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SUMMARY:Adrian Clough (NYU Abu Dhabi)
DTSTART:20240416T150000Z
DTEND:20240416T163000Z
DTSTAMP:20260422T174412Z
UID:tandg/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/tandg/18/">H
 omotopical calculi and the smooth Oka principle</a>\nby Adrian Clough (NYU
  Abu Dhabi) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\
 nAbstract\nI will present a new proof of Berwick-Evans\, Boavida de Brito\
 , and Pavlov’s theorem that for any smooth manifold A\, and any sheaf X 
 on the site of smooth manifolds\, the mapping sheaf Hom(A\,X) has the corr
 ect homotopy type. The talk will focus on the main innovation of this proo
 f\, namely the use of test categories to construct homotopical calculi on 
 locally contractible ∞-toposes. With this tool in hand I will explain ho
 w a suitable homotopical calculus may be constructed on the ∞-topos of s
 heaves on the site of smooth manifolds using a new diffeology on the stand
 ard simplices due to Kihara. The main theorem follows using a similar argu
 ment that for any CW-complex A\, and any topological space X the set of co
 ntinuous maps Hom(A\,X) equipped with compact-open topology models the map
 ping-homotopy-type map(A\,X).\n
LOCATION:https://researchseminars.org/talk/tandg/18/
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