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Zur Bewerbung
Veranstaltungen
Sommerschulen
2002
2003
2004
2005
2006
2007
Personen
Themenschwerpunkte
Kontakt
Zusammenfassung
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Sommerschule 2007:
Algorithmic D-module theory.
Several algorithmic aspects of D-module theory:
- The Weyl algebra D=A_n(k). Filtrations and graduations. Simplicity
and left ideals.
- Division theorem in D=A_n(k), Gröbner bases
- Modules over the Weyl algebra, dimension and
multiplicity, characteristic variety
- Bernstein inequality. holonomic D-modules
- b-functions, k[x]_f is holonomic
- Computational methods in logarithmic D-modules
- Annihilating ideals of meromorphic functions
- K[x]/LK[x]=D/(LD+Dd). Integration algorithm in one variable
- D/I holonomic implies D/(I+dD) holonomic
- Middle dimensional logarithmic cohomology group as K[x]/ \sum_i
L_i K[x]. Algorithm and implementation
- Correctness of the algorithm. Hypergeometric integral and the
logarithmic cohomology group. Hypergeometric integral and the de Rham
cohomology group.
- Hypergeometric functions
- Toric varieties
- A-hypergeometric systems a la GKZ
- Toric modules, Euler-Koszul functor
- Rank-jumping
- Slopes, regularity
- Monodromy
The summer school takes place in the week from 3-7 September
2007, at the Söllerhaus in
Kleinwalsertal (Austria)
(english).
Arrival day is Sunday the 2nd of September.
Detailed location and travelling information can be found on the homepage of the
Söllerhaus (in German).
For information in english the Söllerhaus pointed us to a
flyer, which was created for a
workshop some years ago. The nearest airport is
Friedrichshafen.
From there, there is a direct transfer service for 20 Euros to the
Söllerhaus, which one should reserve in advance. Other airports are Stuttgart and Munich, but the transfer to
the Söllerhaus is more complicated. If, for some reason, you prefer to
land near Aachen, then the nearest airports are Duesseldorf, Koeln-Bonn, and
Maastricht. We reserved 3 university buses (each for 8 persons) from
Aachen to the Söllerhaus leaving at
9:00 (9:00 am) on Sunday the 2nd (in front of the Hauptgebäude) and back
to Aachen at 14:00 (2:00 pm) on Friday the 7th. A fourth bus will collect the
participants of the summer school arriving at the Duesseldorf airport between
14:00 and 14:30 on Sunday the 2nd of September and take them to the
Söllerhaus directly. This bus will leave Aachen at 13:00 (1:00 pm)
(in front of the Hauptgebäude). The bus trip (from Aachen or Duesseldorf
to the Söllerhaus) will take approximately 7 hours.
If you are interested in renting a car during or after the school check www.franke-autovermietung.de.
If you are not already on the list below
and want to participate please
send me an email.
If you are not one of the invited speakers you should cover your travel
expenses. There are no registration fees.
The accommodation will also be in the Söllerhaus. We reserved 33 beds,
mainly in double rooms (the single rooms are primarily for the invited
experts and the seniors). Please do not contact the Söllerhaus directly, but
send me an email.
The participants of the summer school will prepare
introductory talks about several aspects of D-module theory and related
subjects. The content of these talks will be suggested by the experts. The
more advanced talks will be held by the experts:
- Francisco-Jesús Castro-Jiménez (Sevilla)
- Javier Fernández de Bobadilla de Olazabal (UNED)
- Nobuki Takayama (Kobe)
- Uli Walther (Purdue)
The detailed plan for all the talks will be placed here.
On Wednesday we will organize a walking-tour in the region.
- J.-E. Björk: Rings of Differential Operators,
- North-Holland, 1979.
- A. Borel et al.: Algebraic D-modules,
- Perspectives in Mathematics, Academic Press, 1987.
- R. Bott, Raoul and L.W. Tu: Differential forms in algebraic topology,
- Graduate Texts in Mathematics, 82, Springer, 1982.
- E. Brieskorn: Die Monodromie der isolierten Singularitäten von Hyperflächen,
- Manuscripta Math. 2 1970, 103-161.
- S.C. Coutinho: A Primer of Algebraic D-modules,
- LMS, Student Texts 33, 1995.
- Grauert and Remmert, Coherent Analytic sheaves,
- Grundlehren der Mathematischen Wissenschaften, 265, Springer, 1984.
- G.-M. Greuel, G. Pfister: A Singular Introduction to Commutative Algebra,
- Springer, 2002.
- J.C. McConnell, J. C. Robson: Noncommutative Noetherian Rings,
- Graduate Studies in Mathematics 30, AMS, 2000.
- M. Saito, B. Sturmfels, N. Takayama: Gröbner deformations of
hypergeometric differential equations,
- Algorithms and Computation in Mathematics, 6. Springer-Verlag, Berlin, 2000.
- W. Plesken: Differentialalgebra I/II,
- Vorlesungsskript WS2006/SS2007, Lehrstuhl B für Mathematik, RWTH-Aachen.
Uli Walther: Prerequisites to the Summerschool
Moritz Schröer: Kategorien und
Funktoren, derivierte Funktoren und der Koszul-Komplex
Markus Lange-Hegermann: Affine algebraische
Geometrie und die Weylalgebra
Mohamed Barakat
Lehrstuhl B für Mathematik
Templergraben 64
Room 328
Tel.: +49-241-80-93507
Email: mohamed.barakat@post.rwth-aachen.de
The pictures of the summer school.
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