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Abstract. We study the prank stratiﬁcation of the moduli space of cyclic degree ! covers of the projective line in characteristic p for distinct primes p and !. The main result is about the intersection of the prank 0 stratum with the boundary of the moduli space of curves. When ! = 3 and p ≡ 2 mod 3 is an odd prime, we prove that there exists a smooth trielliptic curve in characteristic p, for every genus g, signature type (r,s), and prank f satisfying the clear necessary conditions.more » « less

null (Ed.)In the search for life beyond Earth, distinguishing the living from the nonliving is paramount. However, this distinction is often elusive, as the origin of life is likely a stepwise evolutionary process, not a singular event. Regardless of the favored origin of life model, an inherent “grayness” blurs the theorized threshold defining life. Here, we explore the ambiguities between the biotic and the abiotic at the origin of life. The role of grayness extends into later transitions as well. By recognizing the limitations posed by grayness, life detection researchers will be better able to develop methods sensitive to prebiotic chemical systems and life with alternative biochemistries.more » « less

Let p ∈ Z p\in {\mathbb {Z}} be an odd prime. We show that the fiber sequence for the cyclotomic trace of the sphere spectrum S {\mathbb {S}} admits an “eigensplitting” that generalizes known splittings on K K theory and T C TC . We identify the summands in the fiber as the covers of Z p {\mathbb {Z}}_{p} Anderson duals of summands in the K ( 1 ) K(1) localized algebraic K K theory of Z {\mathbb {Z}} . Analogous results hold for the ring Z {\mathbb {Z}} where we prove that the K ( 1 ) K(1) localized fiber sequence is selfdual for Z p {\mathbb {Z}}_{p} Anderson duality, with the duality permuting the summands by i ↦ p − i i\mapsto pi (indexed mod p − 1 p1 ). We explain an intrinsic characterization of the summand we call Z Z in the splitting T C ( Z ) p ∧ ≃ j ∨ Σ j ′ ∨ Z TC({\mathbb {Z}})^{\wedge }_{p}\simeq j \vee \Sigma j’\vee Z in terms of units in the p p cyclotomic tower of Q p {\mathbb {Q}}_{p} .more » « less

Abstract The detection of GW170817, the first neutron starneutron star merger observed by Advanced LIGO and Virgo, and its following analyses represent the first contributions of gravitational wave data to understanding dense matter. Parameterizing the high density section of the equation of state of both neutron stars through spectral decomposition, and imposing a lower limit on the maximum mass value, led to an estimate of the stars’ radii of
km and km (Abbottet al 2018Phys. Rev. Lett .121 161101). These values do not, however, take into account any uncertainty owed to the choice of the crust lowdensity equation of state, which was fixed to reproduce the SLy equation of state model (Douchin and Haensel 2001Astron. Astrophys .380 151). We here reanalyze GW170817 data and establish that different crust models do not strongly impact the mass or tidal deformability of a neutron star—it is impossible to distinguish between lowdensity models with gravitational wave analysis. However, the crust does have an effect on inferred radius. We predict the systematic error due to this effect using neutron star structure equations, and compare the prediction to results from full parameter estimation runs. For GW170817, this systematic error affects the radius estimate by 0.3 km, approximately of the neutron stars’ radii.