Products of conjugacy classes in finite unitary groups GU(3,q2)GU(3,q^2) and SU(3,q2)SU(3,q^2)

For the finite groups GU(3), SU(3), GL(3), SL(3) over a finite field we solve the class product problem, i.e., we give a complete list of $m$-tuples of conjugacy classes whose product does not contain the identity matrix

Signatures of real algebraic curves via plumbing diagrams

We define and calculate signature and nullity invariants for complex schemes for curves in the real projective plane. We use an analog of the Murasugi-Tristram inequality to prohibit certain schemes from being realized by real algebraic curves. We give new formulas for Casson-Gordon invariants of graph manifolds, and signatures of graph links.Comment: 28 page