[Alta-Logic] Peripatetic seminar: Wednesday and Friday (double dipping!!)

[Robin Cockett]

Speaker: Robin Cockett
Where and when: ICT 616, Wednesday, 16th March, 3:30pm
Title: On the Totals of a Turing Category

Abstract:
A Turing category is an abstract setting for describing computability. 

I put the following question to Pavel (Hrubes):
         "Can the polynomial time functions be the totals of a Turing 
category?"
Pavel responded by making some interesting general observation about the 
totals of a Turing category which
have allowed a completely characterization of the (Cartesian) categories 
which can be the total maps
of a Turing category ....  and not only are the polynomial time maps 
included but possibly also
classes of even lower complexity.

The aim of the talk is to begin to describe these results and, possibly, 
to discuss some other desirable
structural aspects which are really needed in order to bring these 
observations to bear.

(Joint work with Pavel Hrubes)


Speaker Geoff Crutwell
Where and when: ICT 616, Friday, 18th March, 3:00pm

Title: Embeddings of Atlas Categories

Abstract:
A few months ago, I talked about Marco Grandis' construction of the
atlas-completion of a join restriction category.  This generalizes the
idea of "atlas" so that one can describe atlases in virtually any setting
in which one has a well-behaved notion of partial map.

However, in many contexts, a "manifold" need not be given by an atlas:
instead, it can be seen as a type of "space" which locally looks like one
of the modeling spaces.  For example, instead of describing schemes as
atlases of affine schemes, they can be (and typically are) described as
locally ringed spaces which locally look like an affine space.  This is
not always obviously possible: there is no obvious notion of "space" in
which manifolds modeled on infinite dimensional vector spaces (eg.,
convenient vector spaces, or Frechet spaces) live in.  Thus these
manifolds are typically described by atlases.

In the talk, after reviewing Grandis' generalized atlases, I'll talk a bit
about work-in-progress on trying to make the above idea work generally:
showing that every atlas can be seen as a kind of space which locally
looks like one of the modeling spaces.