MERCOLEDÌ 28 MAGGIO 2014
14:30 (seminario Baby-geometri)
Alex Suciu (Northeastern University, Boston)
Topology of hyperplane arrangements
ABSTRACT:
Much of the fascination with arrangements of complex
hyperplanes comes from the rich interplay between the combinatorics
of its intersection lattice and the algebraic topology of its complement.
A key bridge between the two is provided by the geometry of two sets
of algebraic varieties associated to the complement: the resonance
varieties of the cohomology ring and the characteristic varieties of
the fundamental group.
SEMINARIO DI ALGEBRA, TOPOLOGIA E COMBINATORIA
GIOVEDI' 29 MAGGIO 2014
16:00-17:00, Sala Riunioni (Dip. Matematica)
Alex Suciu (Northeastern University, Boston)
Combinatorial covers, abelian duality, and propagation of resonance
ABSTRACT:
We revisit and generalize a result of Eisenbud,
Popescu, and Yuzvinsky, which says that the resonance
varieties of a hyperplane arrangement complement propagate.
It turns out that the topological underpinning for this
phenomenon is a certain abelian duality property, coupled
with the minimality property enjoyed by arrangement
complements and related spaces, such as Cohen-Macaulay
toric complexes. The key ingredient in the proof is a general,
cohomological vanishing result for spaces that admit suitable
`combinatorial' covers.
This is joint work with Graham Denham and Sergey Yuzvinsky.
SEMINARIO DI ALGEBRA, TOPOLOGIA E COMBINATORIA
GIOVEDI' 29 MAGGIO 2014
17:00-18:00, Sala Riunioni (Dip. Matematica)
Stefan Papadima (IMAR)
Milnor fibrations of arrangements and modular inequalities
ABSTRACT:
A central question in the theory of complex hyperplane arrangements
is to determine whether the characteristic polynomial of the algebraic
monodromy acting on the rational homology of the associated Milnor fiber
may be described solely in terms of the underlying combinatorics. I will
discuss an approach based on the associated resonance varieties in positive
characteristic.