2021 Fall Colloquium and Teaching Seminar Schedule |
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September 21 | Logic Seminar | Kameryn Williams (SHSU) |

October 12 | Logic Seminar | Thomas Brommage (SHSU) |

October 19 | Logic Seminar | Thomas Brommage (SHSU) |

October 26 | Logic Seminar | Tim Trujillo (SHSU) |

October 27 | Colloquium | Xiyuan Liu (Louisiana Tech University) |

November 2 | Logic Seminar | Tim Trujillo (SHSU) |

November 9 | Logic Seminar | Tim Trujillo (SHSU) |

#### Logic Seminar November 9

**The Galvin-Prikry theorem for the Rado graph**

Tim Trujillo, Assistant Professor of Mathematics, Sam Houston State University

We discuss the recent proof in [1] of the infinite-dimensional Galvin-Prikry theorem for the Rado graph. We focus mainly on the construction of the space of strong Rado coding trees.

[1] Natasha Dobrinen (2020) Borel Sets of Rado graphs and Ramsey’s theorem arXiv:1904.00266

#### Logic Seminar November 2

**The Rado graph**

Tim Trujillo, Assistant Professor of Mathematics, Sam Houston State University

The Rado graph is the unique (up to isomorphism) graph with the following property: for every pair of finite disjoint vertices, U and V there exists a vertex x outside of U and V such that there is an edge between x and every vertex in U, and no edges between x and any vertex of V. We discuss some properties of the graph and show that if its vertices are partitioned into finitely many parts then at least one of the induced subgraphs by the partition is isomorphic to the Rado graph.

#### Colloquium October 27

**Introduction to Machine Learning and Statistical approaches in Classification and Clustering analysis**

Xiyuan Liu, Assistant Professor, Louisiana Tech University

Xiyuan Liu, Assistant Professor, Louisiana Tech University

Machine learning plays an essential role in today's era of big data analysis. One of the most important research problems in big data analysis is classifying observations into different groups. There are two approaches to this problem: clustering and classification. The clustering analysis is unsupervised learning, such as Principal Components Analysis, K-Means Clustering, and Hierarchical Clustering. On the other hand, classification is supervised learning, such as Logistic Regression, Linear Discriminant Analysis, and Conditional Random Field. This presentation will briefly introduce some classical approaches and closely introduce Conditional Random Field.

**Logic Seminar October 26**

**Topological Ramsey theory**

Tim Trujillo, Assistant Professor of Mathematics, Sam Houston State University

Tim Trujillo, Assistant Professor of Mathematics, Sam Houston State University

We review some of the main results of higher-dimensional Ramsey theory, including the Nash-Williams theorem, the Galvin theorem, the Galvin-Prikry theorem, and the Ellentuck theorem. We will conclude with a discussion of the abstract Ellentuck theorem and some examples of topological Ramsey spaces.

#### Logic Seminar October 19

**Modal Logic Before Kripke, Part II**

Thomas Brommage, Lecturer of Philosophy, Sam Houston State University

Thomas Brommage, Lecturer of Philosophy, Sam Houston State University

In the second part of the talk, I will discuss the developments following C. I. Lewis' development of modal propositional logic. Discussion will include the minimal normal modal system K, and the Feys-Von Wright systems M (T), Oskar Becker and Kurt Gödel's axiomatization of the system S4, and the “Brouwerian System” B. I conclude by discussing some of the logical relationships between the various systems and their application to philosophical problems ranging from ethics (deontic logic) to the metaphysics of time (tense logic).

#### Logic Seminar October 12

**Modal Logic Before Kripke, Part I**

Thomas Brommage, Lecturer of Philosophy, Sam Houston State University

Thomas Brommage, Lecturer of Philosophy, Sam Houston State University

In the first part of the talk I will begin with discussing the history of modal logic, from its initial development in Aristotle. Some background on the modal syllogistic logic from the Prior Analytics and the relations between modal propositions from On Interpretation will be discussed, with some attention to the developments through the middle ages. This background will culminate in understanding the motivations behind the development of C. I. Lewis' system of strict implication—the so-called “paradoxes of material implication”—which motivated the developments of the first systems of modal propositional logic (S1-S5).