Difference between revisions of "Graduate Logic Seminar"

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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.
 
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
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* '''When:''' Mondays 3:30-4:30 PM
* '''Where:''' on line (ask for code).
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* '''Where:''' Van Vleck B139
* '''Organizers:''' [https://www.math.wisc.edu/~jgoh/ Jun Le Goh]
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* '''Organizers:''' Karthik Ravishankar and [https://sites.google.com/wisc.edu/antonio Antonio Nakid Cordero]
  
 
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
  
== Fall 2021 - Tentative schedule ==
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== Fall 2022 ==
  
To see what's happening in the Logic qual preparation sessions click [[Logic Qual Prep|here]].
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=== September 12 - Organizational Meeting ===
  
== Spring 2021 - Tentative schedule ==
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We will meet to assign speakers to dates.
  
=== February 16 3:30PM - Short talk by Sarah Reitzes (University of Chicago) ===
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=== '''September 19 - Karthik Ravishankar''' ===
 +
TItle: '''Lowness for Isomorphism'''
  
Title: Reduction games over $\mathrm{RCA}_0$
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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.
  
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.
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=== '''September 26 - Antonio Nakid Cordero''' ===
  
=== March 23 4:15PM - Steffen Lempp ===
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=== '''October 3 - Yunting Zhang''' ===
  
Title: Degree structures and their finite substructures
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=== '''October 10 - Yuxiao Fu''' ===
  
Abstract: Many problems in mathematics can be viewed as being coded by sets of natural numbers (as indices).
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=== '''October 17 - Alice Vidrine''' ===
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 ===
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=== '''October 24 - Hongyu Zhu''' ===
  
Title: Categorical logic for realizability, part I: Categories and the Yoneda Lemma
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=== '''October 31 - Break for Halloween''' ===
  
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.
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=== '''November 7 - John Spoerl''' ===
  
[https://hilbert.math.wisc.edu/wiki/images/Cat-slides-1.pdf Link to slides]
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=== '''November 14 - Josiah Jacobsen-Grocott''' ===
  
=== April 27 4PM - Alice Vidrine ===
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=== '''November 21 - Karthik Ravishankar''' ===
  
Title: Categorical logic for realizability, part II
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=== '''November 28 - Logan Heath''' ===
  
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.
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=== '''December 5 - Logan Heath''' ===
  
==Previous Years==
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=== '''December 12 - TBA''' ===
 +
 
 +
== 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 01:39, 19 September 2022

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 B139
  • Organizers: Karthik Ravishankar and Antonio Nakid Cordero

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 2022

September 12 - Organizational Meeting

We will meet to assign speakers to dates.

September 19 - Karthik Ravishankar

TItle: Lowness for Isomorphism

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.

September 26 - Antonio Nakid Cordero

October 3 - Yunting Zhang

October 10 - Yuxiao Fu

October 17 - Alice Vidrine

October 24 - Hongyu Zhu

October 31 - Break for Halloween

November 7 - John Spoerl

November 14 - Josiah Jacobsen-Grocott

November 21 - Karthik Ravishankar

November 28 - Logan Heath

December 5 - Logan Heath

December 12 - TBA

Previous Years

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