This series of seminars/study group sessions will start in week 1 of the spring 2012 term - Thursday 12th January and weekly thereafter, initially for 11 sessions.
If successful, the series may run for longer, e.g. continuing into the summer or on other occasions.
The seminar is intended to be particularly useful for research students in mathematics (or computer science or philosophy) interested in learning a new topic in mathematical logic. For spring 2012 the theme will be arithmetic and complexity. The study group will concentrate on a range of theorems and their proofs - both old and new - based around the stated theme. There will additionally be research talks. Thomas Forster and Peter Cholak, amongst others, are expected in Spring 2012.
Normally, each week, we will have
In unusual cases, this schedule would allow for a longer research seminar with extended discussion, or a longer presentation of a important theorem. Exactly how our time is used will be open for discussion and I am always willing to hear suggestions.
The study group sessions will be written up and available as printed notes. If you miss a session you should be able to read up what you have missed. Make sure you get on the email list to receive the notes. If you would like to contribute to writing up notes, please contact Richard Kaye.
The theme for spring 2012, I suggest, will be "complexity theory and systems of arithmetic" (By "arithmetic" I mean the study of structures similar to (N,+,.,<) or (Z,+,.,<) sharing with these many first-order statements, and we will be concentrating on the weaker end of the spectrum of theories of arithmetic.) A number of results connect these two disciplines, and some results in the area of "pure" complexity theory and "pure" arithmetic are also of interest. The intention is to work through relevant background material and some of the key results in the area, including proofs.
An initial list of topics (too much for one term!) that suggests itself is as follows.
This is a very ambitious list and we cannot cover it all. And I am sure to think up other related topics, and suggestions along these lines are always welcome too. So rather than prescribe I would rather keep the exact choice of topics rather fluid within these areas and would welcome suggestions.
Detailed notes will be developed over the course of the series and I invite anyone interested to take notes, and LaTeX them, so that these can be distributed amongst the participants.
Alongside the study group I plan to hold research-level talks or seminars on current work. As well as inviting respected names etc, I also very much want to give research students who have something interesting to say the chance to discuss their work.
This part of the programme is still rather more fluid than the other, so I welcome suggestions or volunteers, either for a 60 minute session or 30 minute sesssion.
Time and place: We will meet from 3.00 in the Staff common room (room 221) of School of Maths, Watson building, University of Birmingham. The first session will be at 3.30 in 222 (next door). The second session will follow on directly after 5 minutes to strentch legs etc., and including time for questions etc we shoud be finished by 6pm at the latest.
The times and dates planned are: THURSDAYS 3.30pm to 6pm, 12th January to 22nd March.
A number of other seminars take place in Birmingham on Thursdays, in particular the combinatorics seminar from 2pm (also in 222) and I will provide details when I have them.
If you wish to stay longer, there will be a chance to drink a beer or two and go for an inexpensive meal on the Bristol Road nearby (usually Indian).
If you are thinking of attending from outside Birmingham please email Richard Kaye (rwkaye AT gmail.com) and/or Mike Cox (mcox235 AT gmail.com) in advance.
Week 1 (12th January) from 3.30pm in 222 with tea/biscuits in 221 from 3pm
We kick-start the "Study group" on arithmetic and complexity with TWO introductory talks, both of which should be accessible to anyone with a general mathematical background and also a minimal exposure to first order logic and to computability theory.
A. Introduction to models of arithmetic and subtheories of PA (Mike Cox)
B. Introduction to Complexity Theory and some important classes between P and PR (Richard Kaye)
C. Short discussion and requests/suggestions for future study groups
Week 2 (19th January) from 3.30pm in 222 with tea/biscuits in 221 from 3pm
A. Study group, session 3, as discussed the previous week.
B. Mike Cox (Birmingham). "Nonstandard topological set theory" (Abstract forthcoming!)
Week 3 (26th January) from 3.30pm in 222 with tea/biscuits in 221 from 3pm
A. Study group, session 4, as discussed.
B. Thomas Forster (Cambridge). TBA
Week 4 (2nd February) from 3.30pm in 222 with tea/biscuits in 221 from 3pm
A. Study group, session 5, as discussed.
B. Alan Reading (Birmingham). Coset Enumeration for nonstandard groups
Week 5 (9th February) from 3.30pm in 222 with tea/biscuits in 221 from 3pm
Week 6 (16th February) from 3.30pm in 222 with tea/biscuits in 221 from 3pm
Week 7 (23rd February) from 3.30pm in 222 with tea/biscuits in 221 from 3pm
Week 8 (1st March) from 3.30pm in 222 with tea/biscuits in 221 from 3pm
Week 9 (8th March) from 3.30pm in 222 with tea/biscuits in 221 from 3pm
Week 10 (15th March) from 3.30pm in 222 with tea/biscuits in 221 from 3pm
Week 11 (22nd March) from 3.30pm in 222 with tea/biscuits in 221 from 3pm
Whoops! You may have seen a previous email announcement said "2011" where it should have been 2012 of course! I hope I will get used to saying "2012" sometime before it's 2013 ;)
Richard Kaye School of Mathematics The University of Birmingham Edgbaston Birmingham, B15 2TT, U.K., Fax: +44 121 414 3389
or email at R.W.Kaye AT bham.ac.uk or rwkaye AT gmail.com