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There are now many examples of integer homology spheres which cannot be written as surgery on a knot, but examples which cannot be surgery on some 2-component link have remained out of reach. From one perspective, the difficulty is that the trace of the surgery is an *indefinite 4-…*

Abstract:

Under certain natural sufficient conditions on the sequence of uniformly bounded closed sets E_k⊂ℝ of admissible coefficients, we construct a polynomial

P_n(x)=1+∑_{k=1}^n ε_kx^k,

ε_k∈E_k, with at least c√n distinct roots in [0,1…

Abstract

Random surfaces are central paradigms in equilibrium statistical mechanics. As these surfaces become larger, their statistical behaviors become strongly dependent on how their boundaries are pinned down. This can lead to phase transitions, such as facet edges separating a flat region of the…

Abstract