Generalities on Hilbert-series, rational generating functions and real rooted polynomials.
Generalities on simplicial complexes and their Stanley-Reisner rings.
Alexander duality, multigraded modules and finite free resolutions.
Koszul-algebras and infinite free resolutions.
Lefschetz-algebras and g-theorems.
Vertex cover algebras.
Groebner bases with squarefree initial ideals.
Transformations preserving real rootedness and applications to algebra.
Stanley decompositions, partionable simpicial complexes and prime filtrations.
Calendars of seminars
July 14 2008
Free Resolutions (Herzog)
Hilbert series (Welker)
July 15 2008
Resolutions of powers of ideals (Herzog)
Kruskal-Katona snd Macaulay Theorems (Welker)
July 17 2008
Resolutions of powers of ideals II (Herzog)
Koszul algebras (Welker)
July 18 2008
Edge ideals (Herzog)
Real rooted polynomials (Welker)
July 21 2008
Vertex cover algebras (Herzog)
The Neggers-Stanley conjecture and Koszula algebras (Welker)
July 22 2008
Stanley depth I (Herzog)
Lefschetz algebras I (Welker)
July 24 2008
Stanley depth II (Herzog)
Lefschetz algebras II (Welker)
July 25 2008
Algebraic shifting I (Herzog)
Algebras with special Groebner basis I (Welker)
July 29 2008
Algebraic shifting II (Herzog)
Algebras with special Groebner basis II (Welker)
July 31 2008 and August 1 2008
Presentations by the participants
(Anda Georgiana Olteanu - Loredana Sorrenti) When are lexsegment ideals componentwise linear or Gotzmann?
(Le Din Nam) When are vertex cover algebras of quasi forests standard graded?
(Benjamin Nill) The linear ordering polytope is Gorenstein.
(Benjamin Nill - Katherin Vorwek) The Stanley depth of certain monomial ideals.
(Eric Emtander - Veronica Crispin Quinonez) When are symbolic powers of certain classes of monomial ideals componentwise linear?
(Matteo Varbaro - Alexandru Constantinescu) The Hilbert series of the algebra of essential vertex covers for a graph.
(Giancarlo Rinaldo) Find and implement a "good" algorithm for determining the Stanley depth of a monomial ideal.
(Bruno Benedetti - Alexandru Constantinescu - Katherin Vorwek) Give a term order of the defining ideal of the Grassmannian that is Stanley-Reisner ideal of a polytope.
(Gesa Kempf - Martina Kubitzke) The behavior of t-uples of generic linear forms on graded modules over the exterior algebra.
(Vincenzo Micale - Cristina Bertone) The Hilbert series and the ohen Macaulay type of the algebra of essential vertex covers for unmixed graphs..
(Oscar Fernandez) Characterization of the graphs G whose corresponding edge ideal I(G) is Stanley-Reisner of a shellable simplicial complex.
(Anargyros Katsabekis) The Groebner basis of the defining ideal of the vertex cover algebra of higher dimensional trees.
(Anargyros Katsabekis) Upper bounds on the triangle density of graphs using Bar resolution.
(Mircea Cimpoeas) The relation of Stanley of a module M and its depth.
(Gioia Failla) The polynomial growth of Betti numbers of powers of ideals is independent on the homological degree.
(Leila Sharifan - Matteo Varbaro) The linear quotients ideals are componentwise linear and computation of their Betti numbers.