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SUMMARY:Maryna Viazovska (École Polytechnique Fédérale de Lausanne)
DTSTART;VALUE=DATE-TIME:20210616T141500Z
DTEND;VALUE=DATE-TIME:20210616T151500Z
DTSTAMP;VALUE=DATE-TIME:20220528T204738Z
UID:Azat/1
DESCRIPTION:Title: Sph
ere packings\, universal optimality\, and Fourier interpolation\nby Ma
ryna Viazovska (École Polytechnique Fédérale de Lausanne) as part of Az
at Miftakhov Day\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Azat/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Bufetov (CNRS & Institut Institut de Mathématiques de M
arseille & Steklov\, IITP RAS)
DTSTART;VALUE=DATE-TIME:20210616T151500Z
DTEND;VALUE=DATE-TIME:20210616T161500Z
DTSTAMP;VALUE=DATE-TIME:20220528T204738Z
UID:Azat/2
DESCRIPTION:Title: Det
erminantal point processes: quasi-symmetries\, minimality\, and interpolat
ion\nby Alexander Bufetov (CNRS & Institut Institut de Mathématiques
de Marseille & Steklov\, IITP RAS) as part of Azat Miftakhov Day\n\n\nAbst
ract\nWhat is the relation between a determinantal point process and the H
ilbert space that governs it? For the sine-process of Dyson\, almost ever
y realization with one particle removed is a complete and minimal set for
the Paley-Wiener space\, while if two particles are removed\, then one obt
ains azero set for the Paley-Wiener space. Quasi-invariance of the sine-p
rocess under compactly supported diffeomorphisms plays a key role. In joi
nt work with Qiu\, the Patterson-Sullivan construction is used to interpol
ate Bergman functions from the zero set of a random series with independen
t complex Gaussian entries. The determinantal property\, due to Peres and
Virg\, and the invariance of the zero set under the isometries of the Lob
achevsky plane play a key role.\n
LOCATION:https://researchseminars.org/talk/Azat/2/
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BEGIN:VEVENT
SUMMARY:Peter Scholze (Universität Bonn)
DTSTART;VALUE=DATE-TIME:20210616T161500Z
DTEND;VALUE=DATE-TIME:20210616T171500Z
DTSTAMP;VALUE=DATE-TIME:20220528T204738Z
UID:Azat/3
DESCRIPTION:Title: Con
densed mathematics\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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