Graduate Logic Seminar: Difference between revisions

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The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly 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.
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 4p-5p
* '''When:''' Mondays 3:30-4:30 PM
* '''Where:''' Van Vleck B223.
* '''Where:''' Van Vleck B123
* '''Organizers:''' [https://www.math.wisc.edu/~omer/ Omer Mermelstein]
* '''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]


== 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 [mailto:soskova@wisc.edu Mariya Soskova].


== Fall 2019 - Tentative schedule ==
Presentation Schedule: [https://docs.google.com/spreadsheets/d/1ect-dgHdoHOgq4-5BGFiDh6pPThLfDg69Yg__-b_5RY/edit?usp=sharing Sign up here.]


=== September 5 - 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.


=== September 9 - No seminar ===
<!--Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)-->


=== September 16 - Daniel Belin ===
=== '''September 9 - Organizational Meeting''' ===
Title: Lattice Embeddings of the m-Degrees and Second Order Arithmetic


Abstract: Lachlan, in a result later refined and clarified by Odifreddi, proved in 1970 that initial segments of the m-degrees can be embedded as an upper semilattice formed as the limit of finite distributive lattices. This allows us to show that the many-one degrees codes satisfiability in second-order arithmetic, due to a later result of Nerode and Shore. We will take a journey through Lachlan's rather complicated construction which sheds a great deal of light on the order-theoretic properties of many-one reducibility.
Mariya Soskova will start with the first sections from the notes.


=== September 23 - Daniel Belin ===
We will then assign speakers to dates and topics.


Title: Lattice Embeddings of the m-Degrees and Second Order Arithmetic - Continued
=== '''September 16 - Sections 1.2-1.4''' ===


=== September 30 - Josiah Jacobsen-Grocott ===
Kanav Madhura will continue with Sections 1.2-1.4.


Title: Scott Rank of Computable Models
=== '''September 23 -  Sections 1.3-1.4 and 2.1-2.2''' ===


Abstract: Infinatary logic extends the notions of first order logic by allowing infinite formulas. Scott's Isomorphism Theorem states that any countable structure can be characterized up to isomorphism by a single countable sentence. Closely related to the complexity of this sentence is what is known as the Scott Rank of the structure. In this talk we restrict our attention to computable models and look at an upper bound on the Scott Rank of such structures.
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.  


=== October 7 - Josiah Jacobsen-Grocott ===
=== '''September 30 - Sections 2.2 and 2.3-2.5''' ===


Title: Scott Rank of Computable Codels - Continued
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''' ===


=== October 14 - Tejas Bhojraj ===
Karthik Ravishankar will  finish, 2.4, and 2.5.  Liang Yu will give a talk at 4:00pm.


Title: Solovay and Schnorr randomness for infinite sequences of qubits.
=== '''October 14th -  Sections 2.6 and 2.7''' ===


Abstract : We define Solovay and Schnorr randomness in the quantum setting. We then prove quantum versions of the law of large numbers and of the Shannon McMillan Breiman theorem (only for the iid case) for quantum Schnorr randoms.
Bjarki Gunnarsson  will present Sections 2.6 and 2.7


=== October 23 - Tejas Bhojraj ===
=== '''October 21th - Section 3.1''' ===


Title: Solovay and Schnorr randomness for infinite sequences of qubits - continued
Karthik Ravishankar will present Section 3.1 


Unusual time and place: Wednesday October 23, 4:30pm, Van Vleck B321.
=== '''October 28th -  Sections 3.2 and 3.3''' ===


=== October 28 - Two short talks ===
Karthik Ravishankar will finish Sections 3.2  and John Spoerl will begin Section 3.3


'''Iván Ongay Valverde''' - Exploring different versions of the Semi-Open Coloring Axiom (SOCA)
=== '''November 4th -  Sections 3.3 and 3.4''' ===


In 1985, Avraham, Rubin and Shelah published an article where they introduced different coloring axioms. The weakest of them, the Semi-Open Coloring Axiom (SOCA), states that given an uncountable second countable metric space, $E$, and $W\subseteq E^{\dagger}:=E\times E\setminus \{(x, x) :x \in E\}$ open and symmetric, there is an uncountable subset $H\subseteq E$ such that either $H^{\dagger}\subseteq W$ or $H^{\dagger}\cap W=\emptyset$. We say that $W$ is an open coloring and $H$ is a homogeneous subset of $E$. This statement contradicts CH but, as shown also by Avraham, Rubin and Shelah, it is compatible with the continuum taking any other size. This classic paper leaves some questions open (either in an implicit or an explicit way):
John Spoerl will finish Sections 3.3 and 3.4


- Is the axiom weaker if we demand that $W$ is clopen?
=== '''November 11th - Section 4.1''' ===
- If the continuum is bigger than $\aleph_2$, can we ask that $H$ has the same size as $E$?
- Can we expand this axiom to spaces that are not second countable and metric?


These questions lead to different versions of SOCA. In this talk, we will analyze how they relate to the original axiom.
Antonion Nakid-Cordero will present Section 4.1


'''James Earnest Hanson''' - Strongly minimal sets in continuous logic
=== '''November 19th -  Sections 4.1 and 4.2''' ===


The precise structural understanding of uncountably categorical theories given by the proof of the Baldwin-Lachlan theorem is known to fail in continuous logic in the context of inseparably categorical theories. The primary obstacle is the absence of strongly minimal sets in some inseparably categorical theories. We will develop the concept of strongly minimal sets in continuous logic and discuss some common conditions under which they are present in an $\omega$-stable theory. Finally, we will examine the extent to which we recover a Baldwin-Lachlan style characterization in the presence of strongly minimal sets.
Start 4:00PM in VV901! Antonion Nakid-Cordero will continue with Section 4.1, Ang Li will begin Section 4.2.


=== November 4 - Two short talks ===


'''Manlio Valenti''' - The complexity of closed Salem sets (20 minutes version)
=== '''November 25th -  Sections 4.2 and 4.3''' ===


A central notion in geometric measure theory is the one of Hausdorff dimension. As a consequence of Frostman's lemma, the Hausdorff dimension of a Borel subset A of the Euclidean n-dimensional space can be determined by looking at the behaviour of probability measures with support in A. The possibility to apply methods from Fourier analysis to estimate the Hausdorff dimension gives birth to the notion of Fourier dimension. It is known that, for Borel sets, the Fourier dimension is less than or equal to the Hausdorff dimension. The sets for which the two notions agree are called Salem sets.
Back to the usual time and place. Ang Li will begin Section 4.2.
<br/>
In this talk we will study the descriptive complexity of the family of closed Salem subsets of the real line.  


'''Patrick Nicodemus''' - Proof theory of Second Order Arithmetic and System F
=== '''December 2nd -  Section 4.3''' ===


A central theme in proof theory is to show that some formal system has the property that whenever A is provable, there is a proof of A in "normal form" - a direct proof without any detours. Such results have numerous and immediate consequences - often consistency follows as an easy corollary. The Curry Howard correspondence describes of equivalences between normalization of proofs and program termination in typed lambda calculi. We present an instance of this equivalence, between the proof theory of intuitionistic second order arithmetic and the second order polymorphic lambda calculus of Girard and Reynolds, aka system F.
Ang Li will present Section 4.3.


=== November 11 - Manlio Valenti ===
=== '''December 9nd - Section 5.1''' ===


Title: The complexity of closed Salem sets (full length)
Last seminar for this semester. Sapir Ben-Shahar will begin Section 5.1


Abstract:
<!-- Template
A central notion in geometric measure theory is the one of Hausdorff dimension. As a consequence of Frostman's lemma, the Hausdorff dimension of a Borel subset A of the Euclidean n-dimensional space can be determined by looking at the behaviour of probability measures with support in A. The possibility to apply methods from Fourier analysis to estimate the Hausdorff dimension gives birth to the notion of Fourier dimension. It is known that, for Borel sets, the Fourier dimension is less than or equal to the Hausdorff dimension. The sets for which the two notions agree are called Salem sets.
<br/>
In this talk we will study the descriptive complexity of the family of closed Salem subsets of the real line.


=== November 18 - Iván Ongay Valverde ===
=== '''September 18 - xxx''' ===
'''Title:''' TBA ([https://wiki.math.wisc.edu/images/***.pdf Slides])


Title: A couple of summer results
'''Abstract:''' TBA


Abstract: Lately, I have been studying how subsets of reals closed under Turing equivalence behave through the lenses of algebra, measure theory and orders.
-->


In this talk I will classify which subsets of reals closed under Turing equivalence generate subfields or $\mathbb{Q}$-vector spaces of $\mathbb{R}$. We will show that there is a non-measurable set whose Turing closure becomes measurable (and one that stays non-measurable) and, if we have enough time, we will see a model where there are 5 possible order types for $\aleph_1$ dense subsets of reals, but just 1 for $\aleph_1$ dense subsets of reals closed under Turing equivalence.
== Previous Years ==
 
=== November 25 - Anniversary of the signing of the Treaty of Granada - No seminar ===
 
=== December 2 - Anniversary of the Battle of Austerlitz - No seminar ===
 
=== December 9 - Anniversary of the death of Pope Pius IV - No seminar  ===
 
==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 19:29, 2 December 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.


November 25th - Sections 4.2 and 4.3

Back to the usual time and place. Ang Li will begin Section 4.2.

December 2nd - Section 4.3

Ang Li will present Section 4.3.

December 9nd - Section 5.1

Last seminar for this semester. Sapir Ben-Shahar will begin Section 5.1


Previous Years

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

Retrieved from "https://wiki-dev.math.wisc.edu/index.php?title=Graduate_Logic_Seminar&oldid=27704"