Combinatorial Methods in Topology and Algebra

1 Introduction.- 2 Part I.- 3 Extremal graph theory and face numbers of flag triangulations of manifolds.- 4 Combinatorial stratifications and minimality of 2-arrangements.- 5 Rota's conjecture, the missing axiom, and prime cycles in toric varieties.- 6 Random triangular groups.- 7 Generalized involution models of projective reflection groups.- 8 Universal Gröbner bases for maximal minors of matrices of linear forms.- 9 Milnor fibrations of arrangements.- 10 Decompositions of Betti diagrams of powers of monomial ideals.- 11 Matroids over a ring.- 12 A Minimal Irreducible Triangulation of S3.- 13 Tropical Oriented Matroids.- 14 A combinatorial classification of Buchsbaum simplicial posets.- 15 Differences Between Nonnegative Polynomials and Sums of Squares.- 16 Interpolation, box splines, and lattice points in polytopes.- 17 Root polytopes of crystallographic root systems.- 18 Product formulas for volumes of flow polytopes.- 19 On the Topology of the Cambrian Semilattices.- 20 cd-index for CW-posets.- 21 Bipartite Rigidity.- 22 Balanced manifolds and pseudomanifolds.- 23 Some combinatorial constructions and relations with Artin groups.- 24 Deterministic Abelian Sandpile and square-triangle tilings.- 25 A special feature of quadratic monomial ideals.- 26 Resonant bands, local systems and Milnor fibers of real line arrangements.- 27 Full research papers.- 28 On Highly Regular Embeddings.- 29 Positive sum systems.- 30 The Sn+1 action on spherical models and supermaximal models of tipe An-1.- 31 h-vectors of matroid complexes.