I am wondering, how hard or competitive is it to obtain a slot for short oral presentation(20-minute talk) at the International Congress of Mathematicians?
Generally, how many slots are allotted for such presentation?
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Short answer: I don't know, I've never been on an Organizing Committee.
Long answer: You likely can look at statistics for attendance versus capacity of venue. At the last few International Congresses I have attended, usually there are about 2000 or more from the host country, and anywhere from 1000 to 2000 from other countries. There are about 20 plenary lectures, about 150 invited lectures, about 1000 Oral Communications and not quite as many posters. Also some interesting prize lectures, roundtables, and a few other items. (I am doing this from memory. I don't think attendance has surpassed 5000 lately, but I won't guarantee it. I could be off on any of the numbers by a factor of 2, but I don't think so.)
I have submitted abstracts for short communications since 1994, and have had them accepted in all but one case (and in that case there were facilities for last minute "impromptu" sessions: the organizers kindly let me have a slot for one of those). My unscientific guess is that the rejection rate is determined mostly by capacity, and that about half the local attendees and more than half of the non-local attendees submit abstracts, which would lead to about 2500 petitions for 2000 slots. My estimate of the population whose desire to satisfy vanity overcomes their fear of public speaking would suggest that 2000 petitions are for oral communication, and so roughly half are filled.
FUZZY DATA: I submitted two abstracts this year, one a week or so before the first deadline and one a few days afterward, possibly after the first and before the extended deadline. They were given designation numbers below 1900; this supports my guesstimates.
LESS FUZZY DATA: at this writing, about one month before the 2014 Congress, registrations are pouring in and number near 2900. There are almost 500 posters accepted and a little over 700 short communications, with some designation numbers reaching over 2300. Not substantive, but if the code numbers reflect submissions, this would imply an acceptance rate near 7 out of 24 for oral presentations, and a little less than half for all presentations. Off by less than an order of magnitude.