Please refer to the website set up for this event by the organizers: https://sites.google.com/view/arrwest/home . All talks will take place in Middlesex College 107 (map).

The theory of hyperplane arrangements originated from classical enumerative problems in combinatorics, the study of configuration spaces in topology, and the study of braid groups and reflection groups in algebra. Today, the subject draws techniques, problems, and inspiration from algebra, combinatorics, topology, representation theory, singularity theory, invariant theory, and discrete geometry, and informs on these diverse areas as well. Hyperplane arrangements are linear representations of matroids, and their study provides new techniques for the study of enumerative questions related to matroids. Beginning with classical work of Arnol'd, Brieskorn, and Orlik-Solomon on the cohomology of the complement of a complex hyperplane arrangement, the relationship between the geometry, topology and combinatorics of these objects is a long-standing focal point in the subject. One aspect is the theory of cohomology jump loci, which provides a unifying framework for the study of a host of questions, both quantitative and qualitative, concerning a topological space and its fundamental group. These loci come in two basic flavors: the {em resonance varieties}, which are the jump loci for the homology of the cochain complexes arising from multiplication by degree one classes in the cohomology ring of the space, and the {em characteristic varieties}, which are the jump loci for cohomology with coefficients in rank one local systems. These varieties emerged some 20 years ago as a central object of study in the theory of hyperplane arrangements. The initial impetus for their study was geared towards understanding their precise nature (in terms of combinatorial data available in that context), and using this information to compute the homology of certain covering spaces, and numerical invariants attached to the fundamental group. As the field continued to develop, the study of jump loci started to expand to other classes of spaces and groups, revealing new and often unexpected phenomena. In the process, the relationship between the geometry and topology of a space and the qualitative nature of its jump loci came into sharper focus, leading to hitherto unexpected applications. A second current theme in arrangement theory also originates in work of Brieskorn and Solomon on reflection groups and invariant theory, in the context of singularity theory. Kyoji Saito's theory of logarithmic derivations has led to an extensive study of the homological properties of modules of logarithmic derivations on arrangement complements and, in particular, an elusive conjecture of Terao from 1985 on their freeness. A relatively recent application of this work was a striking paper of Abe, Barakat, Cuntz, Hoge, and Terao, who used it to prove a conjecture of Sommers and Tymoczko on the cohomology of Hessenberg varieties. Current work of Abe and collaborators has led to some interesting further directions. Finally, modern singularity theory applied to the complements of complex hypersurfaces offers some tantalizing prospects to unify the themes above and lead to further advances. In particular, the study of D-modules and the Bernstein-Sato polynomial of arrangements has made recent progress (Walther) that relates to the Solomon-Terao algebra of Abe and Numata. Complementary work, via perverse sheaves on more general complex algebraic varieties, has been developed by Chonqiang Liu, Maxim, and Botong Wang. This has considerable explanatory power for some phenomena observed in the cohomology jump loci of arrangements. Some new directions, such as the singular loci of certain hypersurfaces associated with Feynman integrals, are also likely to be of interest at the time of the meeting (Denham, Schulze, Walther).