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Lecture 1:             Topology of quasi-projective varieties

4:00 p.m., Tuesday, 20 April 2010, in 100 Willamette Hall

Alexander polynomial is a classical invariant in knot theory but its construction is group theoretical and as such it can be used to study the groups coming up in algebraic geometry as well. The purpose of these lectures is to describe generalizations of Alexander polynomials and their relation to other algebrao-=20 geometric ob jects and constructions. In the first talk I will discuss several classical problems related to the study of Alexander invariants which include singularities of plane curves and hypersurfaces, characterization of fundamental groups of Kahler, pro jective and quasi-=20= projective manifolds, methods for calculation of the fundamental groups of the complements to plane curves, complements to arrangements and their symplectic analogs.