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 an space focus principally in  practicing presentation skills or learning materials that are not usually presented on 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, 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]
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* '''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.
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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 ==
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Sign up for the graduate logic seminar mailing list:  join-grad-logic-sem@lists.wisc.edu
  
=== January 29, Organizational meeting ===
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== 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, Uri Andrews ===
+
Title: Reduction games over $\mathrm{RCA}_0$
  
Title: Building Models of Strongly Minimal Theories - Part 1
+
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: Since I'm talking in the Tuesday seminar as well, I'll use
+
=== March 23 4:15PM - Steffen Lempp ===
the Monday seminar talk to do some background on the topic and some
 
lemmas that will go into the proofs in Tuesday's talk. There will be
 
(I hope) some theorems of interest to see on both days, and both on
 
the general topic of answering the following question: What do you
 
need to know about a strongly minimal theory in order to compute
 
copies of all of its countable models. I'll start with a definition
 
for strongly minimal theories and build up from there.
 
  
=== February 12, James Hanson ===
+
Title: Degree structures and their finite substructures
  
Title: Finding Definable Sets in Continuous Logic
+
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: In order to be useful the notion of a 'definable set' in
+
=== March 30 4PM - Alice Vidrine ===
continuous logic is stricter than a naive comparison to discrete logic
 
would suggest. As a consequence, even in relatively tame theories
 
there can be very few definable sets. For example, there is a
 
superstable theory with no non-trivial definable sets. As we'll see,
 
however, there are many definable sets in omega-stable,
 
omega-categorical, and other small theories.
 
  
=== February 19, Noah Schweber ===
+
Title: Categorical logic for realizability, part I: Categories and the Yoneda Lemma
  
Title: Proper forcing
+
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: Although a given forcing notion may have nice properties on
+
[https://hilbert.math.wisc.edu/wiki/images/Cat-slides-1.pdf Link to slides]
its own, those properties might vanish when we apply it repeatedly.
 
Early preservation results (that is, theorems saying that the
 
iteration of forcings with a nice property retains that nice property)
 
were fairly limited, and things really got off the ground with
 
Shelah's invention of "proper forcing." Roughly speaking, a forcing is
 
proper if it can be approximated by elementary submodels of the
 
universe in a particularly nice way. I'll define proper forcing and
 
sketch some applications.  
 
  
=== February 26, Patrick Nicodemus ===
+
=== April 27 4PM - Alice Vidrine ===
  
Title: A survey of computable and constructive mathematics in economic history
+
Title: Categorical logic for realizability, part II
  
=== March 5, Tamvana Makulumi ===
+
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.
 
 
Title: Convexly Orderable Groups
 
 
 
=== March 12, Dan Turetsky (University of Notre Dame) ===
 
 
 
Title: Structural Jump
 
 
 
=== March 19, Ethan McCarthy ===
 
 
 
Title: Networks and degrees of points in non-second countable spaces
 
 
 
=== April 2, Wil Cocke ===
 
 
 
Title: Characterizing Finite Nilpotent Groups via Word Maps
 
 
 
Abstract: In this talk, we will examine a novel characterization of finite
 
nilpotent groups using the probability distributions induced by word
 
maps. In particular we show that a finite group is nilpotent if and
 
only if every surjective word map has fibers of uniform size.
 
 
 
=== April 9, Tejas Bhojraj ===
 
 
 
Title: Quantum Randomness
 
 
 
Abstract: I will read the paper by Nies and Scholz where they define a notion of
 
algorithmic randomness for infinite sequences of quantum bits
 
(qubits). This talk will cover the basic notions of quantum randomness
 
on which my talk on Tuesday will be based.
 
 
 
=== April 16, [http://www.math.wisc.edu/~ongay/ 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, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] (Thesis Defense) ===
 
 
 
Title: TBA
 
 
 
Abstract: TBA
 
 
 
=== April 30, [http://www.math.uconn.edu/~westrick/ Linda Brown Westrick] (from University Of Connecticut) ===
 
 
 
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 12:48, 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.