Graduate Logic Seminar: Difference between revisions
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* '''When:''' Mondays 3:30-4:30 PM | * '''When:''' Mondays 3:30-4:30 PM | ||
* '''Where:''' Van Vleck | * '''Where:''' Van Vleck B211 | ||
* ''' | * '''Organizer:''' Joseph Miller | ||
The talk schedule is arranged at the beginning of each semester. If you would like to participate, please contact | The talk schedule is arranged at the beginning of each semester. If you would like to participate, please contact the organizers. | ||
Sign up for the graduate logic seminar mailing list: [mailto:join-grad-logic-sem@lists.wisc.edu join-grad-logic-sem@lists.wisc.edu] | <!--Sign up for the graduate logic seminar mailing list: [mailto:join-grad-logic-sem@lists.wisc.edu join-grad-logic-sem@lists.wisc.edu]--> | ||
== Fall | ==Fall 2025== | ||
The seminar will be run as a 1-credit seminar Math 975 | The seminar will be run as a 1-credit seminar Math 975. In Fall 2025 students will present a logic topic of their choice (it could be original work, but does not have to be). If you are not enrolled but would like to audit it, please contact [mailto:jmiller@math.wisc.edu Joe Miller]. | ||
Presentation Schedule: [https://docs.google.com/spreadsheets/d/1uRSaI1edJ5sepz57NV07ohIfBSKL9FgkvJvMAewk1ms/edit?usp=sharing Sign up here.] | |||
<!--Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)--> | |||
=== September | ==='''September 8 - Organizational Meeting'''=== | ||
We will meet to | We will meet to arrange the schedule | ||
< | ==='''September 15 - Karthik Ravishankar: Contrasting the halves of an Ahmad pair''' === | ||
Abstract: We study Ahmad pairs in the $\Sigma^0_2$ enumeration degrees. We say $(A,B)$ form an Ahmad pair if $A \not \leq_e B$ and every $Z <_e A$ satisfies $Z \leq_e B$. Ahmad pairs have recently drawn interest as they are a key obstacle in solving the $\forall\exists$ theory of the local structure. | |||
In this talk we characterize the left halves of an Ahmad pair as precisely the low$_3$ and join irreducible degrees. We also show that right halves cannot be low$_3$. This is a natural separation between the two halves and is a significant strengthening of previous work. | |||
We then define a hierarchy of join irreducibility notions using which we characterize the left halves of Ahmad $n$-pairs as those that are low$_3$ and $n$-join irreducible. This allows us to extend and clarify previous work to show that for any $n$ there is a set $A$ which is the left half of an Ahmad $n$-pair but not of an Ahmad $(n+1)$-pair. | |||
- | === '''September 22 - Dan Turetsky: An introduction to the method of true stages. Part 1.''' === | ||
Abstract: True stages are a method for organizing complex constructions in computability theory. Over several lectures, I'll explain the method of true stages by working through some examples in computable structure theory. We'll start with some necessary computability background. Time permitting, I may discuss some of the applications of true stages to descriptive set theory. | |||
=== '''September 29 - Dan Turetsky: An introduction to the method of true stages. Part 3.''' === | |||
Abstract: True stages are a method for organizing complex constructions in computability theory. Over several lectures, I'll explain the method of true stages by working through some examples in computable structure theory. We'll start with some necessary computability background. Time permitting, I may discuss some of the applications of true stages to descriptive set theory. | |||
== Previous Years == | === '''October 6 - Dhruv Kulshreshtha: Classification by countable structures''' === | ||
Abstract: Self-homeomorphisms of the interval [0,1] can be classified up to conjugacy by using certain countable structures as invariants. On the other hand, Hjorth showed that there is no definable way to classify self-homeomorphisms of the square [0,1]^2 in this manner. | |||
In this talk, upon making these notions precise, we briefly discuss the machinery that is used to prove the aforementioned negative result. We then take a step towards studying the more general interplay between dimension and classifiability by arguing that homeomorphisms of the Sierpiński carpet, the one-dimensional universal plane curve, also cannot be classified in this manner. This result is based on joint work with Aristotelis Panagiotopoulos. | |||
=== '''October 13 - Chiara Travesset''' === | |||
==='''October 20 -''' === | |||
=== '''October 27 - Yiqing Wang''' === | |||
=== '''November 3 - Logan Heath''' === | |||
==='''November 10 - Antonio Nakid Cordero''' === | |||
==='''November 17 - Hongyu Zhu''' === | |||
==='''November 24 - Taeyoung Em''' === | |||
==='''December 1 - Lucas Duckworth''' === | |||
==='''December 8 - John Spoerl''' === | |||
== Previous Years== | |||
The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semesters|here]]. | The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semesters|here]]. | ||
Latest revision as of 19:04, 29 September 2025
The Graduate Logic Seminar is an informal space where graduate students and professors present topics related to logic which are not necessarily original or completed work. This is a space focused principally on practicing presentation skills or learning materials that are not usually presented in a class.
- When: Mondays 3:30-4:30 PM
- Where: Van Vleck B211
- Organizer: Joseph Miller
The talk schedule is arranged at the beginning of each semester. If you would like to participate, please contact the organizers.
Fall 2025
The seminar will be run as a 1-credit seminar Math 975. In Fall 2025 students will present a logic topic of their choice (it could be original work, but does not have to be). If you are not enrolled but would like to audit it, please contact Joe Miller.
Presentation Schedule: Sign up here.
September 8 - Organizational Meeting
We will meet to arrange the schedule
September 15 - Karthik Ravishankar: Contrasting the halves of an Ahmad pair
Abstract: We study Ahmad pairs in the $\Sigma^0_2$ enumeration degrees. We say $(A,B)$ form an Ahmad pair if $A \not \leq_e B$ and every $Z <_e A$ satisfies $Z \leq_e B$. Ahmad pairs have recently drawn interest as they are a key obstacle in solving the $\forall\exists$ theory of the local structure.
In this talk we characterize the left halves of an Ahmad pair as precisely the low$_3$ and join irreducible degrees. We also show that right halves cannot be low$_3$. This is a natural separation between the two halves and is a significant strengthening of previous work.
We then define a hierarchy of join irreducibility notions using which we characterize the left halves of Ahmad $n$-pairs as those that are low$_3$ and $n$-join irreducible. This allows us to extend and clarify previous work to show that for any $n$ there is a set $A$ which is the left half of an Ahmad $n$-pair but not of an Ahmad $(n+1)$-pair.
September 22 - Dan Turetsky: An introduction to the method of true stages. Part 1.
Abstract: True stages are a method for organizing complex constructions in computability theory. Over several lectures, I'll explain the method of true stages by working through some examples in computable structure theory. We'll start with some necessary computability background. Time permitting, I may discuss some of the applications of true stages to descriptive set theory.
September 29 - Dan Turetsky: An introduction to the method of true stages. Part 3.
Abstract: True stages are a method for organizing complex constructions in computability theory. Over several lectures, I'll explain the method of true stages by working through some examples in computable structure theory. We'll start with some necessary computability background. Time permitting, I may discuss some of the applications of true stages to descriptive set theory.
October 6 - Dhruv Kulshreshtha: Classification by countable structures
Abstract: Self-homeomorphisms of the interval [0,1] can be classified up to conjugacy by using certain countable structures as invariants. On the other hand, Hjorth showed that there is no definable way to classify self-homeomorphisms of the square [0,1]^2 in this manner.
In this talk, upon making these notions precise, we briefly discuss the machinery that is used to prove the aforementioned negative result. We then take a step towards studying the more general interplay between dimension and classifiability by arguing that homeomorphisms of the Sierpiński carpet, the one-dimensional universal plane curve, also cannot be classified in this manner. This result is based on joint work with Aristotelis Panagiotopoulos.
October 13 - Chiara Travesset
October 20 -
October 27 - Yiqing Wang
November 3 - Logan Heath
November 10 - Antonio Nakid Cordero
November 17 - Hongyu Zhu
November 24 - Taeyoung Em
December 1 - Lucas Duckworth
December 8 - John Spoerl
Previous Years
The schedule of talks from past semesters can be found here.