Geometry and topology: Polynomial hulls, knots, and holomorphic motions

  • Date: –15:15
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Mark Lawrence (Nazarbayev University).
  • Organiser: Matematiska institutionen
  • Contact person: Georgios Dimitroglou
  • Seminarium

Abstract: The study of polynomial hulls of compact sets in Cn is too challenging to have a useful general answer. Even for smooth manifolds, there is little known. One restriction is to look at tori or unions of tori in S1 × C which fiber over the circle. The knot class of the torus plays a crucial role, both in a positive and negative direction. The main positive result of the author and J. Duval is that a torus modeled on a square root has a polynomial hull which is fibered by varieties. On the negative side, it appears that the knot type of the torus can exclude any hull from appearing over the unit disc, but only preliminary results exist in this direction. Using the theorem of Lawrence and Duval, new types of holomorphic motions
can be constructed, which have a limited amount of branching.