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BEGIN:VEVENT
SUMMARY:Calculus of Fractions
DTSTART:20211102T141500
DTEND:20211102T151500
DTSTAMP:20260919T215533Z
UID:388a2003e0e39e58a90331c646adbb1ca3745627569ff28e0c33c8e5
CATEGORIES:Conferences - Seminars
DESCRIPTION:Denis-Charles Cisinski\, Universität Regensburg\nThe purpose 
 of abstract homotopy theory is to provide category theoretic constructions
  which are compatible with suitable notions of weak homotopy equivalences.
  One can revisit the concepts that have lead to Quillen's notion of model 
 category as devices to compute mapping spaces of localizations in terms of
  Kan extensions\, which\, in turns provide tools to compute (co)limits in 
 localized infinity-categories as homotopy (co)limits. From there\, one can
  produce a perfect dictionary between (co)complete infinity-categories and
  their models together with a good theory of derived functors as Kan exten
 sions\, revisiting the work of Szumiło\, Kapulkin and Mazel-Gee. Reformul
 ating homotopy theory properly as suggested above\, using mainly the langu
 age of Kan extensions is not only a pleasant way to revisit classical cons
 tructions (although that would be good enough)\, but also a way to interna
 lize homotopy theory in any higher topos (in fact in any directed type the
 ory). This will have applications\, for instance\, to formulate and prove 
 the universal property of Morel and Voevodsky's motivic homotopy theory (p
 ossibly formulated within derived geometry\, thus generalizing the contri
 butions of Drew and Gallauer)\, as well as to study condensed/pyknotic mat
 hematics (e.g. one can see the pro-étale topos of a scheme as a condensed
 /pyknotic presheaf topos on the the associated Galois category constructed
  by Barwick\, Glasman and Haine).
LOCATION:MA A1 12 https://plan.epfl.ch/?room==MA%20A1%2012 https://epfl.zo
 om.us/j/94351048760
STATUS:CONFIRMED
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