Midwest
Computability Seminar
XXV
Part ii
The Midwest Computability
Seminar is meeting remotely in the fall of 2020. The recurring Zoom link is:
https://notredame.zoom.us/j/99754332165?pwd=RytjK1RFZU5KWnZxZ3VFK0g4YTMyQT09
Meeting ID: 997 5433 2165
Passcode: midwest
Slides YouTube
video Panopto
video
This session will be held jointly with the
Computability Theory and Applications Online Seminar.
DATE: Tuesday, September 1st, 2020
TIME: 3:00 - 4:00 PM CDT
SPEAKER: Patrick Lutz - University of California, Berkeley
TITLE: Part 1 of Martin's Conjecture for Order Preserving
Functions
ABSTRACT:
Martin's conjecture is an attempt to make precise the idea that the only
natural functions on the Turing degrees are the constant functions, the
identity, and transfinite iterates of the Turing jump. The conjecture is
typically divided into two parts. Very roughly, the first part states that
every natural function on the Turing degrees is either eventually constant
or eventually increasing and the second part states that the natural
functions which are increasing form a well-order under eventual
domination, where the successor operation in this well-order is the Turing
jump.
In the 1980's, Slaman and Steel proved that the second part of Martin's
conjecture holds for order-preserving Borel functions. In joint work with
Benny Siskind, we prove the complementary result that (assuming analytic
determinacy) the first part of the conjecture also holds for
order-preserving Borel functions (and under AD, for all order-preserving
functions). Our methods also yield several other new results, including an
equivalence between the first part of Martin's conjecture and a statement
about the Rudin-Keisler order on ultrafilters on the Turing degrees.
In my talk, I will give an overview of Martin's conjecture and then
describe our new results.
Past and Future Sessions
- August 18th, 2020 Joe Miller -
University of
Wisconsin–Madison YouTube video
Panopto
video
- September 15th, 2020: Justin Miller - University of Notre Dame
- September 29th, 2020: Christopher Porter - Drake University
- October 13th, 2020: Leszek Kołodziejczyk - University of Warsaw
- October 27th, 2020: Li Ling Ko - University of Notre Dame
- November 10th, 2020: Paul Shafer - University of Leeds
- November 24th, 2020: Karen Lange - Wellesley College
- December 8th, 2020: Linda Westrick - The Pennsylvania State University
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
- October 24th, 2017 Noah Schweber
- Don Stull - Dan Turetsky - Rose Weisshaar
- April 17th, 2018 Peter Cholak -
Meng-Che "Turbo" Ho - Ethan McCarthy - Joe Miller
- October 9th, 2018 Uri Andrews -
Timothy McNicholl - Alexandra Soskova
- April 18th, 2019 Wesley Calvert - Russell Miller - Steffen Lempp
- February 11th, 2020 Rachael Alvir - Tejas Bhojraj - Jun Le Goh - Neil Lutz
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.