[Alta-Logic] Peripatetic Seminar Monday 13:30 in MS 427

[Matthew Burke]

Speaker: Michael Ching

Time and Location: 13:30 12th Mar in MS 427

Title: Day convolution, infinity-operads and Goodwillie calculus

Abstract: Goodwillie calculus is a branch of homotopy theory that
provides systematic approximations to a suitable functor (say from the
category of topological spaces to itself) in the form of a "Taylor
tower", analogous to the Taylor series from ordinary calculus. In this
talk, I will describe how some aspects of the Taylor tower construction
are related via Day convolution. The slogan will be that "the nth
derivative is an n-fold Day convolution of the first derivative".

An important consequence of this observation is that the derivatives of
an identity functor on a category C are a coloured operad (or symmetric
multicategory), with the derivatives of a functor from C to D forming a
bimodule over the operads corresponding to C and D. The context for all
of this work is Lurie's theory of infinity-categories though no
technical background from that theory will be required in this talk.

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