solira.blogg.se - Homologie hyperplan

#HOMOLOGIE HYPERPLAN SERIES#
#HOMOLOGIE HYPERPLAN FREE#

Applications - generalized hypergeometric functions, Gauss-Manin connections, KZ equations, quantization, elliptic and $q$KZ equations, discriminants, flat connections and braid group representations, Artin groups, moduli spaces and Grassmann strata, subspace arrangements, wonderful models.

#HOMOLOGIE HYPERPLAN SERIES#

Commutative and skew-commutative algebra - modules of derivations, resolutions, Orlik-Solomon algebras, Koszul duality and lower central series formulas.

Topology of the complement - characteristic and resonance varieties, fundamental groups, higher homotopy groups, cohomology of local systems.

This semester-long program will focus on several inter-related aspects of current research in the field: Recent progress has revealed unexpected connections between generalized hypergeometric functions, topological and algebraic invariants of arrangements, and several touchstones of classical mathematics: pencils of algebraic curves, Cartan matrices, classical point configurations, Latin squares. In addition, arrangements are intrinsically fascinating objects, simple enough in their definition to submit to explicit calculations, but complicated enough to display interesting and surprising properties. Applications of the theory now include conformal field theory, braid group representations and knot invariants, general Artin groups, and many other areas. Indeed, since its beginnings the main feature of the theory has been its location at the intersection of combinatorics, topology, and algebra. On the other hand, the study of complex hyperplane arrangements really began around 1970 with work of Arnold, Brieskorn, Deligne, Aomoto, Hattori, and others, motivated by applications to the topology of configuration space and the discriminant, the algebraic structure of the braid group, and the construction of multivariable hypergeometric functions.īy now there has developed a rich and extensive theory of hyperplane arrangements in general, which draws techniques and inspiration from diverse fields of mathematics. When the underlying field is $$ or $GF(q)$ there are natural enumerative, combinatorial and geometric questions that have been studied in great detail over much of the last century. Swift.Ī hyperplane arrangement is a finite collection of linear or affine hyperplanes in a fixed vector space. Japan Acad., 56(1980), 389-392.Figures produced in DPGraph by James W.

#HOMOLOGIE HYPERPLAN FREE#

Terao- Free arrangements of hyperplanes and unitary reflection groups, Proc. Terao - Generalized exponents of a free arrangement of hyperplanes and Shepherd-Todd-Brieskorn formula, Inv. Terao - Arrangements of hyperplanes and their freeness I II, Journ.

Todd - Finite unitary reflection groups, Can.J.Math., 6 (1954), 274-304. Saito - Theory of logarithmic differential forms and logarithmic vector fields, Journ. Solomon - Unitary reflection groups and cohomology, Inv.Math. Solomon - Combinatorics and topology of complements of hyperplanes, Inv. Arnold), Séminaire Bourbaki, 24e année, 1971/2, Lect. Brieskorn - Sur les groupes de tresses (d'après V.I. Bourbaki - Groupes et Algèbres de Lie, chapitres 4 à 6, Hermann, Paris ,1968. Arnold - The cohomology ring of the colored braid group, Mat. Folkman - The homology groups of a lattice, J. Baclawski - Whitney numbers of geometric lattices, Adv. Whitney - On the abstract properties of linear dependence, Amer.J.Math. Rota- On the Foundations of Combinatorial Theory I : Theory of Möbius Functions, Zeit. Las Vergnas - Convexity in oriented matroids, J.Comb.Theory B, 29(1980), 231- 243. Rota - On the Foundations of Combinatorial Theory : Combinatorial Geometries, M.I.T. Crapo - A higher invariant for matroids, J.Comb.Theory, 2(1967), 406-417. Brylawski - A decomposition for combinatorial geometries,. Zaslavsky - Facing up to arrangements : face-count formulas for partition of space by hyperplanes, Memoirs.

Winder - Partitions of N-space by hyperplanes, SIAM J.Appl.Math. Second Luisiana Conference on Combinatorics, Graph Theory, and Computing, R.C. Grünbaum - Arrangements of hyperplanes, Proc.

Grünbaum - Convex polytopes, Interscience, New York, 1976.