THE θ OPERATOR by Nick Ramsey

The Overconvergent Shimura Lifting

Degree Ramsey numbers for even cycles

Let H s − → G denote that any s-coloring of E(H) contains a monochromatic G. The degree Ramsey number of a graph G, denoted by R∆(G, s), is min{∆(H) : H s − → G}. We consider degree Ramsey numbers where G is a fixed even cycle. Kinnersley, Milans, and West showed that R∆(C2k, s) ≥ 2s, and Kang and Perarnau showed that R∆(C4, s) = Θ(s 2). Our main result is that R∆(C6, s) = Θ(s 3/2) and R∆(C10, ...

ar X iv : 0 90 6 . 32 55 v 1 [ m at h . N T ] 1 7 Ju n 20 09 THE OVERCONVERGENT SHIMURA LIFTING by Nick Ramsey

— We construct a rigid-analytic map from the the author’s half-integral weight cuspidal eigencurve (see [10]) to its integral weight counterpart that interpolates the classical Shimura lifting.

Empirical Adequacy and Ramsification

Structural realism has been proposed as an epistemological position interpolating between realism and sceptical anti-realism about scientific theories. The structural realist who accepts a scientific theory Θ thinks that Θ is empirically correct, and furthermore is a realist about the ‘structural content’ of Θ. But what exactly is ‘structural content’? One proposal is that the ‘structural conte...

BSen VIA DISTRIBUTIONS ON WEIGHT SPACE by Nick Ramsey