Ruth Luo (Illinois Math) The maximum number of cliques in graphs without long cycles Abstract: The ErdősGallai Theorem states that for $k\geq 3$ every graph on $n$ vertices with more than $\frac{1}{2}(k1)(n1)$ edges contains a cycle of length at least $k$. Kopylov proved a strengthening of this result for 2connected graphs with extremal examples $H_{n,k,t}$ and $H_{n,k,2}$. In this talk, we generalize the result of Kopylov to bound the number of $s$cliques in a graph with circumference less than $k$. Furthermore, we show that the same extremal examples that maximize the number of edges also maximize the number of cliques of any fixed size. Finally, we obtain the extremal number of $s$cliques in a graph with no path on $k$vertices. 
