Difference between revisions of "Graduate Logic Seminar"

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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:''' Tuesdays 4-5 PM
* '''Where:''' Van Vleck B215.
+
* '''Where:''' Van Vleck 901
* '''Organizers:''' [https://www.math.wisc.edu/~omer/ Omer Mermelstein]
+
* '''Organizers:''' [https://www.math.wisc.edu/~jgoh/ Jun Le Goh]
  
 
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 one of the organizers.
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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:  join-grad-logic-sem@lists.wisc.edu
  
== Spring 2020 - Tentative schedule ==
+
== Fall 2021 tentative schedule ==
  
=== January 28 - Talk by visitor - No seminar ===
+
To see what's happening in the Logic qual preparation sessions click [[Logic Qual Prep|here]].
=== February 3 - Talk by visitor - No seminar ===
 
=== February 10 - James Hanson ===
 
=== February 17 - James Hanson ===
 
=== February 24 - Two short talks - Tejas Bhojraj and Josiah Jacobsen-Grocott ===
 
=== March 2 - Patrick Nicodemus ===
 
=== March 9 - Patrick Nicodemus ===
 
=== March 16 - Spring break - No seminar ===
 
=== March 23 - TBD ===
 
=== March 30 - Two short talks - Harry Main-Luu and Daniel Belin ===
 
=== April 6 - TBD ===
 
=== April 13 - Faculty at conference - No seminar ===
 
=== April 20 - Harry Main-Luu ===
 
=== April 27 - Harry Main-Luu ===
 
  
 +
=== September 14 - organizational meeting ===
  
 +
We met to discuss the schedule.
  
== Fall 2019 ==
+
=== September 28 - Ouyang Xiating ===
  
=== September 5 - Organizational meeting ===
+
Title: First-order logic, database and consistent query answering
  
=== September 9 - No seminar ===
+
Abstract: Databases are a crucial component of many (if not all) modern
 +
applications. In reality, the data stored are often dirty and contain
 +
duplicated/missing entries, and it is a natural practice to clean the data
 +
first before executing the query. However, the same query might return
 +
different answers on different cleaned versions of the dataset. It is then
 +
helpful to compute the consistent answers: the query answers that will always
 +
be returned, regardless of how the dirty data is cleaned. In this talk, we
 +
first introduce the connection between first-order logic and query languages
 +
on databases, and then discuss the problem of Consistent Query Answering
 +
(CQA): How to compute consistent answers on dirty data? Finally, we show
 +
when the CQA problem can be solved using first-order logic for path queries.
  
=== September 16 - Daniel Belin ===
+
=== October 12 - Karthik Ravishankar ===
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.
+
Title: Notions of randomness for subsets of the Natural Numbers
  
=== September 23 - Daniel Belin ===
+
Abstract: There are a number of notions of randomness of sets of natural numbers. These notions have been defined based on what a 'random object' should behave like such as being 'incompressible' or being 'hard to predict' etc. There is often a interplay between computability and randomness aspects of subsets of natural numbers. In this talk we motivate and present a few different notions of randomness and compare their relative strength.
  
Title: Lattice Embeddings of the m-Degrees and Second Order Arithmetic - Continued
+
=== October 26 - Alice Vidrine ===
  
=== September 30 - Josiah Jacobsen-Grocott ===
+
Title: Categorical logic for realizability, part III: Actual realizability
  
Title: Scott Rank of Computable Models
+
Abstract: Realizability is an approach to semantics for non-classical logic that interprets propositions by sets of abstract computational data. In the present talk we describe the notion of a Schonfinkel algebra (also called a partial combinatory algebra), which gives us a very general notion of computation. We then describe the construction of a topos whose notions of morphism and subobject must respect the computational structure, and describe the unusual features of these toposes, closing with some discussion of Lawvere-Tierney topologies on such toposes.
  
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.
+
(The abstracts for parts I and II, which were given in spring 2021, can be found [https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Logic_Seminar,_previous_semesters#March_30_4PM_-_Alice_Vidrine here].)
  
=== October 7 - Josiah Jacobsen-Grocott ===
+
=== November 9 - Antonio Nákid Cordero ===
  
Title: Scott Rank of Computable Codels - Continued
+
=== November 23 - Antonio Nákid Cordero? ===
  
=== October 14 - Tejas Bhojraj ===
+
=== December 7 - John Spoerl ===
  
Title: Solovay and Schnorr randomness for infinite sequences of qubits.
+
== Previous Years ==
 
 
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.
 
 
 
=== October 23 - Tejas Bhojraj ===
 
 
 
Title: Solovay and Schnorr randomness for infinite sequences of qubits - continued
 
 
 
Unusual time and place: Wednesday October 23, 4:30pm, Van Vleck B321.
 
 
 
=== October 28 - Two short talks ===
 
 
 
'''Iván Ongay Valverde''' - Exploring different versions of the Semi-Open Coloring Axiom (SOCA)
 
 
 
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):
 
 
 
- Is the axiom weaker if we demand that $W$ is clopen?
 
- 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.
 
 
 
'''James Earnest Hanson''' - Strongly minimal sets in continuous logic
 
 
 
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.
 
 
 
=== November 4 - Two short talks ===
 
 
 
'''Manlio Valenti''' - The complexity of closed Salem sets (20 minutes version)
 
 
 
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.
 
 
 
'''Patrick Nicodemus''' - Proof theory of Second Order Arithmetic and System F
 
 
 
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.
 
 
 
=== November 11 - Manlio Valenti ===
 
 
 
Title: The complexity of closed Salem sets (full length)
 
 
 
Abstract:
 
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 ===
 
 
 
Title: A couple of summer results
 
 
 
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.
 
 
 
=== 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]].

Revision as of 19:45, 21 October 2021

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: Tuesdays 4-5 PM
  • Where: Van Vleck 901
  • Organizers: Jun Le Goh

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

Sign up for the graduate logic seminar mailing list: join-grad-logic-sem@lists.wisc.edu

Fall 2021 tentative schedule

To see what's happening in the Logic qual preparation sessions click here.

September 14 - organizational meeting

We met to discuss the schedule.

September 28 - Ouyang Xiating

Title: First-order logic, database and consistent query answering

Abstract: Databases are a crucial component of many (if not all) modern applications. In reality, the data stored are often dirty and contain duplicated/missing entries, and it is a natural practice to clean the data first before executing the query. However, the same query might return different answers on different cleaned versions of the dataset. It is then helpful to compute the consistent answers: the query answers that will always be returned, regardless of how the dirty data is cleaned. In this talk, we first introduce the connection between first-order logic and query languages on databases, and then discuss the problem of Consistent Query Answering (CQA): How to compute consistent answers on dirty data? Finally, we show when the CQA problem can be solved using first-order logic for path queries.

October 12 - Karthik Ravishankar

Title: Notions of randomness for subsets of the Natural Numbers

Abstract: There are a number of notions of randomness of sets of natural numbers. These notions have been defined based on what a 'random object' should behave like such as being 'incompressible' or being 'hard to predict' etc. There is often a interplay between computability and randomness aspects of subsets of natural numbers. In this talk we motivate and present a few different notions of randomness and compare their relative strength.

October 26 - Alice Vidrine

Title: Categorical logic for realizability, part III: Actual realizability

Abstract: Realizability is an approach to semantics for non-classical logic that interprets propositions by sets of abstract computational data. In the present talk we describe the notion of a Schonfinkel algebra (also called a partial combinatory algebra), which gives us a very general notion of computation. We then describe the construction of a topos whose notions of morphism and subobject must respect the computational structure, and describe the unusual features of these toposes, closing with some discussion of Lawvere-Tierney topologies on such toposes.

(The abstracts for parts I and II, which were given in spring 2021, can be found here.)

November 9 - Antonio Nákid Cordero

November 23 - Antonio Nákid Cordero?

December 7 - John Spoerl

Previous Years

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