I am mostly interested in distance-related problems. These include explicit distances (such as distance oracles) and implicit distances (such as edit distance). Distance-related problems arise naturally in combinatorial pattern matching and more generally in planar graph algorithms (where distance problems have tight connections to flow and cut problems). I am interested in both these domains and in the intersection between them. In particular, I develop algorithms, data structures, and lower bounds that utilize the fascinating structural properties of planar graphs.