australian Mathematical Society, Melbourne, September 28
- October 1, 2004. Here
is the most comprehensive version of it.
Recent
and
upcoming conferences:
- 2006
IMA Summer Programme: Symmetries and Overdetermined Systems of Partial
Differential Equations, July 17 - August 4, 2006, Minneapolis;
- IV
International Meeting on Lorentzian Geometry, Santiago de Compostela,
February
5 - 8, 2007;
- 2007
Annual Meeting of the German Mathematical Society, March 25 -
30,
2007, Berlin;
- 2007 Midwest
Geometry Conference, to be held in the honour of Tom P. Branson
(1953 -2006), May 18 - 20, 2007, Iowa City.
- Oberwolfach Seminar Recent Developments in Conformal
Differential Geometry,
Mathematisches
Forschungsinstitut Oberwolfach,
November 18th - November 24th, 2007.
- Workshop
"Holonomy
Groups and Applications in String Theory", Hamburg
University, July, 14-18, 2008.
- Lorentzian
Geometry.
Analysis
and Geometry of pseudo-Riemannian Manifolds , Alfried
Krupp Kolleg Greifswald, July 20-22, 2009.
Last update: April 01, 2009 by T.
Leistner