[Alta-Logic] Re: Peripatetic seminar: Tangent structure and synthetic differential geometry

[Robin Cockett]

Responding to popular demand (actually Peter  Z.) I am going to move
the time forward to 2:00pm
I have booked ICT658 which is a rather small room however we may be
able to get into the usual room if we are lucky ...

-robn

> Time: 18th April, Wednesday 3:00pm
>
> Place: ICT 616 (University of Calgary)
>
> Speaker: Robin Cockett
>
> Title: Tangent structure and synthetic differential geometry
>
> Abstract:
>
> I am going to describe some aspects of current work with Geoff
> Cruttwell on tangent structure.
>
> A category with tangent structure is an abstract setting for
> differential geometry.  The notion was first proposed by Jiri Rosicky
> in 1984 in a paper remarkable for its brevity.  Rosicky promised a
> follow on paper which would contain details of proofs, however, it
> seems that this never happened.   Geoff and I stumbled into this area
> as we were looking for abstract characterizations for categories of
> differential manifolds. Anders Kock kindly pointed out Rosicky's
> remarkable paper to us.
>
> A particularly, fascinating aspect of Rosiky's paper is that he
> initiates the attempt to completely characterize synthetic
> differential geometry (SDG) as "representable" tangent structure.  As
> we had not even seriously considered the possibility that these SDG
> settings would be included under this sort of abstract formulation,
> Geoff and I have been scrambling to understand this connection.
> Approaching SDG though representable tangent structure provides a
> rather different perspective as to what these models bring to the
> table and this --together with (I hope) a discussion of a particular
> model -- will be the main focus of the talk.
>
>  What seems quite remarkable is that the concept of tangent structure
> seems to subsumes ALL the notions of differential geometry of which we
> are aware!