RWTH Aachen: Hierarchie und Symmetrie in mathematischen Modellen
Ein Graduiertenkolleg, gefördert von der DFG.

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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

Location und dates

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


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

Students preparations

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


The pictures of the summer school.


Anmerkungen zu diesen Seiten bitte an Felix Noeske. Letzte Änderung: Dienstag, 28. Aug. 2007 (08:32:00 CEST)