Aomoto complexes and monodromy of Milnor fibers of hyperplane arrangements
speaker: Pauline Bailet (Bremen University)abstract: In the first part of the course, I will recall some geometrical and combinatorial objects associated to an hyperplane arrangement such as complement, Milnor fiber, Orlik-Solomon algebra and Aomoto complex. Then I will talk about local system cohomology of complements, cohomology of Milnor fibers and monodromy. In the second part of the course, we will study a graph which is determined by the arrangement's combinatorics. It has been conjectured by Salvetti and Serventi that the connectivity of this graph implies the triviality of the monodromy on the Milnor fiber for a complex line arrangement. We will discuss some particular cases, relying on a key inequality du to Papadima and Suciu, that involves local system cohomology of complements and cohomology of Aomoto complexes with finite field coefficients.
timetable:
Fri 9 Sep, 10:00 - 11:00, Sala Conferenze Centro De Giorgi
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