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Milliken's Tree Theorem and Its Applications: A Computability-Theoretic Perspective
Milliken's tree theorem is a deep result in combinatorics that generalizes a vast number of other results in the subject, most notably Ramsey's theorem and its many variants and …
A Sharp Threshold for Random Graphs With a Monochromatic Triangle in Every Edge Coloring
Let $\cal{R}$ be the set of all finite graphs $G$ with the Ramsey property that every coloring of the edges of $G$ by two colors yields a monochromatic triangle. In this paper we …
The Triangle-Free Process and the Ramsey Number R (3,k)
Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume
We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish …
Angled Crested Like Water Waves with Surface Tension II: Zero Surface Tension Limit
This is the second paper in a series of papers analyzing angled crested like water waves with surface tension. We consider the 2D capillary gravity water wave equation and assume …