Departmental Colloquium
Sergey Yuzvinsky
University of Oregon
RESONANCE VARIETIES OF HYPERPLANE COMPLEMENTS
Abstract: The idea to view the cohomology ring A^* of a space as a cochain complex with
the differential d_a (a \in A^1 ) given by the multiplication by a appeared first in
the Farber-Novikov spectral sequence. The first sheet of the sequence is formed
by cohomology H^* (A^* , d_a ). For a compact space X the sequence converges to the
cohomology of X with local coefficients determined by a. Independently the cochain
complex has been studied for complex hyperplane arrangement compelments which
led to the notion of resonance varieties.
These varieties will constitute the main character of the talk. Recently they
have been related to classical geometric structures on the complex projective plane,
pencils of algebraic curves, and also the Bernstein-Sato polynomials. If time allows,
we will briefly discuss some generalizations of properties of the resonance varieties
to other classes of spaces.
Friday April 9, 2010 at 3:00 PM in SEO 636