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 an space focus principally in practicing presentation skills or learning ma)
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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 an space focus principally in  practicing presentation skills or learning materials that are not usually presented on 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, 4:00 PM – 5:00 PM (unless otherwise announced).
* '''When:''' TBA
* '''Where:''' Van Vleck B235 (unless otherwise announced).
* '''Where:''' on line (ask for code).
* '''Organizers:''' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava]
* '''Organizers:''' [https://www.math.wisc.edu/~jgoh/ Jun Le Goh]


Talks schedule are arrange and decide 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.


== Spring 2018 ==
Sign up for the graduate logic seminar mailing list:  join-grad-logic-sem@lists.wisc.edu


=== January 29, Organizational meeting ===
== Spring 2021 - Tentative schedule ==


This day we decided the schedule for the semester.
=== February 16 3:30PM - Short talk by Sarah Reitzes (University of Chicago) ===


=== February 5, (person) ===
Title: Reduction games over $\mathrm{RCA}_0$


Title:  
Abstract: In this talk, I will discuss joint work with Damir D. Dzhafarov and Denis R. Hirschfeldt. Our work centers on the characterization of problems P and Q such that P $\leq_{\omega}$ Q, as well as problems P and Q such that $\mathrm{RCA}_0 \vdash$ Q $\to$ P, in terms of winning strategies in certain games. These characterizations were originally introduced by Hirschfeldt and Jockusch. I will discuss extensions and generalizations of these characterizations, including a certain notion of compactness that allows us, for strategies satisfying particular conditions, to bound the number of moves it takes to win. This bound is independent of the instance of the problem P being considered. This allows us to develop the idea of Weihrauch and generalized Weihrauch reduction over some base theory. Here, we will focus on the base theory $\mathrm{RCA}_0$. In this talk, I will explore these notions of reduction among various principles, including bounding and induction principles.


Abstract:  
=== March 23 4:15PM - Steffen Lempp ===


=== February 12, (Person) ===
Title: Degree structures and their finite substructures


Title:  
Abstract: Many problems in mathematics can be viewed as being coded by sets of natural numbers (as indices).
One can then define the relative computability of sets of natural numbers in various ways, each leading to a precise notion of “degree” of a problem (or set).
In each case, these degrees form partial orders, which can be studied as algebraic structures.
The study of their finite substructures leads to a better understanding of the partial order as a whole.


Abstract:
=== March 30 4PM - Alice Vidrine ===


=== February 19, (Person) ===
Title: Categorical logic for realizability, part I: Categories and the Yoneda Lemma


Title:  
Abstract: An interesting strand of modern research on realizability--a semantics for non-classical logic based on a notion of computation--uses the language of toposes and Grothendieck fibrations to study mathematical universes whose internal notion of truth is similarly structured by computation. The purpose of this talk is to establish the basic notions of category theory required to understand the tools of categorical logic developed in the sequel, with the end goal of understanding the realizability toposes developed by Hyland, Johnstone, and Pitts. The talk will cover the definitions of category, functor, natural transformation, adjunctions, and limits/colimits, with a heavy emphasis on the ubiquitous notion of representability.


Abstract:  
[https://hilbert.math.wisc.edu/wiki/images/Cat-slides-1.pdf Link to slides]


=== February 26, (Person) ===
=== April 27 4PM - Alice Vidrine ===


Title:  
Title: Categorical logic for realizability, part II


Abstract:  
Abstract: Realizability is an approach to semantics for non-classical logic that interprets propositions by sets of abstract computational data. One modern approach to realizability makes heavy use of the notion of a topos, a type of category that behaves like a universe of non-standard sets. In preparation for introducing realizability toposes, the present talk will be a brisk introduction to the notion of a topos, with an emphasis on their logical aspects. In particular, we will look at the notion of a subobject classifier and the internal logic to which it gives rise.
 
=== March 5, (Person) ===
 
Title:
 
Abstract:
 
=== March 12, (Person) ===
 
Title:
 
Abstract:
 
=== March 19, (Person) ===
 
Title:
 
Abstract:
 
=== April 2, (Person) ===
 
Title:
 
Abstract:
 
=== April 9, (Person) ===
 
Title:
 
Abstract:
 
=== April 16, Iván Ongay-Valverde ===
 
Title: What can we say about sets made by the union of Turing equivalence classes?
 
Abstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type 'the rationals' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes?
 
This topic hasn't been deeply studied. In this talk I will focus principally on famous order types and answer whether they can be achieved or not. Furthermore, I will explain some possible connections with the automorphism problem of the Turing degrees.
 
This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation (hopefully).
 
=== April 23, Ethan (Defense) ===
 
Title: TBA
 
Abstract: TBA
 
=== April 30, Linda ===
 
Title: TBA
 
Abstract: TBA
 
=== May 7, TBA ===
 
Title: TBA
 
Abstract: TBA
 
== Fall 2017 ==
 
=== September 11, Organizational meeting ===
 
This day we decided the schedule for the semester.
 
=== September 18, (person) ===
 
Title:
 
Abstract:
 
=== September 25, (Person) ===
 
Title:
 
Abstract:
 
=== October 2, (Person) ===
 
Title:
 
Abstract:
 
=== October 9, (Person) ===
 
Title:
 
Abstract:
 
=== October 16, (Person) ===
 
Title:
 
Abstract:
 
=== October 23, (Person) ===
 
Title:
 
Abstract:
 
=== October 30, Iván Ongay-Valverde ===
 
Title:
 
Abstract:
 
=== November 6, (Person) ===
 
Title:
 
Abstract:
 
=== November 13, (Person) ===
 
Title:
 
Abstract:
 
=== November 20, (Person) ===
 
Title:
 
Abstract:
 
=== November 27, (Person) ===
 
Title: TBA
 
Abstract: TBA
 
=== December 4, (Person) ===
 
Title: TBA
 
Abstract: TBA
 
=== December 11, (Person) ===
 
Title: TBA
 
Abstract: TBA


==Previous Years==
==Previous Years==


The schedule of talks from past semesters can be found [[Logic Graduate Seminar, previous semesters|here]].
The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semesters|here]].

Revision as of 17:48, 21 April 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: TBA
  • 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

Spring 2021 - Tentative schedule

February 16 3:30PM - Short talk by Sarah Reitzes (University of Chicago)

Title: Reduction games over $\mathrm{RCA}_0$

Abstract: In this talk, I will discuss joint work with Damir D. Dzhafarov and Denis R. Hirschfeldt. Our work centers on the characterization of problems P and Q such that P $\leq_{\omega}$ Q, as well as problems P and Q such that $\mathrm{RCA}_0 \vdash$ Q $\to$ P, in terms of winning strategies in certain games. These characterizations were originally introduced by Hirschfeldt and Jockusch. I will discuss extensions and generalizations of these characterizations, including a certain notion of compactness that allows us, for strategies satisfying particular conditions, to bound the number of moves it takes to win. This bound is independent of the instance of the problem P being considered. This allows us to develop the idea of Weihrauch and generalized Weihrauch reduction over some base theory. Here, we will focus on the base theory $\mathrm{RCA}_0$. In this talk, I will explore these notions of reduction among various principles, including bounding and induction principles.

March 23 4:15PM - Steffen Lempp

Title: Degree structures and their finite substructures

Abstract: Many problems in mathematics can be viewed as being coded by sets of natural numbers (as indices). One can then define the relative computability of sets of natural numbers in various ways, each leading to a precise notion of “degree” of a problem (or set). In each case, these degrees form partial orders, which can be studied as algebraic structures. The study of their finite substructures leads to a better understanding of the partial order as a whole.

March 30 4PM - Alice Vidrine

Title: Categorical logic for realizability, part I: Categories and the Yoneda Lemma

Abstract: An interesting strand of modern research on realizability--a semantics for non-classical logic based on a notion of computation--uses the language of toposes and Grothendieck fibrations to study mathematical universes whose internal notion of truth is similarly structured by computation. The purpose of this talk is to establish the basic notions of category theory required to understand the tools of categorical logic developed in the sequel, with the end goal of understanding the realizability toposes developed by Hyland, Johnstone, and Pitts. The talk will cover the definitions of category, functor, natural transformation, adjunctions, and limits/colimits, with a heavy emphasis on the ubiquitous notion of representability.

Link to slides

April 27 4PM - Alice Vidrine

Title: Categorical logic for realizability, part II

Abstract: Realizability is an approach to semantics for non-classical logic that interprets propositions by sets of abstract computational data. One modern approach to realizability makes heavy use of the notion of a topos, a type of category that behaves like a universe of non-standard sets. In preparation for introducing realizability toposes, the present talk will be a brisk introduction to the notion of a topos, with an emphasis on their logical aspects. In particular, we will look at the notion of a subobject classifier and the internal logic to which it gives rise.

Previous Years

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