The 24th National Algebra School
EMS Summer School on Multigraded Algebra and Applications
1724 August 2016, Moieciu de Sus, Romania
We gratefully acknowledge the support from the European Mathematical Society
and the Foundation Compositio Mathematica.
Slides available for download (.pdf files):
Course I: Monomial and binomial ideals, by Juergen Herzog and Apostolos Thoma

Juergen Herzog, Universitaet DuisburgEssen, 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: BiCohenMacaulay 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]
Course II: Applicable combinatorial commutative algebra, by Thomas Kahle and Ezra Miller

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 25: Real applied multigraded commutative algebra, cont'd [Notes]
Contributed talks:
 Hara Charalambous, Binomial fibers and indispensable binomials.
[Slides]
 Alessio D'Ali, Resolutions of letterplace and coletterplace 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 JuhnkeKubitzke, Lefschetz properties for balanced 3polytopes.
[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]