Date and Time | Location | Contents | Homework |
---|---|---|---|

Mon 8 Jan, 10:30-12:30 | F3.20 | Project Introduction; Sections 1.1, 1.2, 1.3 up to Lemma 1.12. | Sec. 1.1: 2, 3, 4, 5*, 6*, 8; Sec. 1.2: 10, 12(a), 12(b)+, 13(a)-(e)*, (f)+, 15, 18+, 19*; Sec. 1.3: 20, 21(a)-(c), (d)+ Typos / Feedback for 1.1 and 1.2. |

Tue 9 Jan, 10:30-12:30 | F1.15 |
Section 1.3, Some general remarks on Duality, Section 2.1. | Last time's homework, and Sec. 1.3: 22, 23*, 24*, 26 (separate file in Dropbox); Sec. 2.1: 1+, 3+, 5*, 6+, 9* (give a reference); Typos / Feedback for 1.3 and 2.1. |

Thu 11 Jan, 15:30-17:30 |
F3.20 | Section 2.3, with outline of 2.2 and 2.4; Section 3.1. | Sec 2.2: 11, 15; Sec 2.3: 16, 18, 19; Sec 3.1: 4, 5, 7; Typos / Feedback for Chapter 2 and 3.1. |

Fri 12 Jan, 13:30-15:30 |
F3.20 | Section 3.1 and 3.2. | Sec 3.1: 8; Sec 3.2: 10, 11, 12* (f is optional). |

Mon 15 Jan, 10:30-12:30 | F2.19 | Recap of last week in Category-Theoretic Language; Completeness of classical propositional logic; Duality for Operators on finite distributive lattices. | Catch up with old homework. |

Tue 16 Jan, 10:30-12:30 | F2.19 | Operators on distributive lattices; Completeness of modal logic; Completeness of classical predicate logic. | Problem set (in Dropbox) |

Tue 16 Jan, 15:00-17:00 | F2.01 | Exercise Session | |

Thu 18 Jan, 10:30-12:30 | F2.19 | Applications of duality to CS part 1: Languages, automata, monoids, Schutzenberger's Theorem (slides in Dropbox) | Submit list of three choices for individual paper (see Dropbox) before Friday 5pm |

Fri 19 Jan, 10:30-12:30 | F2.19 | Applications of duality to CS part 2: Varieties, Profinite monoids, Recent applications (slides in Dropbox) | Problem set (in Dropbox) |

Week of 22 Jan - 26 Jan | See Dropbox | Individual Meetings | Prepare Presentations |

Mon 29 Jan, 12:30-14:00 | SP 904 D1.111 | Practice Presentations | |

Tue 30 Jan, 10:30-12:30 | F2.19 | Practice Presentations | |

Wed 31 Jan, 13:30-16:30 | F2.19 | Final Presentations (A|C Seminar) | |

Fri 2 Feb, 17:00 | Deadline for submitting final report |

- There may be changes in the schedule, please check this page regularly.
- All rooms are in building SP107, unless noted otherwise.
- * Starred exercises are particularly important, and their results may be used in the course.
- + Plussed exercises are optional.
- Lecture Notes are available in the Dropbox shared with participants. As part of the homework, every participant will annotate the lecture notes with typos and/or other feedback. Annotations can be made either in the paper copy in Sam's mailbox, or digitally in Dropbox.

This project invites students to dive into (some of) these recent applications of Stone duality and its generalizations. Students will also gain experience reading and presenting research papers in the area, and active participation in this project could lead students to research directions suitable for a Master's thesis.

The first half of this project will be an

- Mai Gehrke, Duality, inaugural speech, Radboud University Nijmegen, 2009.

A general introduction to Stone duality, written with a broad, non-mathematical audience in mind. - Sam van Gool, Machines, Models, Monoids, and Modal logic (version with animations), TbILLC tutorial, 2017.

Slides introducing some of the more advanced research topics that we will look at in this project. Also see the further references in these slides. - Lecture notes for the first part will be made available during the course.
- Click the links in the first paragraph above for a sample of relevant books and research articles. A definitive list will be compiled during the project, based on students' input.