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 B139 in fall, B215 in spring
* '''Where:''' Van Vleck B123
* '''Organizers:''' Karthik Ravishankar and [https://sites.google.com/wisc.edu/antonio Antonio Nakid Cordero] in fall; Steffen Lempp and Manlio Valenti in spring
* '''Organizer:''' Mariya Soskova


The talk schedule is arranged at the beginning of each semester. If you would like to participate, please contact one of the organizers.
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:  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]


== Spring 2023 ==
== Fall 2024 ==


The seminar will be run as a 1-credit seminar Math 975 in spring, check out the [https://canvas.wisc.edu/courses/335062 Canvas page].If you are not enrolled but would like to audit it, please contact [mailto:lempp@math.wisc.edu Steffen Lempp] and [mailto:mvalenti2@wisc.edu Manlio Valenti].
The seminar will be run as a 1-credit seminar Math 975 . In Fall 2024, the topic will be Higher Computability Theory. We will follow notes by Noam Greenberg. If you are not enrolled but would like to audit it, please contact [mailto:soskova@wisc.edu Mariya Soskova].


== Fall 2022 ==
Presentation Schedule: [https://docs.google.com/spreadsheets/d/1ect-dgHdoHOgq4-5BGFiDh6pPThLfDg69Yg__-b_5RY/edit?usp=sharing Sign up here.]


=== September 12 - Organizational Meeting ===
Notes: [https://uwmadison.box.com/s/j3xftdj1i70d4lblxhzswhg9e25ajcpq Download the notes here.] You will need your UW-login. Please, do not distribute these notes without permission from the author.


We will meet to assign speakers to dates.
<!--Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)-->


=== '''September 19 - Karthik Ravishankar''' ===
=== '''September 9 - Organizational Meeting''' ===
'''Title:''' Lowness for Isomorphism ([https://wiki.math.wisc.edu/images/Karthik_talk.pdf Slides])


'''Abstract:''' A Turing degree is said to be low for isomorphism if it can only compute an isomorphism between computable structures only when a computable isomorphism already exists. In this talk, we show that the measure of the class of low for isomorphism sets in Cantor space is 0 and that no Martin Lof random is low for isomorphism.
Mariya Soskova will start with the first sections from the notes.


=== '''September 26 - Antonio Nakid Cordero'''  ===
We will then assign speakers to dates and topics.
'''Title:''' When Models became Polish: an introduction to the Topological Vaught Conjecture ([[Media:GradLogSem - Topological Vaught Conjecture.pdf|Slides]])


'''Abstract:''' Vaught's Conjecture, originally asked by Vaught in 1961, is one of the most (in)famous open problems in mathematical logic. The conjecture is that a complete theory on a countable language must either have countably-many or continuum-many non-isomorphic models. In this talk, we will discuss some of the main ideas that surround this conjecture, with special emphasis on a topological generalization in terms of the continuous actions of Polish groups.
=== '''September 16 -  Sections 1.2-1.4''' ===


=== '''October 10 - Yunting Zhang''' ===
Kanav Madhura will continue with Sections 1.2-1.4.  
'''Title:''' Some History of Logic ([[Media:Godel.pdf|Slides]])


'''Abstract:''' The lives of great thinkers are sometimes overshadowed by their achievements-and there is perhaps no better illustration of this phenomenon than the life and work of Gödel. Take a look at Gödel's own timeline and see how wars and other mathematicians influenced him.
=== '''September 23 -  Sections 1.3-1.4 and 2.1-2.2''' ===


=== '''October 17 - Alice Vidrine''' ===
Kanav Madhura will continue with Sections 1.3-1.4. Lucas Duckworth will be ready with Sections 2.1 and 2.2 should there be time.  
'''Title:''' Local operators, bilayer Turing reducibility, and enumeration Weihrauch degrees ([[Media:LTeW-talk.pdf|Slides]])


'''Abstract:''' Realizability toposes have a rich variety of subtoposes, corresponding to their local operators. These local operators are somewhat difficult to study in their usual form, which seems far removed from the usual objects of computability theoretic study. Recent work by Takayuki Kihara has given a characterization of the local operators on the effective topos in computability theoretic terms related to Weihrauch reduction, and which generalizes to several other realizability toposes of possible interest to computability theorists. This narrative-focused talk outlines what a realizability topos looks like, what local operators are, what Kihara's bilayer Turing reduction looks like, and how this leads to preliminary questions about a relative of the Weihrauch degrees based on enumeration reduction.
=== '''September 30 - Sections 2.2 and 2.3-2.5''' ===


=== '''October 24 - Hongyu Zhu''' ===
Lucas Duckworth will finish Section 2.2. Karthik Ravishankar will begin 2.3, 2.4, and 2.5.
'''Title:''' Investigating Natural Theories through the Consistency Operator ([[Media:ConsistencyOperator.pdf|Slides]])
=== '''October 7th - Sections 2.4 and 2.5''' ===


'''Abstract:''' The phenomenon that "natural" theories tend to be linearly ordered in terms of consistency strength is a long-standing mystery. One approach to solving the problem is Martin's Conjecture, which roughly claims that the only natural functions on the Turing degrees are transfinite iterates of the Turing jump. In this talk we will focus on a similar approach, working inside the Lindenbaum algebra of elementary arithmetic instead of the Turing degrees. Here, the consistency operator takes the role of the jump. We will see that while some nice analogous claims can be established, there are also counterexamples that prevent us from strengthening the results in various ways.  
Karthik Ravishankar will  finish, 2.4, and 2.5. Liang Yu will give a talk at 4:00pm.


=== '''October 31 - Break for Halloween''' ===
=== '''October 14th - Sections 2.6 and 2.7''' ===


=== '''November 7 - John Spoerl''' ===
Bjarki Gunnarsson  will present Sections 2.6 and 2.7  
'''Title:''' Universal Algorithms


'''Abstract:''' Among the many ways we can flex Gödel’s Incompleteness theorems, there is one that feels especially strange: there is a partial computable function F, such that F gives no output in the standard model of arithmetic, but for any function G on natural numbers (computable or not) there is a non-standard model in which F behaves exactly as G. I’ll discuss some related arguments and some philosophical questions this may raise about our notions of finiteness and determinism.
=== '''October 21th -  Section 3.1''' ===


=== '''November 14 - Josiah Jacobsen-Grocott''' ===
Karthik Ravishankar will present Section 3.1 
'''Title:''' The Paris-Harrington Theorem


'''Abstract:''' In this talk, I will present the proof of the Paris-Harrington theorem. The
=== '''October 28th - Sections 3.2 and 3.3''' ===
Paris-Harrington theorem states that over PA the consistency of Peano arithmetic is equivalent to
a strengthening of the finite Ramsey theorem. This was the first example of a result from "ordinary
mathematics" that can not be proven by PA. The aim of this talk is to cover the main logical
steps in this proof and give some of the combinatorics.


=== '''November 21 - Karthik Ravishankar''' ===
Karthik Ravishankar will finish Sections 3.2  and John Spoerl will begin Section 3.3
'''Title:''' The computing power of Baire space vs Cantor Space


'''Abstract:''' Generic Muchnik reducibility extends the notion of Muchnik reducibility to the uncountable setting. In this talk we'll look at some recent work which comes up with another technique of constructing a structure of degree strictly between Cantor space and Baire Space. We'll see that there is a generic copy of Cantor space which computes no escaping function while every copy of Baire space computes a dominating function. We then construct a structure of intermediate degree which always computes an escaping function but no dominating function.
=== '''November 4th -  Sections 3.3 and 3.4''' ===


=== '''November 28 - Logan Heath''' ===
John Spoerl will finish Sections 3.3 and 3.4
'''Title''': A Mathematical Analysis of Theories of Generative Grammar: The Peters-Ritchie Theorem ([[Media:Peters Ritchie Theorem-2.pdf|Slides]])


'''Abstract''': This is a preview of a talk intended primarily for undergraduate students in linguistics who have just completed a first course in syntax. The goal of the talk is to spark interest in applications of mathematical techniques to the study of theories of syntax. We will focus on the Peters-Ritchie Theorem which shows that transformational grammars can generate languages which are c.e., but not computable.
=== '''November 11th -  Section 4.1''' ===


=== '''December 12 - Yuxiao Fu''' ===
Antonion Nakid-Cordero will present Section 4.1
'''Title:''' Brief Introduction to Modal Logic ([[Media:Intro to Modal Logic.pdf|Slides]])


'''Abstract:''' In this talk, I plan to give a mathematical introduction to modal logic and its applications, covering its syntax and semantics, Kripke frames and models, bisimulations, filtrations, frame definability, automatic first-order correspondence, canonical models, and conclude with the completeness of normal modal logics.
=== '''November 19th -  Sections 4.1 and 4.2''' ===
 
Start 4:00PM in VV901! Antonion Nakid-Cordero will continue with Section 4.1, Ang Li will begin Section 4.2.
 
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=== '''September 18 - xxx''' ===
'''Title:''' TBA ([https://wiki.math.wisc.edu/images/***.pdf Slides])
 
'''Abstract:''' TBA
 
-->


== Previous Years ==
== 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 19:37, 18 November 2024

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 B123
  • Organizer: Mariya Soskova

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: join-grad-logic-sem@lists.wisc.edu

Fall 2024

The seminar will be run as a 1-credit seminar Math 975 . In Fall 2024, the topic will be Higher Computability Theory. We will follow notes by Noam Greenberg. If you are not enrolled but would like to audit it, please contact Mariya Soskova.

Presentation Schedule: Sign up here.

Notes: Download the notes here. You will need your UW-login. Please, do not distribute these notes without permission from the author.


September 9 - Organizational Meeting

Mariya Soskova will start with the first sections from the notes.

We will then assign speakers to dates and topics.

September 16 - Sections 1.2-1.4

Kanav Madhura will continue with Sections 1.2-1.4.

September 23 - Sections 1.3-1.4 and 2.1-2.2

Kanav Madhura will continue with Sections 1.3-1.4. Lucas Duckworth will be ready with Sections 2.1 and 2.2 should there be time.

September 30 - Sections 2.2 and 2.3-2.5

Lucas Duckworth will finish Section 2.2. Karthik Ravishankar will begin 2.3, 2.4, and 2.5.

October 7th - Sections 2.4 and 2.5

Karthik Ravishankar will finish, 2.4, and 2.5. Liang Yu will give a talk at 4:00pm.

October 14th - Sections 2.6 and 2.7

Bjarki Gunnarsson will present Sections 2.6 and 2.7

October 21th - Section 3.1

Karthik Ravishankar will present Section 3.1

October 28th - Sections 3.2 and 3.3

Karthik Ravishankar will finish Sections 3.2 and John Spoerl will begin Section 3.3

November 4th - Sections 3.3 and 3.4

John Spoerl will finish Sections 3.3 and 3.4

November 11th - Section 4.1

Antonion Nakid-Cordero will present Section 4.1

November 19th - Sections 4.1 and 4.2

Start 4:00PM in VV901! Antonion Nakid-Cordero will continue with Section 4.1, Ang Li will begin Section 4.2.


Previous Years

The schedule of talks from past semesters can be found here.

Retrieved from "https://wiki.math.wisc.edu/index.php?title=Graduate_Logic_Seminar&oldid=27618"