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SUMMARY:The entropy-degree theorem for Alexandrov spaces [MPIM]
DTSTART:20260611T113000Z
DTEND:20260611T130000Z
DTSTAMP:20260607T031100Z
UID:indico-event-1372@math-events.uni-bonn.de
DESCRIPTION:Speakers: Pablo Suarez-Serrato (UNAM/U. California\, Santa Bar
 bara/MPIM)\n\nOberseminar Differentialgeometrie\nI will present an entropy
 -degree theorem for Lipschitz maps between Alexandrov spaces with curvatur
 e bounded below and negatively curved locally symmetric spaces\, extending
  the classical volume-entropy rigidity of Besson–Courtois–Gallot to th
 is singular setting. A central component of this result is a new degree th
 eory for Alexandrov spaces\, which I develop using the Ambrosio–Kirchhei
 m theory of integral currents to show the equivalence of analytical and to
 pological degrees. This framework provides a unified approach to diverse g
 eometric problems\, including volume stability for Alexandrov spaces\, vol
 ume bounds for cone-manifolds\, and topological obstructions for negativel
 y curved Einstein metrics on 4-orbifolds. Furthermore\, by synthesizing th
 ese methods with metric doublings\, I derive quantitative volume inequalit
 ies for hyperbolic convex cores and lower bounds on the asymptotic transla
 tion lengths of end-periodic homeomorphisms. While time will not permit a 
 full discussion of all these applications\, I welcome further inquiries ab
 out these topics following the presentation.\n\nhttps://math-events.uni-bo
 nn.de/event/1372/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1372/
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