When: Sunday, March 26, 10am
Where: Schreiber 309
Speaker: Mykhaylo Tyomkyn (Tel Aviv University)
Title: Lagrangians of hypergraphs: The Frankl-Furedi conjecture holds almost everywhere
Frankl and Furedi conjectured in 1989 that the maximum Lagrangian of all r-uniform hypergraphs of given size m is realised by the initial segment of the colexicographic order. For r=3 this was partially solved by Talbot, but for r\geq 4 the conjecture was widely open. We verify the conjecture for all r\geq 4, whenever
$\binom{t-1}{r} \leq m \leq \binom{t}{r}- \gamma_r t^{r-2}$
for a constant $\gamma_r>0$. This range includes the principal case $m=\binom{t}{r}$ for large enough $t$
