Mathematical Background: We expect that the student is comfortable with basic mathematics at the level of a U.S. first-year college STEM student. This includes basic notions such as sets and functions ...

We consider ferromagnetic Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We ...

Recently, Knuth and Ciucu independently proved the surprising fact, conjectured by Stanley, that one connected component of the tensor product of a path with itself (the so-called "Aztec diamond graph ...