# Difference between revisions of "Graduate Logic Seminar"

Line 13: | Line 13: | ||

This day we decided the schedule for the semester. | This day we decided the schedule for the semester. | ||

− | === February 5, | + | === February 5, Uri Andrews === |

− | Title: | + | Title: Building Models of Strongly Minimal Theories - Part 1 |

− | Abstract: | + | Abstract: Since I'm talking in the Tuesday seminar as well, I'll use |

+ | 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, | + | === February 12, James Hanson === |

− | Title: | + | Title: Finding Definable Sets in Continuous Logic |

− | Abstract: | + | Abstract: In order to be useful the notion of a 'definable set' in |

+ | 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, | + | === February 19, Noah Schweber === |

− | Title: | + | Title: Proper forcing |

− | Abstract: | + | Abstract: Although a given forcing notion may have nice properties on |

+ | 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, | + | === February 26, Patrick Nicodemus === |

− | Title: | + | Title: A survey of computable and constructive mathematics in economic history |

− | + | === March 5, Tamvana Makulumi === | |

− | + | Title: Convexly Orderable Groups | |

− | + | === March 12, Dan Turetsky (University of Notre Dame) === | |

− | + | Title: Structural Jump | |

− | === March | + | === March 19, Ethan McCarthy === |

− | Title: | + | 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 | |

− | Abstract: | + | (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] === | === April 16, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] === |

## Revision as of 19:01, 18 April 2018

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.

**When:**Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).**Where:**Van Vleck B235 (unless otherwise announced).**Organizers:**Mariya Soskava

Talks schedule are arrange and decide at the beginning of each semester. If you would like to participate, please contact one of the organizers.

## Spring 2018

### January 29, Organizational meeting

This day we decided the schedule for the semester.

### February 5, Uri Andrews

Title: Building Models of Strongly Minimal Theories - Part 1

Abstract: Since I'm talking in the Tuesday seminar as well, I'll use 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: Finding Definable Sets in Continuous Logic

Abstract: In order to be useful the notion of a 'definable set' in 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: Proper forcing

Abstract: Although a given forcing notion may have nice properties on 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

Title: A survey of computable and constructive mathematics in economic history

### March 5, Tamvana Makulumi

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, 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 McCarthy (Thesis Defense)

Title: TBA

Abstract: TBA

### April 30, 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

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