Computability- and Category theoretic Perspectives on Descriptive Set Theory
July 16th - 18th 2018
Bay Campus, Swansea University, Swansea, UK
Background:
Computability
theory and descriptive set theory (DST) are no strangers, but have a
long and fruitful interaction in the form of descriptive set theory.
Recent years have seen several results showing that computability
theoretic arguments can be very useful even to obtain theorems in
classical descriptive set theory. Studying computability theoretic
properties of topological spaces in a broader sense thus seems to be a
very promising approach.
In a related development there are
signs that employing category-theoretic language can allow us to see
DST in a new and uniform way. In particular, there connections between
traditional DST concepts such as point classes, endofunctors in the
category of represented spaces and models of hypercomputation. This
touches upon notions from formal topology and topos theory.
The
DST community itself has started to extend their work to generalized
Baire space, and thus reinforced the connection to set theory. Studying
the computability- and category theoretic aspects of this should on the
one hand try these new perspectives, and on the other hand, might
provide a guiding light in the proper generalization of the known
theory.
The workshop:
The workshop will bring
together a select number of experts in the various topics related to
its theme. Our ambition is that a combination of advanced but
expository talks and ample discussion in groups will help us to
elucidate the directions this research area should take, prove some
theorems, forge new collaborations and reinforce existing ones.
Attendance is by invitation only, but feel free to contact Arno Pauly
(arno.m.pauly@gmail.com) to ask for an invitation, if you have not
received one.
Practical arrangements:
The workshop
will take place in the Bay Campus of Swansea University from Monday,
July 16th (starting in the morning) to Wednesday 18th (ending
noon-early afternoon). Lunch and coffee breaks will be provided. A
number of rooms are available (see here
for details) for the nights Sunday - Wednesday, which come with
breakfast. There are also a number of hotels closer to the town center,
from where the Bay campus can easily be reched by bus. The dinner
arrangements will be left to the participants (some restaurant
recommendations will follow).
Registration:
Please respond to the invitation to attend the workshop by filling out the registration form.
A quick response will make the planning much easier. A tentative but
quick answer is preferred to a later, definite one (please update once
circumstances change!).
Schedule:
A prelimary schedule is found here.
