The Interaction of Geometry and Representation
Theory.

Organizers: 
Andreas Cap (University of Vienna) 
andreas.cap@univie.ac.at 
Alan Carey (Australian National University) 
alan.carey@gmail.com 

A. Rod Gover (University of Auckland) 
r.gover@auckland.ac.nz 

C. Robin Graham (University of Washington) 
robin@math.washington.edu 

Jan Slovak (Masaryk University) 
slovak@math.muni.cz 
Schedule for week 1 (September 3  7)
Mon. Sep. 3  no lectures  
Tue. Sep. 4  10:00 B. Doubrov (Minsk): Cone structures: definitions, local equivalence, examples Abstract  14:30 D. The (ANU): The gap phenomenon in parabolic geometries Abstract 
Wed. Sep. 5  10:00 P. Nurowski (Warsaw): Split signature 4dimensional metrics, real totally null planes and (2,3,5) distributions Abstract, Notes  14:30 T. Willse (ANU): Generic plane fields and special holonomy Abstract 
Thu. Sep. 6  10:00 K. Neusser (ANU): Some complexes of differential operators Abstract  14:30 J. Silhan (Brno): Invariant bilinear operators on AHS structures Abstract 
Fri. Sep. 7  10:00 P. Somberg (Prague): The branching problem for generalized Verma modules, with application to the pair (SO(7),G_{2}) Abstract 
Schedule for week 2 (with links to abstracts and presentations).
Background and aims: The algebraic machinery discovered by Bernstein, Gelfand, Gelfand and generalized by Lepowsky went unnoticed in differential geometry for many years. But, as exposed by Eastwood and collaborators, this beautifully and systematically packages into a single framework a vast collection of equations and theory central to geometry, mathematical physics, and analysis on manifolds. The scope for extension was then realized immediately, and there has been somewhat of a revolution in the way many questions are attacked and solved. This has revealed data and structures not previously conceived of, often with strong links to classical problems, and the differential BGG complexes are a prototypical example. In some cases there are strong links to integral geometry. Overall, it is an open problem how to best harness the new information, and we hope that our workshop will help making further steps towards a solution.
The application of representation theory to differential geometry is also suggesting novel and unexpected links between different geometric structures. For example the deformations of Riemannian structures are controlled by a complex originating in projective geometry. Related observations have already motivated new and successful treatments of classical problems. There is enormous scope for further exploration of this principle, which will certainly play a major role in the workshop.
In a completely different way, links between different geometric structures were introduced by Fefferman, and FeffermanGraham as a tool for treating the invariant theory of conformal, CR, and related parabolic geometries. These were their "ambient metric", "Fefferman metric" and "PoincareEinstein metric" constructions. The influence of these, and the general ideas they suggest, cannot be overstated; the AdS/CFT correspondence of Physics is a variation on this theme and indeed most mathematical and scattering approaches to this correspondence draw heavily on the formal theory of the constructions mentioned. In different and limited senses it is understood how to link these studies to the representation theory picture above, extending this understanding has the potential for great impact.
Specific topics for the activity inlcude:
Poster session and preprints: To give all participants the
opportunity to present their results, we will organize a poster
session as part of the conference. An important part of this activity
will be an online presentation of the posters, which will be
accessible from this page.
All participants also have the possibility to post preprints which are
related to their talk or which they would like to discuss during the
meeting via this page, to give others the opportunity to prepare for
the activity.
Proceedings: While we do not plan to publish proceedings, there will be a special issue of the journal Differential Geometry and its Applications associated to the workshop. All participants of the meeting are invited to contribute an article and all submitted articles will undergo regular peer review procedure following the same high standards as the regular issues of the journal. The five organisers of the meeting, Andreas Cap, Alan Carey, A. Rod Gover, C. Robin Graham, and Jan Slovák, will serve as Guest Editors. All participants of the workshop will obtain a free print of this special issue.
Submission and deadlines:
The contributions should be submitted the same way as the regular
papers of the DGA journal, i.e. as LaTeX produced pdffile sent by
email to dga@math.muni.cz (link to an arxiv preprint is welcome as
well). Please tell explicitly the contribution is meant for this special issue!
The Editors will very much appreciate to get the manuscripts before
December 31, 2012, the final deadline will be February 28, 2013.
Participants: The following people have agreed to take part in the activity.
J. Alt (Witwatersrand) 
P. Baird (Brest) 
H. Baum (Berlin) 
J. Bland (Toronto) 
R. Bryant (Berkeley) 
N. Buchdahl (Adelaide) 
D. Calderbank (Bath) 
S. Casey (Cambridge) 
A. D'Agnolo (Padova) 
B. Doubrov (Minsk) 
M. Dunajski (Cambridge) 
M. Eastwood (Canberra) 
V. Ejov (Adelaide) 
S. Gindikin (Rutgers) 
M. Hammerl (Vienna) 
K. Hirachi (Tokyo) 
A. Isaev (Canberra) 
A. Juhl (Uppsala) 
H. Kato (Osaka) 
T. Kobayashi (Tokyo) 
B. Kruglikov (Tromsø) 
S. Krysl (Prague) 
J.M. Landsberg (Texas A&M) 
C. LeBrun (SUNY Stony Brook) 
T. Leistner (Adelaide) 
G. Manno (Milano) 
L. Mason (Oxford) 
V. Matveev (Jena) 
T. Mettler (ETH Zurich) 
T. Morimoto (Kyoto) 
K. Neusser (Canberra) 
P. Nurowski (Warsaw) 
B. Ørsted (Arhus) 
M. Randall (Canberra) 
K. Sagerschnig (Canberra) 
J. Sawon (UNC Chapel Hill) 
G. Schmalz (Armidale) 
R. Schroff (Canberra) 
J. Silhan (Brno) 
P. Somberg (Prague) 
V. Soucek (Prague) 
A. TaghaviChabert (Brno) 
D. The (Canberra) 
P. Tod (Oxford) 
V. Tutcek (Prague) 
P. Vassiliou (Canberra) 
R. Wells (Jacobs) 
T. Willse (Canberra) 
J.A. Wolf (Berkeley) 
K. Yamaguchi (Sapporro) 
V. Zadnik (Brno) 
L. Zalabova (Zlin) 