Pragmatic 2008

Scientific activities

During the courses the teachers introduced the basic notions and techniques from commutative algebra and combinatorics for studying the polynomials h_A(t), for the use of Alexander duality and the analysis of vertex covers and Stanley decompositions. During the seminars they also exhibited the basic techniques on important examples and example classes and related the subject to neighboring fields. In particular, they addressed the following topics with related open research problems:
  1. Generalities on Hilbert-series, rational generating functions and real rooted polynomials.

  2. Generalities on simplicial complexes and their Stanley-Reisner rings.

  3. Alexander duality, multigraded modules and finite free resolutions.

  4. Koszul-algebras and infinite free resolutions.

  5. Lefschetz-algebras and g-theorems.

  6. Vertex cover algebras.

  7. Groebner bases with squarefree initial ideals.

  8. Transformations preserving real rootedness and applications to algebra.

  9. Stanley decompositions, partionable simpicial complexes and prime filtrations.

Calendars of seminars

July 14 2008

  1. Free Resolutions (Herzog)

  2. Hilbert series (Welker)

July 15 2008

  1. Resolutions of powers of ideals (Herzog)

  2. Kruskal-Katona snd Macaulay Theorems (Welker)

July 17 2008

  1. Resolutions of powers of ideals II (Herzog)

  2. Koszul algebras (Welker)

July 18 2008

  1. Edge ideals (Herzog)

  2. Real rooted polynomials (Welker)

July 21 2008

  1. Vertex cover algebras (Herzog)

  2. The Neggers-Stanley conjecture and Koszula algebras (Welker)

July 22 2008

  1. Stanley depth I (Herzog)

  2. Lefschetz algebras I (Welker)

July 24 2008

  1. Stanley depth II (Herzog)

  2. Lefschetz algebras II (Welker)

July 25 2008

  1. Algebraic shifting I (Herzog)

  2. Algebras with special Groebner basis I (Welker)

July 29 2008

  1. Algebraic shifting II (Herzog)

  2. Algebras with special Groebner basis II (Welker)

July 31 2008 and August 1 2008

Presentations by the participants