DATE: Tuesday, September 23, 2008
PLACE: Ryerson Annex 277.
University of Chicago.
1100 East 58th Street, Chicago, IL 60637.
Lunch: 12:00 at the Medici. 1327 E. 57th St, Hyde Park.
Dinner: 6pm at Thai restaurant
on 55th St, Hyde Park.
- 1:30-2:30: Antonio Montalbán - U. of Chicago.
information is no information.
- 3:00-4:00: Logan
Axon - U. of Notre Dame.
- 4:30-5:30: Joe Miller - U. of Wisconsin.
is always guessing wrong?
1:30-2:30: Antonio Montalbán - U. of Chicago.
Title: When low information is no
Abstract: It is been conjectured that if a Boolean algebra has a
presentation, it has a computable presentation. We look at
class of structures where this behavior does occur, namely, the
of linear orderings with infinitely many descending cuts. This is
joint work with Asher Kach and Joe Miller.
We will also look at the atom relation of Boolean algebras.
have that complete information implies high information. We show
every high_3 computably enumerable degree appears in the
the atom relation of any computable Boolean algebra with
3:00-4:00: Logan Axon - U. of Notre Dame.
Title: Random closed sets and
Abstract: Barmpalias, Broadhead, Cenzer, Dashti, and Weber
defined a notion of
randomness for closed subsets of Cantor space by coding each
binary tree without dead ends as a ternary real. The set of paths
through such a tree is said to be random if the ternary code for
tree is (Martin-Loef) random. Every closed set of Cantor space
set of paths through a unique binary tree without dead ends and
have a well founded definition of random closed set. Probability
theorists, on the other hand, have defined a random closed set
something quite different. A random closed set as defined in the
literature of probability theory is a measurable map from a
probability space to the space of closed sets of a topological
(where this space is equipped with the Fell topology and the
corresponding Borel sigma-algebra). In particular a random
of Cantor space is simply a measurable map from any probability
to the space of closed sets of Cantor space.
This talk addresses one way of reconciling these two notions of
closed set. First we use the probability theory framework to
measure-based theory of randomness for the space of closed sets
Cantor space. Then we show that random closed sets in the sense
Barmpalias et. al. are a specific example of randomness with
to this new framework. To conclude we will look at some other
of randomness for closed sets that arise from this framework.
4:30-5:30: Joe Miller - U. of Wisconsin.
Title: What good is always guessing wrong?
Abstract: We'll discuss connections between diagonally noncomputable
functions and algorithmic randomness.