BEGIN:VCALENDAR
PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
 M3//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20261009T095641Z
DTSTART:20261012T130000Z
SUMMARY:Dynamical Systems and Analysis Seminar - Lasse Rempe
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}qbh-mv0sji6
 2-1b1ewp
DESCRIPTION:Speaker: Lasse Rempe (University of Manchester)\n\nTitle: Abs
 ence of bounded-orbit wandering domains\n\nAbstract: Let f be an analyti
 c self-map of either the complex plane or the Riemann sphere. We may con
 sider f as describing the transition rule of a dynamical system\, and st
 udy the behaviour of points under iteration (repeated application) of th
 e function f. The Fatou set F(f) consists of those points near which the
  dynamics is stable under small perturbations of the starting value.\n\n
 A connected component of F(f) is called a Fatou component. A Fatou compo
 nent is called wandering if its forward iterates are pairwise disjoint. 
 A famous theorem of Sullivan from 1985 states that rational maps have no
  wandering domains. His proof used quasiconformal deformation theory\, a
 nd relied crucially on the fact that rational maps of fixed degree depen
 d only on finitely many parameters.\n\nTranscendental (i.e.\, non-polyno
 mial) self-maps of the complex plane may have wandering domains. A long-
 standing open question asked whether it is possible for orbits in such a
  domain to remain bounded under iteration. We answer this question by pr
 oving that bounded-orbit wandering domains do not exist.\n\n(This is joi
 nt work with Drach\, Pardo-Simón\, Prochorov\, U?akar and Waterman. Sinc
 e our result was first announced\, Ye also announced a proof of the main
  result.)\n\nThis result was obtained with the help of generative AI\, b
 ased on a new proof of Sullivan's theorem discovered by Ye\, also using 
 generative AI. We have also formalised the proof using the Lean proof as
 sistant. I will discuss some thoughts on what the rapid advances in AI c
 apabilities may mean for holomorphic dynamics (and mathematics) going fo
 rward.\n\nRoom: Frank Adams 1\n\nFurther information: https://personalpa
 ges.manchester.ac.uk/staff/yotam.smilansky/dynamics_analysis
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
END:VEVENT
END:VCALENDAR