Bo Ning (宁博), Substructures and eigenvalues of graphs: Triangles and quadrilaterals

Our talk will mainly focus on the relationship between substructures and eigenvalues of graphs. We will briefly survey recent developments on a conjecture of Bollobás and Nikiforov and a classical result of Nosal on triangles. In particular, we shall present counting results for previous spectral theorems on triangles and quadrilaterals. If time allows, we will give a sketch for the proof of one new counting result on triangles.