Student seminar Tame Topoogy and O-minimal Structures

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: Martijn den Besten, Felix Denis, Ludovico Fischer, Pol van Hoften, Tom van Overbeeke, Niels Voorneveld, Ugur Yikilmaz and Tingxiang Zou. Listener: Jasper Derikx.

The meetings are on Fridays 16:00 (sharp!)--18:00, in room 610. First meeting: Week 39 (Friday September 26) 2014.

Requirements, Learning Goals and Grading

Every student presents material, in a blackboard talk. It is permitted to distribute handouts to the audience. The talk lasts 2x45 minutes, but leave 10 minutes free for discussion.

Additionally, every speaker formulates a homework exercise, which the other participants do, 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.

In the course of the seminar, every student gives two such blackboard presentations (with homework exercise).

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

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

An "O-minimal structure" on an ordered set R is a collection of subsets of R^n (for each n), closed under unions, complements and projections, which satisfies the requirement that the subsets of R (so, n=1) are just finite unions of open intervals and points.

Model Theory has established that there are several interesting such structures. In the seminar, we shall study how from the definition of an O-minimal structure one can do geometry: there are theorems on dimension and Euler characteristic, cell decomposition, local trivialisation. This is laid out in the book by Lou van den Dries (see below), which we shall work through.

Reading Material

The book "Tame Topology and O-minimal Structures" by Lou van den Dries (London Mathematical Society Lecture Notes Series 248, Cambridge University Press 1998).

Schedule

Week 39
Friday September 26: Felix, Chapter 1 First Part. Homework. Model Solution.
Week 40
Friday October 3: Tom, Chapter 1 Second Part. Homework. Model Solution
Week 41
No seminar (teacher abroad)
Week 42
No seminar (teacher abroad)
Week 43
Friday October 24: Martijn, Chapter 2. Homework. Model Solution.
Week 44
Friday October 31: Pol, Chapter 3 First Part. Homework. Model Solution.
Week 45
Friday November 7: Ludovico.
Week 46
Friday November 14: Ugur, Chapter 3, section 2. Homework. Model Solution
Week 47
Friday November 21: Tingxiang, Chapter 4, section 1. Homework. Model Solution
Week 48
Friday November 28: Niels, Chapter 4, section 2. Homework. Model Solution
Week 49
Friday December 5: Felix, Chapter 5, sections 1--2. Homework. Model Solution
Week 50
No seminar (room unavailable)
Week 51
Friday December 19: Tom, Chapter 5, remainder. Homework.
Week 1
Friday January 2: No seminar; building closed.
Week 2
Friday January 9: Seminar moved to Monday January 12, 16-18
Week 3
Monday January 12: Martijn, Chapter 6, sections 1--2. Homework.
Week 3
Friday January 16: Pol, remainder Chapter 6. Homework
Week 4
Friday January 23: Ugur. Chapter 7, sections 1--2. Homework
Week 5
Friday January 30: Seminar from 15:00 to 17:00 in Minnaert 204. Niels. Remainder Chapter 7 and first part of Chapter 8, section 1. Homework
Week 8
Friday February 6: Tingxiang. remainder Chapter 8. Homework
Week 9
Friday February 13:
Week 10
Friday February 20: evaluation and grading.

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