Pseudo-Diagonals and Uniqueness Theorems

We examine a certain type of abelian C*-subalgebras that allow one to give a unified treatment of two uniqueness theorems: for graph C*-algebras and for certain reduced crossed products

Higher Multiplicity in the One-Dimensional Allen-Cahn Action Functional

We prove the ¡-convergence of the Allen-Cahn action functional in the sharp-interface limit. In previous work, good lower bounds were developed under the assumption of single-multiplicity, but the bounds deteriorated in the case of higher-multiplicity interfaces. We develop improved bounds by working directly with the limiting energy measures