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This textbook provides an accessible introduction to the rich and beautiful area of hyperplane arrangement theory, where discrete mathematics, in the form of combinatorics and arithmetic, meets continuous mathematics, in the form of the topology and Hodge theory of complex algebraic varieties. The topics discussed in this book range from elementary combinatorics and discrete geometry to more advanced material on mixed Hodge structures, logarithmic connections and Milnor fibrations. The author covers a lot of ground in a relatively short amount of space, with a focus on defining concepts carefully and giving proofs of theorems in detail where needed. Including a number of surprising results and tantalizing open problems, this timely book also serves to acquaint the reader with the rapidly expanding literature on the subject. Hyperplane Arrangements will be particularly useful to graduate students and researchers who are interested in algebraic geometry or algebraic topology. The book contains numerous exercises at the end of each chapter, making it suitable for courses as well as self-study.

Mathematics. --- Algebraic geometry. --- Commutative algebra. --- Commutative rings. --- Functions of complex variables. --- Algorithms. --- Projective geometry. --- Combinatorics. --- Algebraic Geometry. --- Commutative Rings and Algebras. --- Several Complex Variables and Analytic Spaces. --- Projective Geometry. --- Projective geometry --- Algorism --- Complex variables --- Algebraic geometry --- Math --- Combinatorics --- Geometry, algebraic. --- Algebra. --- Differential equations, partial. --- Partial differential equations --- Mathematics --- Mathematical analysis --- Geometry --- Algebra --- Arithmetic --- Foundations --- Combinatorial analysis --- Cohomology operations --- Geometry, Algebraic --- Lattice theory --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Transformations (Mathematics) --- Crystallography, Mathematical --- Operations (Algebraic topology) --- Algebraic topology --- Cohomology operations. --- Rings (Algebra) --- Geometry, Modern --- Elliptic functions --- Functions of real variables

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These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research. .

Representations of groups --- Cohomology operations --- Operations (Algebraic topology) --- Algebraic topology --- Algebra. --- Topological Groups. --- Group theory. --- Category Theory, Homological Algebra. --- Topological Groups, Lie Groups. --- Associative Rings and Algebras. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Groups, Topological --- Continuous groups --- Mathematics --- Mathematical analysis --- Category theory (Mathematics). --- Homological algebra. --- Topological groups. --- Lie groups. --- Associative rings. --- Rings (Algebra). --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Homological algebra --- Algebra, Abstract --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory