Midwest
Computability Seminar
XV
The Midwest Computability
Seminar is a joint venture between the University of Chicago, the University
of Notre Dame, and the University of WisconsinMadison. It
meets once or twice per semester at the
University of Chicago, and is attended by faculty and students from these
universities and others
in the area. The seminar started in the
fall of 2008.
DATE: Tuesday, September 30, 2014.
PLACE: Ryerson Hall 352 (the
Barn), The University of
Chicago.
1100 East 58th Street, Chicago, IL 60637.
Speakers:

Eric Astor  Chicago
 Quinn Culver  Notre Dame
 Jack Lutz  Iowa State University
 Timothy McNicholl  Iowa State University
Schedule:
 12:00  1:00: Lunch
 1:00  1:25: Eric Astor
 1:35  2:00: Quinn Culver
 2:00  2:30: Coffee break
 2:30  3:20: Jack Lutz
 3:30  4:10: Coffee break
 4:10  5:00: Timothy McNicholl
 6:00: Dinner  La Lagartija, 132 S. Ashland Ave.
Abstracts:
Eric Astor
Title: Asymptotic density, immunity, and randomness
Abstract: We investigate a computablyinvariant restriction of asymptotic
density.
This new pseudomeasure on the natural numbers has strong connections to
randomness and classical computability theory; we use it to define a new
immunity property, recognize a new form of stochasticity, and find an
unexpected connection to functions avoiding weak computable approximation.
We also apply similar ideas to create computablyinvariant restrictions of
the genericcase computability defined by Jockusch and Schupp, and prove a
generalization of Rice's Theorem as a lower bound on their strength.
Quinn Culver
Title: The interplay between varieties of algorithmically random
objects
Abstract: We study algorithmically random closed subsets of cantor space,
algorithmically random continuous functions from cantor space to cantor
space, and algorithmically random Borel probability measures on cantor
space; especially the interplay between the three. Our main tools are
preservation of randomness and its converse, no randomness ex nihilo, which
say together that given an a.e.defined computable map between an
effectively compact probability space and an effective polish space, a real
is (MartinLöf) random for the pushforward measure if and only if its
preimage is random for the domain's measure. These tools allow us to prove
new facts, many of which were previously open questions, and reprove some
known results more simply. This work is joint with Chris Porter.
Timothy McNicholl
Title: Interactions between computability and complex analysis
Abstract: We will discuss computability issues in the study of analytic
functions; in particular recent work on computability properties of
functions in the Hardy spaces.
Jack Lutz
Title: Mutual dimension
Abstract: The search for a satisfactory notion of the mutual information between two
infinite sequences is a major open problem in algorithmic information
theory. This talk discusses our recent solution of a closely related
problem, the correct formulation of the mutual dimension (density of shared
information) between two points in Euclidean space. We define mutual
dimension and show that it satisfies the desiderata for such a quantity,
most crucially the data processing inequality, which says that the action of
a computable Lipschitz function cannot increase a point's mutual dimension
with any other point. Extensions and applications will be discussed as time
permits.
This is joint work with Adam Case.
Previous Seminars:
 Sept 23th 2008. Antonio
Montalbán  Logan Axon  Joe Miller
 Nov 11th 2008. Chris
Conidis  Keng Meng (Selwyn) Ng  Peter Gerdes
 Feb 3rd 2009. David
Diamondstone  Bart Kastermans  Richard A. Shore
 April 21th 2009. Dan Turetsky
 Julia Knight  Ted Slaman
 Sept 29th 2009. Carl Jockusch
 Rachel Epstein  Rebecca Weber
 Jan 26th 2010. Sara Quinn 
John Wallbaum  Steffen Lempp  Reed Solomon
 May 11th 2010. Adam Day 
Liang Yu  Rod Downey  Boris Zilber
 Sept 28th 2010. Maurice
Chiodo  Peter Gerdes  Damir Dzhafarov  Andy Lewis
 Feb 15th 2011. Uri Andrews 
Paola D'Aquino  David Diamondstone  Christopher Porter 
Rebecca Steiner.
 Nov 1st 2011. Mingzhong Cai 
Chris Conidis  Stephen Flood 
Jeff Hirst  Asher Kach.
 Nov 15th 2012 Achilles Beros
 Rod Downey  Jesse Johnson  Sam Sanders  Steven VanDendriessche 
Matthew Wright.
 April 2nd 2013 Howard
Becker  Denis Hirschfeldt  Paul Schupp.
 October 1st 2013 Peter Cholak
 Mushfeq Khan  Victor OcasioGonzález  Jonathan Stephenson
 April 29th, 2014 Rod Downey 
Noam Greenberg  Gregory Igusa  Alexander Melnikov  Kyle Riggs
If you haven't
been receiving the announcements and would like to be included
in the list, send an email to drh@math.uchicago.edu.