Venue: B1044 Date: 19:00 - 22:00, June 8, 9, 10, 11, 12, 13, 14,15 Yitang Zhang, Bounded gaps between primes http://annals.math.princeton.edu/articles/7954 "In late April 2013 Yitang Zhang of the University of New Hampshire submitted a paper to the Annals of Mathematics proving that there are infinitely many pairs of primes that differ by less than 70 million. The proof of this amazing result was verified with high confidence by several experts in the field and accepted for publication..." "Zhang's theorem is a huge step forward in the direction of the twin prime conjecture. We now know for the first time that there are actually infinitely many pairs of primes that differ by some fixed number. The proof does not specify any specific number, only that there is at least one that is less than 70 million. (We actually expect that every even number will occur as the difference of two primes infinitely often.) Since the average spacing of primes around x is logx which grows to infinity slowly, this sequence of pairs defy this isolating trend. If not twins, then certainly siblings..."                                                                                       - - - by Dan Goldston All are welcome!