Some recent results and open questions on polynomial graphs

In this talk I will describe the ideas behind 1) a new lower bound on Turan number of 14-cycle, due to A. Terlep and J. Williford; 2) a new proof for the lower bound on the girth of graphs CD(k, q), due to V. Taranchuk; 3) a construction of polynomial graphs with small automorphism group and its corollaries, due to V. Taranchuk and myself. At the end, several related open questions will be mentioned.