[Alta-Logic] a very special peripatetic seminar

[Jonathan Gallagher]

Join us for the penultimate peripatetic seminar tomorrow at 2pm!

http://peripatetic-seminar.cpsc.ucalgary.ca/wp/

or

*Speaker:* Kristine Bauer
*Location: *ICT 616 on Tuesday December 12, 2 pm
*Title: *Abelian functor calculus, derivatives, and operads

*Abstract: *The first chain rules in functor calculus were established by
Arone-Ching and Klein-Rognes, who considered functors of spaces or
spectra.  The Arone-Ching chain rule stemmed from earlier work of M. Ching,
in which he established that the derivatives of the identity functor form
an operad, whose homology is the classical Lie operad.  The chain rule, in
conjunction with Ching's earlier work, lead to a classification theorem for
all functors of spaces or spectra.  That is, it explained how you could
produce a functor from its derivatives.  However, Arone-Ching's work was
quite complicated and difficult.  One of the motivations for establishing a
chain rule for abelian functor calculus was to try to look for a
simplification of their work.  Indeed, in BJORT, we established the chain
rule by first establishing that the category of abelian categories is a
cartesian differential category.  This, together with the associated
tangent structure, lead to a much simpler proof of the chain rule.
Following the program laid out by Arone and Ching, we are now looking for
the expected operad structure and classification theorems.  In this talk, I
will explain the derivative (as opposed to the directional derivative) for
abelian functor calculus, and the candidate for our operad.
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