Time and place: January 12, 2026, Monday, at 2:00 pm, in Room 578, Institute of Mathematics and Informatics – Bulgarian Academy of Sciences
Lecturer: Valdemar Tsanov (IMI-BAS)
Title: Geometry of Milnor fibrations of equivariant plane curves
Abstract: The local knot of an irreducible C*-equivariant complex plane curve singularity is a torus knot, and the Milnor fiber is a Seifert surface for this knot. I will describe an explicit universal cover of the Milnor fiber by the hyperbolic plane, using automorphic forms for triangle groups. The characteristic morphism of the Milnor fibration can also be recovered, and used to construct geometric structures by universal covers on the knot complement in the 3-sphere, as well as on the complement of the singular curve in the complex plane.
Abstract: The local knot of an irreducible C*-equivariant complex plane curve singularity is a torus knot, and the Milnor fiber is a Seifert surface for this knot. I will describe an explicit universal cover of the Milnor fiber by the hyperbolic plane, using automorphic forms for triangle groups. The characteristic morphism of the Milnor fibration can also be recovered, and used to construct geometric structures by universal covers on the knot complement in the 3-sphere, as well as on the complement of the singular curve in the complex plane.