Date & Time: Thursday, February 26, 2015, 14:00-15:30.
Venue: Ramanujan Hall
Title: On maximum number of points in a maximal intersecting family of finite sets
Speaker: Kaushik Majumder, ISI Bangalore
Abstract: Paul Erd\H{o}s and L\'{a}szl\'{o} Lov\'{a}sz proved that, for any positive integer $k$, up to isomorphism there are only finitely many maximal intersecting families of $k-$sets. So they posed the problem of determining or estimating the largest number $\N{k}$ of the points in such a family. They proved by means of an example that $N(k)\geq2k-2+\frac{1}{2}\binom{2k-2}{k-1}$. In 1985, Zsolt Tuza proved that the upper bound of $N(k)$ is best possible up to $2\binom{2k-2}{k-1}$. In this talk, we discuss the recent development of the upper bound on $N(k)$.