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.
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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 4p-5p
* '''Where:''' Van Vleck B215.
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* '''Where:''' on line (ask for code).
* '''Organizers:''' [https://www.math.wisc.edu/~omer/ Omer Mermelstein]
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* '''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 ==
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== Fall 2020 - Tentative schedule ==
  
=== January 28 - Talk by visitor - No seminar ===
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=== September 14 - Josiah Jacobsen-Grocott ===
=== February 3 - Talk by visitor - No seminar ===
 
=== February 10 - No seminar (speaker was sick) ===
 
  
=== February 17 - James Hanson ===
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Title: Degrees of points in topological spaces
  
Title: The Topology of Definable Sets in Continuous Logic
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Abstract: An overview of some results from Takayuki Kihara, Keng Meng Ng, and Arno Pauly in their paper Enumeration Degrees and Non-Metrizable Topology. We will look at a range of topological spaces and the corresponding classes in the enumeration degrees as well as ways in which we can distinguish the type of classes using the separation axioms.
  
Abstract: We will look at the topology of certain special subsets of type spaces in continuous logic, such as definable sets. In the process we will characterize those type spaces which have 'enough definable sets' and look at some counterexamples to things which would have been nice.
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=== September 28 - James Hanson ===
  
=== February 24 - Two short talks - Tejas Bhojraj and Josiah Jacobsen-Grocott ===
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Title: The Semilattice of Definable Sets in Continuous Logic
  
Title: A Characterization of Strongly $\eta$-Representable Degrees.
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Abstract: After an analysis-free exposition of definable sets in continuous logic, we will present a fun, illustrated proof that any finite bounded lattice can be the poset of definable subsets of $S_1(T)$ for a continuous theory $T$.
  
Abstract:
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=== October 5 - Tejas Bhojraj from 3:30PM-4:00PM ===
$\eta$-representations are a way of coding sets in computable linear orders that were first
 
introduced by Fellner in his PhD thesis. Limitwise monotonic functions have been used to
 
characterize the sets with $\eta$-representations as well as the sets with subclasses of
 
$\eta$-representations except for the case of sets with strong $\eta$-representations, the only
 
class where the order type of the representation is unique.
 
  
We introduce the notion of a connected approximation of a set, a variation on $\Sigma^0_2$
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Title: A Levin-Schnorr type result for Weak Solovay random states.
approximations. We use connected approximations to
 
give a characterization of the degrees with strong $\eta$-representations as well new
 
characterizations of the subclasses of $\eta$-representations with known characterizations.
 
  
=== March 2 - Patrick Nicodemus ===
+
Abstract: We look at the initial-segment complexity of Weak Solovay quantum random states using MK, a prefix-free version of quantum Kolmogorov complexity. The statement of our result is similar to the Levin-Schnorr theorem in classical algorithmic randomness.
=== March 9 - Patrick Nicodemus ===
 
=== March 16 - Spring break - No seminar ===
 
=== March 23 - Two short talks - Harry Main-Luu and Daniel Belin ===
 
=== March 30 - Josiah Jacobsen-Grocott ===
 
=== April 6 - Josiah Jacobsen-Grocott ===
 
=== April 13 - Faculty at conference - No seminar ===
 
=== April 20 - Harry Main-Luu ===
 
=== April 27 - Harry Main-Luu ===
 
 
 
 
 
 
 
== Fall 2019 ==
 
 
 
=== September 5 - Organizational meeting ===
 
 
 
=== September 9 - No seminar ===
 
 
 
=== September 16 - Daniel Belin ===
 
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.
 
 
 
=== September 23 - Daniel Belin ===
 
 
 
Title: Lattice Embeddings of the m-Degrees and Second Order Arithmetic - Continued
 
 
 
=== September 30 - Josiah Jacobsen-Grocott ===
 
 
 
Title: Scott Rank of Computable Models
 
 
 
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.
 
 
 
=== October 7 - Josiah Jacobsen-Grocott ===
 
 
 
Title: Scott Rank of Computable Codels - Continued
 
 
 
=== October 14 - Tejas Bhojraj ===
 
 
 
Title: Solovay and Schnorr randomness for infinite sequences of qubits.
 
 
 
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==
 
==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 13:18, 1 October 2020

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
  • Where: on line (ask for code).
  • 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 2020 - Tentative schedule

September 14 - Josiah Jacobsen-Grocott

Title: Degrees of points in topological spaces

Abstract: An overview of some results from Takayuki Kihara, Keng Meng Ng, and Arno Pauly in their paper Enumeration Degrees and Non-Metrizable Topology. We will look at a range of topological spaces and the corresponding classes in the enumeration degrees as well as ways in which we can distinguish the type of classes using the separation axioms.

September 28 - James Hanson

Title: The Semilattice of Definable Sets in Continuous Logic

Abstract: After an analysis-free exposition of definable sets in continuous logic, we will present a fun, illustrated proof that any finite bounded lattice can be the poset of definable subsets of $S_1(T)$ for a continuous theory $T$.

October 5 - Tejas Bhojraj from 3:30PM-4:00PM

Title: A Levin-Schnorr type result for Weak Solovay random states.

Abstract: We look at the initial-segment complexity of Weak Solovay quantum random states using MK, a prefix-free version of quantum Kolmogorov complexity. The statement of our result is similar to the Levin-Schnorr theorem in classical algorithmic randomness.

Previous Years

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