Regarding 1, ICM's are a place to acquire new ideas. With rare exception, there will be no "Introduction to ..." type material, just "Motivation for..." and "Teaser to ..." and
"Of course, since we all know ..., the following will be obvious ...", which is true for me after a few pages and perhaps months of study. However, even the last type may contain an idea I can use, even if I don't know what "we all know".
Regarding 2, there are times, places, and opportunities to meet; see below.
I hope one day to compare the lists of attendees from all the ICMs since the one in Berkeley in 1986. I know I am in all of them, and I suspect that I share that distinction with at most 10 other people.
The one in 1986 convinced me to go to Berkeley for graduate school; the others have given me a quick exposure to various fields in mathematics and usually too much to think about. Your mileage may vary, but I found the following routine helpful to me.
1) Each night, plan your lecture tour for the following day. You will need to get a list of programme changes (usually needed only for Short Communications sessions), and select your A, B and C list choices for each hour. (Sometimes your A choice and B choice get rescheduled or canceled.) If you have friends attending and want to split up to cover more lectures, plan with them. At the first few conferences, I had mild sessions of agony because there were more lectures I wanted to attend than slots available. I now have restricted my interests in the afternoons to three or four sections (currently logic, algebra, computing, and combinatorics), to make my planning easier.
2) When you suffer from lecture burnout, try a tour or even just walk around in the part of the city near the conference hall. One of my treats from the 2006 ICM was looking at the inspired architecture in that part of Madrid. Or check out the array of posters.
(Ideally, ask permission before photographing a poster. In any case, don;'t use the
photo beyond personal use without arrangments with the author of the poster.)
3) If you are very social (I was not), figure out how to work that into your visit. Lunch breaks and afternoon breaks are the most opportune for this. I did manage to chat up a few attendees (including Tim Gowers and Greg Kuperberg) during moments in between lectures. There will be a few social occasions, and in most cases informal dress is acceptable (but check the invitations). During the
lecture sessions, there will be limited or no time for questions, so make your question count. Also, unless you find someone to walk to the same lecture with you, it is not likely that you will have much time to chat between lectures.
4) Find the information booth and help desk. If any problems arise, they are your first step towards resolution, even if it is visit related and not conference related. Also,
avoid the temptation to check your email during the conference. You can easily get sucked in to spending too much time on the computer. (You get to choose how much time to devote to computer versus sleep, however.)
Regarding your a and b choices, I would say both are true. In point of a, if I had made a persistent ass of myself, I might have gotten more than a few words with Tim Gowers, but as he had been awarded the Fields Medal recently, I chose to think his time with me would be very limited and in high demand. Thus I did not persist, and being in lecture-attending mode most of the time, I often have the perception that there is little to no time for socializing.
Towards point b., when I relax, I find I can talk to a number of people and create opportunities for socializing quite easily, if I put my focus on it. There will be some inspiring talks, and after hearing a few of these, you can use one or more points from them as icebreakers. I will thus say it depends on what kind of experience you will want to make of your ICM.
Gerhard "Collectors edition ICM T-shirts for sale" Paseman, 2010.04.08
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