Start Date: | 11/17/2014 | Start Time: | 3:00 PM |
End Date: | 11/17/2014 | End Time: | 4:00 PM |
|
Event Description Robin Pemantle, Department of Mathematics, University of Pennsylvania
Abstract: Let M be a random set of integers greater than 1, containing each integer n independently with probability 1/n. Let S(M) be the sumset of M, that is, the set of all sums of subsets of M. How many independent copies of S must one intersect in order to obtain a finite set?
This problem is the limiting form of a problem arising in computational Galois theory. Dixon (1992) conjectured that O(1) was good enough, which was proved shortly thereafter by Luczak and Pyber. Their constant was 2^100 has not been improved until now, though is conjectured that it can be improved to 5 or 4. We show in fact that 4 sets suffice.
JOINT WORK WITH YUVAL PERES AND IGOR RIVIN |
|
Location: Korman Center, Room 245, 15 South 33rd Street, Philadelphia, PA 19104 |
|