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SUMMARY:Peter Scholze (Universität Bonn)
DTSTART:20210616T161500Z
DTEND:20210616T171500Z
DTSTAMP:20260415T055932Z
UID:Azat/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Azat/3/">Con
 densed mathematics</a>\nby Peter Scholze (Universität Bonn) as part of Az
 at Miftakhov Day\n\n\nAbstract\n(Joint with Dustin Clausen)  It is a well-
 known problem that topological spaces have no good categorical properties 
 – for example\, topological abelian groups do not form an abelian  categ
 ory\, and in a complex of topological vector spaces\, differentials may no
 t have closed image\, leading to pathological cohomology groups.  However\
 , we realized that one can replace topological spaces by the closely relat
 ed notion of condensed sets\, resolving all of these foundational problems
 .  This makes it possible to develop new foundations for both nonarchimede
 an and archimedean functional analysis\, even allowing a very general form
 alism of analytic spaces - encompassing complex manifolds\, real manifolds
  of all flavours\, schemes\, formal schemes\, rigid-analytic varieties\, a
 nd adic spaces into one unified framework.  We will try to give an overvie
 w of these ideas.\n
LOCATION:https://researchseminars.org/talk/Azat/3/
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