Let rm and rM be the least and greatest finite boundary slopes of a hyperbolic knot K in S . We show that any cyclic surgery slopes of K must lie in the interval (rm − 1/2, rM + 1/2). AMS Classification 57M25; 57M27

We survey the progress (or lack thereof!) that has been made on some questions about the p-adic slopes of modular forms that were raised by the first author in [Buz05], discuss strategies for making further progress, and examine other related questions.

16 When increasing the rates of subcritical flow on gentle slopes, the bed successively produces 17 ripples, dunes and flat beds. Antidunes (defined here as all bed undulations for which the 18 surface gravity waves are in phase with the bed profile) appear only in high flow rates and 19 may be found in some extreme natural flow events. Inversely, on steep slopes flume 20 experiment (S≥1% appro...

We study here slopes of periodicity of tilings. A tiling is of slope θ if it is periodic along direction θ but has no other direction of periodicity. We characterize in this paper the set of slopes we can achieve with tilings, and prove they coincide with recursively enumerable sets of rationals.

Using the Hatcher–Oertel algorithm for finding boundary slopes of Montesinos knots, we prove the Slope Conjecture and the Strong Slope Conjecture for a family of 3-tangle pretzel knots. More precisely, we prove that the maximal degrees of the colored Jones polynomial of such a knot determine a boundary slope as predicted by the Slope Conjecture, and that the linear terms in the degrees correspo...

Motivation: it would be great if we could understand the p-adic variation of the Up-eigenvalues of modular forms as the weights and/or levels varied. (More generally, it would be really great if we could understand how the local p-adic Galois representations attached to automorphic forms behave – for example, even very weak “equidistribution” results here would presumably imply very strong auto...