Date:
Thu, 19/01/202314:30-15:30
Title: Random graphs, random surfaces and random permutations
Abstract: Let X be a nice topological space with fundamental group G. The correspondence between N-degree covering spaces of X and homomorphisms f:G-->S_N to the symmetric group means that to study random covers of X, one can study random homomorphisms f:G-->S_N. This yields a natural model for studying, in particular, random graphs and random surfaces.In joint works with Michael Magee and Tomer Zimhoni, we consider the random permutation f(g) given by the image of a fixed element g in G. For a big class of groups, including free groups, surface groups and PSL(2,Z), we find algebraic invariants of the element g in G which determine the local asymptotic statistics of the the random permutation f(g).
I will describe some of these works and repeating patterns, and state some questions and conjectures.
Recording will be available at: https://huji.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx?folderID=a6e6beab-eb0e-47c6-9d5d-aeb500acb5ad
Abstract: Let X be a nice topological space with fundamental group G. The correspondence between N-degree covering spaces of X and homomorphisms f:G-->S_N to the symmetric group means that to study random covers of X, one can study random homomorphisms f:G-->S_N. This yields a natural model for studying, in particular, random graphs and random surfaces.In joint works with Michael Magee and Tomer Zimhoni, we consider the random permutation f(g) given by the image of a fixed element g in G. For a big class of groups, including free groups, surface groups and PSL(2,Z), we find algebraic invariants of the element g in G which determine the local asymptotic statistics of the the random permutation f(g).
I will describe some of these works and repeating patterns, and state some questions and conjectures.
Recording will be available at: https://huji.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx?folderID=a6e6beab-eb0e-47c6-9d5d-aeb500acb5ad