In this work, we consider the fractional obstacle problem with a given obstacle ψ in a bounded domain Ω in R, such that Ksψ = {v ∈ H s 0(Ω) : v ≥ ψ a.e. in Ω} 6= ∅, given by u ∈ Ksψ : 〈LAu, v − u〉 ≥… Expand

This work uses basic tools from quantum computation to give a proof that the SO(3) Witten-Reshetikhin-Turaev (WRT) invariant of 3-manifolds is #P-hard to calculate, and applies this result to a question about the combinatorics of Heegaard splittings.Expand

In this paper, we propose different notions of F_zeta-geometry, for zeta a root of unity, generalizing notions of over finite fields, the Grothendieck class, and the notion of torification. We relate… Expand

It is shown that, if NP $\neq \#$P, then there exist infinitely many 3-manifold diagrams which cannot be made logarithmically "thin" (relative to their overall size) except perhaps by an exponentially large number of local moves.Expand

In this paper we propose different notions of F_zeta-geometry, for zeta a root of unity, generalizing notions of F_1-geometry (geometry over the "field with one element") based on the behavior of the… Expand

In this work, we consider the nonlocal obstacle problem with a given obstacle ψ in a bounded Lipschitz domain Ω in R, such that Kψ = {v ∈ H 0(Ω) : v ≥ ψ a.e. in Ω} 6= ∅, given by u ∈ Kψ : 〈Lau, v −… Expand

In this work, we consider the fractional Stefan-type problem in a Lipschitz bounded domain Ω ⊂ R with time-dependent Dirichlet boundary condition for the temperature θ = θ(x, t), θ = g on Ω×]0, T [,… Expand