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PRODID:-//Memento EPFL//
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SUMMARY:Tested functor calculi
DTSTART:20260326T100000
DTEND:20260326T110000
DTSTAMP:20260610T170034Z
UID:f83ac8b3e2713d79940ed3dac99c29b10546f6cdb67a1345b142f588
CATEGORIES:Conferences - Seminars
DESCRIPTION:Niall Taggart\, Queen’s University Belfast\nFunctor calculu
 s refers to a family of homotopy-theoretic frameworks that extend the idea
 s of differential calculus into categorical settings. Existing forms of fu
 nctor calculus have proved remarkably useful\, with applications ranging f
 rom algebraic $K$-theory to a variety of geometric problems. Their ubiquit
 y suggests that it is worthwhile to search for new versions of functor cal
 culus.\n\nRecent work of Bandklayder\, Bergner\, Griffiths\, Johnson\, and
  Santhanam examines the homotopy theory encoded in the degree $n$ approxim
 ations  of Goodwillie calculus and discrete calculus. In each case\, they
  identify (or in the case of discrete calculus\, construct) a model struct
 ure that captures the relevant homotopical data and is controlled by a pre
 scribed collection of test morphisms. By exploiting these test morphisms\,
  they show that the resulting model category is cofibrantly generated\, gi
 ving an explicit description of the generating acyclic cofibrations.\n\nIn
  this talk\, I will describe the observation that these model structures c
 an always be realised as left Bousfield localizations with respect to the 
 corresponding sets of test morphisms. This viewpoint naturally suggests de
 fining new calculi directly from chosen test morphisms. I will explain tha
 t such a ``tested'' calculus exists provided a certain technical condition
  on the test morphisms is satisfied\, and then show how this condition can
  be reformulated in far more familiar terms\, namely\, that a degree $n$ f
 unctor automatically satisfies the conditions of being degree $n+1$. \n\n
 (The latter aspect of this talk is joint work-in-progress with Julie Bergn
 er\, Brenda Johnson\, Rhiannon Griffiths and Rekha Santhanam.)\n\n\n 
LOCATION:MA B1 504 https://plan.epfl.ch/?room==MA%20B1%20504
STATUS:CONFIRMED
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