The scientific event starts on May 31 with a one-day Summer School, followed by a Research Workshop (June 1-3). On Sunday June 4-th, the meeting will close with a mentoring day. The encounter will bring together several experts in Algebraic Combinatorics, Algebraic Topology and Commutative Algebra in a center famous for the P.R.A.G.M.A.T.I.C., an Algebra and Geometry summer school that have been the incubator for many new young researchers in these fields. Download the poster here.

If you are interested in participating, please,
send an email to Ivan Martino or Alex Suciu.

In its simplest form, the Bernstein-Gelfand-Gelfand (BGG) correspondence associates a chain complex of free graded modules over a polynomial algebra to a module over an exterior algebra in way that generalizes the classical Koszul complex. The resonance varieties measure deviations from exactness of this chain complex in a concrete, geometric fashion.

In these introductory lectures, we will explain the algebraic notions underlying these constructions, and present some structural results. We will illustrate the general theory with a number of examples, such as the computation of resonance varieties of the Stanley-Reisner ring associated to a simplicial complex, or of the Orlik-Solomon algebra associated to a hyperplane arrangement. We will indicate how computer algebra can help investigate resonance varieties explicitly, using Macaulay2, and we will conclude with a brief overview of some topics of current research.

Polytopes (like cubes, pyramids, prisms)... have always been studied since the beginning of mankind. They exist in nature and are replicated by architects.
In the past century, with the advent of computers, they've regained central interests also in connection with optimization problems and digital data.

We will focus on the notion of the "graph" of the polytope, namely, the structure formed by its vertices and edges. This apparently easy subject hides important open questions, like the polynomial Hirsch conjecture.
It also hides a fascinating connection with the intersection graphs of arrangements of lines. This opens bridges to old and new techniques in commutative algebra and algebraic geometry.

• G. Denham, A. Suciu, S. Yuzvinsky, Abelian duality and propagation of resonance, preprint;
• G. Denham, Higher resonance varieties of matroids, Configuration Spaces: Geometry, Topology and Representation Theory, 41-66, Springer INdAM series, vol. 14, Springer, Cham, 2016, another link here;
• A. Suciu, Around the tangent cone theorem, Configuration Spaces: Geometry, Topology and Representation Theory, 1-39, Springer INdAM series, vol. 14, Springer, Cham, 2016, another link here;
• S. Papadima, A. Suciu, Jump loci in the equivariant spectral sequence, Mathematical Research Letters 21 (2014), no. 4, 863-883, another link here.

• G. Ziegler, Lectures on Polytopes
• F. Santos, Recent progress on the combinatorial diameter of polytopes and simplicial complexes;
• B. Benedetti, M. Varbaro, On the dual graph of a Cohen-Macaulay algebra, IMRN 2015, 17, 8085-8115.