In this thesis, we study three families of moduli spaces: those of tropical curves, relative stable maps to the Riemann sphere, and weighted stable curves. …
Confluence is an important property in many combinatorial processes. A globally confluent process is one in which a fixed initial state always leads to a …
Arc diagrams are simple, combinatorial objects associated to surfaces with boundary. They consist of homotopy classes of disjoint curves, and can be thought of as …
This thesis studies the integral of an exponential function over an adjoint orbit of a compact Lie group. These integrals are named after Harish-Chandra, who …
We study combinatorial and probabilistic properties of tilings of the plane by $m\times1$ horizontal rectangles and $n\times1$ vertical rectangles also called tilings by bars. In …
This thesis studies three problems stemming from different areas of combinatorics. The first problem is the study of the length of the longest path in …
The moduli space $\M_{g,n}$ is a space that parametrizes isomorphism classes of smooth projective curves of genus $g$ with $n$ marked points. Despite its fundamental …