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Lecture 3: Hodge theoretical methods for the study of Alexander invariants

4:00 p.m., Thursday, 22 April 2010, in 282 Lillis Hall

Deligne’s theory of differential equations with regular singularities and mixed Hodge theory lead to a structure theorem for the jumping loci of Hodge groups of local systems which eventually allows to calculate Alexander invariants and obtain characterization of Alexander invariants in some cases. I will discuss connection with the study of multiplier ideals and log-canonical thresholds allowing to clarify the structure of Alexander invariants. Application to topology of arrangements of hyperplanes= and Bernstein-Sato polynomials and ideals will be discussed.