Slides available for download (.pdf files):

Course I: Monomial and binomial ideals, by Juergen Herzog and Apostolos Thoma

• Juergen Herzog, Universitaet Duisburg-Essen, Germany
  • Lecture 1: Lattice ideals and lattice basis ideals [Slides]
  • Lecture 2: Ideals and Algebras defined by Isotone Maps between Posets [Slides]
  • Lecture 3: Deformations and separations [Slides]
  • Lecture 4: Bi-Cohen-Macaulay graphs [Slides]
  • Lecture 5: Rigidity and separability of simplicial complexes and toric rings [Slides]
  • Exercises and open problems: [Slides]
• Apostolos Thoma, University of Ioannina, Greece
  • Lecture 1: Toric ideals [Slides]
  • Lecture 2: Toric ideals and Groebner bases [Slides]
  • Lecture 3: Toric ideals and toric ideals of graphs [Slides]
  • Lecture 4: Toric ideals of graphs [Slides]
  • Lecture 5: Bouquet Algebra of Toric ideals [Slides]

• Thomas Kahle, Magdeburg University, Germany
  • Lecture 1: What is a Markov basis and what is it good for? [Notes]. [Expanded notes].
  • Lecture 2: Decompositions and connectivity [Notes]
  • Lecture 3: Irreducible decomposition [Notes]
  • Lectures 4 and 5: Irreducible decomposition of binomial ideals [Notes]
• Ezra Miller, Duke University, USA
  • Lecture 1: Real applied multigraded commutative algebra [Slides]
  • Lectures 2-5: Real applied multigraded commutative algebra, cont'd [Notes]

• Hara Charalambous, Binomial fibers and indispensable binomials. [Slides]
• Alessio D'Ali, Resolutions of letterplace and co-letterplace ideals. [Slides]
• Michela Di Marca, Connectedness and regularity for dual graphs of projective curves. [Slides]
• Amin Seyed Fakhari, Stanley depth of powers of monomial ideals associated to graphs. [Slides]
• Martina Juhnke-Kubitzke, Lefschetz properties for balanced 3-polytopes. [Slides]
• Ayesha Asloob Qureshi, Ideals and algebras associated with isotone maps between posets. [Slides]
• Sara Saeedi Madani, On polyomino ideals. [Slides]
• Tomasz Szemberg, On the containment problem. [Slides]