Interlacing families and the Hermitian spectral norm of digraphs

Suil O (오수일)

Department of Mathematics, Simon Fraser University, Burnaby, B.C., Canada

Department of Mathematics, Simon Fraser University, Burnaby, B.C., Canada

2016/6/1 Wed 4PM-5PM

Recently, Marcus, Spielman, and Srivastava proved the existence of infinite families of bipartite Ramanujan graphs of every degree at least 3 by using the method of interlacing families of polynomials. In this talk, we apply their method to prove that for any connected graph G, there exists an orientation of G such that the spectral radius of the corresponding Hermitian adjacency matrix is at most that of the universal cover of G.

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