Thursday, January 31, 2019
01/31/2019 - 4:00pm
We prove a number of tight graph homomorphism inequalities, where, for a fixed H, we wish to maximize the number of homomorphism from G to H (after exponentially normalizing by the size of G) under certain degree constraints on G (e.g., d-regular). A highlight of our results is that, among d-regular graphs of the same size, a disjoint complete bipartite graphs has the most number of proper q-colorings. Our results also extend to irregular graphs and list colorings. These results settle a number of conjectures by Kahn, Galvin-Tetali, Galvin, and Cohen-Csikvári-Perkins-Tetali.
Joint work with Ashwin Sah, Mehtaab Sawhney, and David Stoner
01/31/2019 - 4:15pm
Anosov representations provide a rich and interesting class of discrete subgroups of Lie groups. In this talk we first introduce Anosov representations. Then we show how one can get estimates on the Hausdorff dimension of their limit set, even though the action on the boundary is not conformal.