Midwest
Computability Seminar
XXVI
Part iii
The Midwest Computability
Seminar is meeting remotely in the winter and spring of 2021. The recurring Zoom link is:
https://notredame.zoom.us/j/99754332165?pwd=RytjK1RFZU5KWnZxZ3VFK0g4YTMyQT09
Meeting ID: 997 5433 2165
Passcode: midwest
slides
Panopto
video YouTube video
This session will be held jointly with the Computability Theory and
Applications Online Seminar.
DATE: Monday, March 1st, 2021
TIME: 3:30 - 4:30 PM
Central Time
SPEAKER: Kirsten Eisenträger - The Pennsylvania State
University
TITLE: A topological approach to undefinability in algebraic
extensions of the rationals
ABSTRACT: In 1970 Matiyasevich proved that Hilbert’s Tenth
Problem over
the integers is undecidable, building on work by Davis-Putnam-Robinson.
Hilbert’s Tenth Problem over the rationals is still open, but it could
be resolved by giving an existential definition of the integers inside
the rationals.
Proving whether such a definition exists is still out of reach. However,
we will show that only “very few” algebraic extensions of the rationals
have the property that their ring of integers are existentially or
universally definable. Equipping the set of all algebraic extensions of
the rationals with a natural topology, we show that only a meager subset
has this property. An important tool is a new normal form theorem for
existential definitions in such extensions. As a corollary, we
construct countably many distinct computable algebraic extensions whose
rings of integers are neither existentially nor universally definable.
Joint work with Russell Miller, Caleb Springer, and Linda Westrick.
Past and Future Sessions
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
- August - December, 2020 Nine Online
Talks
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.