Algebra Seminar

Date:     Thursday, 14 October at 12:10 in Eng E 206

Speaker:  Yukihito Kawahara (Tokyo Metropolitan University)

Title:    The local system cohomology for hyperplane arrangements

Abstract: The local system cohomology is an important subject in the
Aomoto-Gelfand multivariable theory of hypergeometric functions. I
will talk vanishing theorems of the local system cohomology by using
combinatorics of hyperplane arrangements via Orlik-Solomon Algebras. 
The cohomology of the complement of hyperplanes is isomorphic to the
Orlik-Solomon Algebra constructed by combinatorics of hyperplane
arrangements. For a generic monodromy or weight, the local system
cohomology is isomorphic to  the cohomology of the Orlik-Solomon
Algebra. I will talk some conditions of monodromy, for which the local
system cohomology vanishs in all but the top dimension. On the other
hand, arrangements with non-vanishing local system cohomology are very
special.  I will show their examples.