Student seminar Ultracategories (WISM550)

Teacher, Time and Venue, Participants

Teacher is Jaap van Oosten. He can be found at room 5.07, tel. 3305. Email: j.vanoosten AT uu.nl

Participants: Feike van Ammers, Tim Baanen, Jack Davies, Bart Keller, Ieke Moerdijk, Loe van Montfort, Matteo Spadetto, Jetze Zoethout.

The meetings are on Wednesdays 13:15--15:00, in room 610, HFG. First meeting: Week 7 (Wednesday February 13, 2019).

Requirements, Learning Goals and Grading

Every student presents material, in a blackboard talk. It is permitted to distribute handouts to the audience. Every presentation lasts twice 45 minutes minus 5 minutes (for discussion). Students of adjacent presentations are encouraged to work together.

Additionally, every student formulates a homework exercise, which the other participants solve, and hand in to the speaker a week later. The speaker then grades this work and hands everything (including a model solution) to the teacher. The teacher, after examination, hands the grades to the participants. Make also a grading scheme: if an exercise consists of more than one part, tell the students what each part is worth.

In the course of the seminar, every student presents twice.

Attendance is compulsory.

Learning goals are:
1. Student is able to rework a given text into a coherent and understandable presentation
2. Student has good understanding of the mathematics in the field of the seminar
3. Student can formulate relevant and challenging exercises
4. Student develops collaboration and communication skills

Your final grade is composed of your grade for the presentation (40%, of which 20% for understanding the mathematics and 20% for communicating it), the formulation and grading of the homework exercise (10%) and your solutions to the other speakers' exercises (50%).

Subject Matter of the Seminar

A celebrated theorem of Makkai, called "Conceptual Completeness for First-Order Logic" states that a first-order theory can be (up to suitable equivalence) recovered from the pretopos-completion of its category of models.

Recently, a strengthening of this result has been given by Jacob Lurie, and laid down in the text "Ultracategories", which can be downloaded here. We intend to work through this text.

Planning

Week 7
Wednesday February 13: Ieke Moerdijk Introduction to the subject, and overview.
Week 8
Wednesday February 20: Matteo. Homework. Model Solution.
Week 9
Wednesday February 27: Bart. Homework. Model Solution.
Week 10
Wednesday March 6: No seminar on account of Loe's illness.
Week 11
Wednesday March 13: Loe. Homework. Model Solution (by Tim).
Week 12
Wednesday March 20: Jetze. Homework. Model Solution.
Week 13
Wednesday March 27: Tim. Homework. Model Solution.
Week 14
Wednesday April 3: No seminar.
Week 15
Wednesday April 10: Jack. Homework. Model Solution.
Week 16
Wednesday April 17: Matteo. Homework. Model Solution.
Week 17
Wednesday April 24: Bart. Homework. Model Solution.
Week 18
Wednesday May 1: Tim. Homework. Model Solution.
Week 21
Wednesday May 22: evaluation and grading.

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