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SUMMARY:Gautam Bharali (Indian Institute of Science\, Bangalore)
DTSTART:20201124T140000Z
DTEND:20201124T150000Z
DTSTAMP:20260422T201810Z
UID:CAvid/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/22/">T
 he Wolff-Denjoy theorem beyond the unit disc</a>\nby Gautam Bharali (India
 n Institute of Science\, Bangalore) as part of CAvid: Complex Analysis vid
 eo seminar\n\nLecture held in N/A.\n\nAbstract\nThe Wolff-Denjoy theorem h
 as been the motivation for a host of results that resemble the classical t
 heorem for holomorphic self-maps of the unit disc. In this talk\, we shall
  look at yet another result in this class. This result applies to a rather
  general class of bounded domains in one and higher dimensions\, which may
  have rough boundaries and aren't necessarily contractible. While our tech
 niques are motivated by the properties of holomorphic maps in several comp
 lex variables\, the theory of such maps turns out to be incidental to thes
 e techniques. In fact\, in this talk\, we shall spend some time examining 
 certain analogies between the Poincaré distance and the Hilbert distance 
 on convex domains. This is relevant as there exists a Wolff--Denjoy-type t
 heorem\, by Beardon\, in the latter setting. It is these analogies that gi
 ve rise to the fundamental concept that underlies our result(s): namely\, 
 a weak notion of negative curvature for spaces equipped with the Kobayashi
  distance (of which the Poincaré distance is a special case). No knowledg
 e of several complex variables will be assumed in this talk: indeed\, most
  of the discussion will focus on basic complex analysis and on the propert
 ies of metric spaces and contractive maps. A large part of this talk will 
 be based on joint work with Andrew Zimmer and Anwoy Maitra.\n
LOCATION:https://researchseminars.org/talk/CAvid/22/
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