| Speaker: David Conlon Affiliation: University of Oxford Time: 14:00 Tuesday, 18 September, 2018 Location: 303-257 |
| For any given graph H, we may define a natural corresponding functional ||.||_H. We then say that H is norming if ||.||_H is a semi-norm. A similar notion ||.||_{r(H)} is defined by || f ||_{r(H)} := || | f | ||_H and H is said to be weakly norming if ||.||_{r(H)} is a norm. Classical results show that weakly norming graphs are necessarily bipartite. In the other direction, Hatami showed that even cycles, complete bipartite graphs, and hypercubes are all weakly norming. Using results from the theory of finite reflection groups, we identify a much larger class of weakly norming graphs. This result includes all previous examples of weakly norming graphs and adds many more. We also discuss a recent application of these results to a celebrated conjecture of Sidorenko. Joint work with Joonkyung Lee. |