Midwest
Computability Seminar
XX
The Midwest Computability
Seminar is a joint venture between the University of Chicago, the University
of Notre Dame, and the University of Wisconsin-Madison. 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, October 24, 2017.
PLACE: Ryerson Hall 352 (the
Barn), The University of
Chicago.
1100 East 58th Street, Chicago, IL 60637.
Speakers:
- Noah Schweber - University of Wisconsin
- Don Stull - Iowa State University
- Dan Turetsky - University of Notre Dame
- Rose Weisshaar - University of Notre Dame
Schedule:
- 12:00 - 1:00: Lunch
- 1:00 - 1:50: Noah Schweber
- 2:00 - 2:50: Don Stull
- 3:30 - 4:00: Rose Weisshaar
- 4:10 - 5:00: Dan Turestky
- 5:30 Dinner at Nella,
1125 E. 55th St.
Abstracts:
Noah Schweber
Title: Computability and Banach-Mazur games
Abstract: We'll look at some questions around Banach-Mazur games. On the
pure computability-theoretic side, after establishing the effectiveness of
some basic facts about Banach-Mazur games we classify the functions
computable from all winning strategies for some Banach-Mazur game as
exactly
the hyperarithmetic sets, using an analogue of Hechler forcing for
building
strategies. On the reverse mathematical side, we parallel this by showing
that Borel Banach-Mazur determinacy is equivalent to ATR0, and
that
this
equivalence goes "level-by-level;" by contrast, we also show that there is
a
Turing ideal satisfying lightface
Σ11-Banach-Mazur determinacy but
not containing 0(ω), this time using an analogue of
Spector
forcing for building strategies.
Don Stull
Title: Effective dimension of points on lines
Abstract: This talk will cover recent work using Kolmogorov complexity to
study the dimension of points on lines in the Euclidean plane and its
application to important questions in fractal geometry. In particular, we
will show that this work strengthens the lower bounds of the dimension of
Furstenberg sets. We will also discuss future research and open problems in
this area. This talk is based on joint work with Neil Lutz.
Dan Turetsky
Title: C.e. equivalence relations and the linear orders they
realize
Abstract: Quotient structures are well studied. In the case of linear
orders, it is known that the order-types realized by c.e. quotient
structures are precisely those realized by Δ02
linear orders. We
come at this from a different perspective, by considering, for each c.e.
equivalence relation, which order-types can be realized as a quotient by
that equivalence relation. We study the relationship between
computability-theoretic properties of the equivalence relation and the
algebraic properties of the order-types it can realize. We also define a
pre-order on equivalence relations by comparing the collection of
order-types realized in each.
Rose Weisshaar
Title: Countable ω-models of KP and paths through computable
ω-branching trees
Abstract: It is well known that the Π01 class CPA
⊆ 2ω of completions of Peano arithmetic is universal among
nonempty Π01 subsets of Cantor space. When we consider Π01
subsets of Baire space, however, there is no such universal example. In this
talk, we consider a Π01 class CKP ⊆
ωω whose paths compute the complete diagrams of countable
ω-models of Kripke-Platek set theory (KP). We develop an analogy
between how elements of CPA and CKP try to
compute members of nonempty Π01 subsets of Cantor space and Baire
space, respectively, and we examine how this analogy breaks down. This is
joint work with Julia Knight and Dan Turetsky.
Previous Seminars:
- Sept 23rd 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 21st 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 Ocasio-González - Jonathan Stephenson
- April 29th, 2014 Rod Downey -
Noam Greenberg - Gregory Igusa - Alexander Melnikov - Kyle Riggs
- September 30th, 2014 Eric Astor -
Quinn Culver - Jack Lutz - Timothy McNicholl
- February 17th, 2015 Carl Jockusch -
Julia Knight - Steffen Lempp
- January 28th, 2016 Reese Johnston -
Rutger Kuyper - Mariya Soskova - Mars Yamaleev
- October 22nd and 23rd, 2016
Special Meeting in Honor of Carl Jockusch's 75th Birthday
- March 16th, 2017 Greg Igusa -
Jack Lutz - Sasha Melnikov - Reed Solomon
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.