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BEGIN:VEVENT
UID:DSC-14580
DTSTART;TZID=Europe/Berlin:20180703T150000
SEQUENCE:1528209994
TRANSP:OPAQUE
DTEND;TZID=Europe/Berlin:20180703T160000
URL:https://www.dresden-science-calendar.de/calendar/de/detail/14580
LOCATION:TUD Willers-Bau\, Zellescher Weg 12-1401069 Dresden
SUMMARY:Gheysens: On\, around\, and beyond Ryll-Nardzewski's theorem III
CLASS:PUBLIC
DESCRIPTION:Speaker: Maxime Gheysens\nInstitute of Speaker: TU Dresden\, In
 stitut für Geometrie\nTopics:\nMathematik\n Location:\n  Name: TUD Willer
 s-Bau (WIL A 120)\n  Street: Zellescher Weg 12-14\n  City: 01069 Dresden\n
   Phone: \n  Fax: \nDescription: 12.06. / 19.06. / 03.07.2018    The lectu
 res will focus on a cornerstone theorem of functional  analysis\, Ryll-Nar
 dzewski's theorem. This powerful result asserts the  existence of a fixed 
 point for a very broad class of actions on convex sets.    I. Ryll-Nardzew
 ski's theorem. After recalling some facts about group  actions and functio
 nal analysis\, we will state and prove Ryll-Nardzewski's  theorem.    II. 
 Applications. The second lecture will focus on applications of  Ryll-Nardz
 ewski's theorem. We will cover in details the existence of Haar  measures 
 for compact groups and the unbounded vs. fixed-point dichotomy for  isomet
 ric actions on reflexive Banach spaces. Other consequences (for  instance\
 , for von Neumann algebras or for compactifications of groups) will  be me
 ntionned\, according to the interest of the audience.    III. Sibling theo
 rems. We will explain three interesting related theorems:  a fixed-point t
 heorem for $\\mathrm{L}^1$-spaces (an unexpected application  of Ryll-Nard
 zewski's theorem)\, a fixed-point theorem for actions on convex  cones (a 
 generalisation thereof)\, and the Day--Rickert characterization of  amenab
 ility (which shows that Ryll-Nardzewski's theorem is somehow optimal).  
DTSTAMP:20260702T033350Z
CREATED:20180529T161054Z
LAST-MODIFIED:20180605T144634Z
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