# Seminars & Colloquia Calendar

Mathematical Physics Seminar

## The constant in Shamir's Problem

#### Jeff Kahn - Rutgers University

Location:  Hill 705
Date & time: Thursday, 29 March 2018 at 12:00PM - 1:00PM

Abstract:   Shamir's Problem (circa 1980) asks:  for fixed r at least 3 and n a (large) multiple of r, how large should M be so that M random r-subsets of $${1 ... n}$$ are likely to contain a perfect matching (that is, n/r disjoint r-sets)?  About ten years ago Johansson, Vu and I proved the natural conjecture that this is true if $$M > C n ln n$$,  for some large $$C=C(r)$$.  I can now show the asymptotically correct statement:  the same behavior holds for any fixed $$C > 1/r$$.

THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM.