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:''' Mondays 4p-5p (unless stated otherwise)
+
* '''When:''' Tuesdays 4-5 PM
* '''Where:''' on line (ask for code).
+
* '''Where:''' Van Vleck 901
 
* '''Organizers:''' [https://www.math.wisc.edu/~jgoh/ Jun Le Goh]
 
* '''Organizers:''' [https://www.math.wisc.edu/~jgoh/ Jun Le Goh]
  
Line 9: Line 9:
 
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 2020 - Tentative schedule ==
+
== Fall 2021 tentative schedule ==
  
=== September 14 - Josiah Jacobsen-Grocott ===
+
To see what's happening in the Logic qual preparation sessions click [[Logic Qual Prep|here]].
  
Title: Degrees of points in topological spaces
+
=== September 14 - organizational meeting ===
  
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.
+
We met to discuss the schedule.
  
=== September 28 - James Hanson ===
+
=== September 28 - Ouyang Xiating ===
  
Title: The Semilattice of Definable Sets in Continuous Logic
+
Title: First-order logic, database and consistent query answering
  
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: Databases are a crucial component of many (if not all) modern
 +
applications. In reality, the data stored are often dirty and contain
 +
duplicated/missing entries, and it is a natural practice to clean the data
 +
first before executing the query. However, the same query might return
 +
different answers on different cleaned versions of the dataset. It is then
 +
helpful to compute the consistent answers: the query answers that will always
 +
be returned, regardless of how the dirty data is cleaned. In this talk, we
 +
first introduce the connection between first-order logic and query languages
 +
on databases, and then discuss the problem of Consistent Query Answering
 +
(CQA): How to compute consistent answers on dirty data? Finally, we show
 +
when the CQA problem can be solved using first-order logic for path queries.
  
=== October 5 - Tejas Bhojraj from 3:30PM-4:00PM ===
+
=== October 12 - Karthik Ravishankar ===
  
Title: A Levin-Schnorr type result for Weak Solovay random states.
+
Title: Notions of randomness for subsets of the Natural Numbers
  
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.
+
Abstract: There are a number of notions of randomness of sets of natural numbers. These notions have been defined based on what a 'random object' should behave like such as being 'incompressible' or being 'hard to predict' etc. There is often a interplay between computability and randomness aspects of subsets of natural numbers. In this talk we motivate and present a few different notions of randomness and compare their relative strength.
  
=== November 9 - Karthik Ravishankar ===
+
=== October 26 - no seminar ===
  
Title: Elementary submodels in infinite combinatorics
+
=== November 9 - Antonio Nákid Cordero ===
  
Abstract: The usage of elementary submodels is a simple but powerful method to prove theorems, or to simplify proofs in infinite combinatorics. In the first part of the talk, we quickly cover the basic concepts involved for proving results using elementary submodels, and move on to provide two examples of application of the technique to prove two popular results from set theory: The Delta System lemma and the Fodors Pressing down lemma . We provide both the classical proof as well as a proof using elementary submodels to contrast the two approaches.
+
Title: Martin's Conjecture: On the uniqueness of the Turing jump
  
=== November 16 - Karthik Ravishankar ===
+
Abstract: The partial order of the Turing degrees is well-known to be extremely complicated. However, all the Turing degrees that appear "naturally" in mathematics turn out to be well-ordered. In the '70s, Martin made a sharp conjecture explaining this phenomenon, the prime suspect: the Turing jump. This talk will explore the precise statement of Martin's conjecture and the interesting mathematics that surround it.
  
Title: Elementary submodels in infinite combinatorics, part II
+
=== November 23 - Antonio Nákid Cordero ===
  
Abstract: In the second part of the talk, we give a proof Fodors Pressing down lemma, along with an overview of the slightly larger proof of the Nash Williams theorem which states that a graph is decomposable as a disjoint union of cycles if and only if it has no odd cut.
+
Title: Two Perspectives on Martin's Conjecture.
  
=== Tuesday, November 24 - Tonicha Crook (Swansea University) from 9:00AM-10:00AM ===
+
Abstract: This time we will dive deeper into the recent developments around Martin's Conjecture. We will focus on two main themes: the uniformity assumption, and the interaction of Martin's conjecture with the theory of countable Borel equivalence relations.
  
Title: The Weihrauch Degree of Finding Nash Equilibria in Multiplayer Games
+
=== December 7 - John Spoerl ===
  
Abstract: Is there an algorithm that takes a game in normal form as input, and outputs a Nash equilibrium? If the payoffs are integers, the answer is yes, and a lot of work has been done in its computational complexity. If the payoffs are permitted to be real numbers, the answer is no, for continuity reasons. It is worthwhile to investigate the precise degree of non-computability (the Weihrauch degree), since knowing the degree entails what other approaches are available (eg, is there a randomized algorithm with positive success change?). The two player case has already been fully classified, but the multiplayer case remains open and is addressed here. As well as some insight into finding the roots of polynomials, which is essential in our research. An in-depth introduction to Weihrauch Reducibility will be included in the presentation, along with a small introduction to Game Theory.
+
Title: Cardinals Beyond Choice and Inner Model Theory
  
=== November 30 - Yvette Ren ===
+
Abstract: This talk will be a general introduction and overview of large cardinal axioms which violate the axiom of choice and their impact on the project of inner model theory.
  
Title, abstract TBA
+
== 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 14:25, 3 December 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: Tuesdays 4-5 PM
  • Where: Van Vleck 901
  • 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 2021 tentative schedule

To see what's happening in the Logic qual preparation sessions click here.

September 14 - organizational meeting

We met to discuss the schedule.

September 28 - Ouyang Xiating

Title: First-order logic, database and consistent query answering

Abstract: Databases are a crucial component of many (if not all) modern applications. In reality, the data stored are often dirty and contain duplicated/missing entries, and it is a natural practice to clean the data first before executing the query. However, the same query might return different answers on different cleaned versions of the dataset. It is then helpful to compute the consistent answers: the query answers that will always be returned, regardless of how the dirty data is cleaned. In this talk, we first introduce the connection between first-order logic and query languages on databases, and then discuss the problem of Consistent Query Answering (CQA): How to compute consistent answers on dirty data? Finally, we show when the CQA problem can be solved using first-order logic for path queries.

October 12 - Karthik Ravishankar

Title: Notions of randomness for subsets of the Natural Numbers

Abstract: There are a number of notions of randomness of sets of natural numbers. These notions have been defined based on what a 'random object' should behave like such as being 'incompressible' or being 'hard to predict' etc. There is often a interplay between computability and randomness aspects of subsets of natural numbers. In this talk we motivate and present a few different notions of randomness and compare their relative strength.

October 26 - no seminar

November 9 - Antonio Nákid Cordero

Title: Martin's Conjecture: On the uniqueness of the Turing jump

Abstract: The partial order of the Turing degrees is well-known to be extremely complicated. However, all the Turing degrees that appear "naturally" in mathematics turn out to be well-ordered. In the '70s, Martin made a sharp conjecture explaining this phenomenon, the prime suspect: the Turing jump. This talk will explore the precise statement of Martin's conjecture and the interesting mathematics that surround it.

November 23 - Antonio Nákid Cordero

Title: Two Perspectives on Martin's Conjecture.

Abstract: This time we will dive deeper into the recent developments around Martin's Conjecture. We will focus on two main themes: the uniformity assumption, and the interaction of Martin's conjecture with the theory of countable Borel equivalence relations.

December 7 - John Spoerl

Title: Cardinals Beyond Choice and Inner Model Theory

Abstract: This talk will be a general introduction and overview of large cardinal axioms which violate the axiom of choice and their impact on the project of inner model theory.

Previous Years

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