We consider a large family F of torus bundles over the circle, and we use recent work of Li–Mak to construct, on each Y ∈ F, a Stein fillable contact structure ξY . We prove that (i) each Stein filling of (Y, ξY ) has vanishing first Chern class and first Betti number, (ii) if Y ∈ F is elliptic, then all Stein fillings of (Y, ξY ) are pairwise diffeomorphic and (iii…

Tahun Terbit

2010

We prove that every del Pezzo surface of degree 2 over a finite field is unirational, building on the work of Manin and an extension by Salgado, Testa, and V´arilly-Alvarado, who had proved this for all but three surfaces. Over general fields of characteristic not equal to 2, we state sufficient conditions for a del Pezzo surface of degree 2 to be unirational.

Tahun Terbit

2010

For any Calder´on–Zygmund operator T, any weight w, and α > 1, the operator T is bounded as a map from L1(ML log log L(log log log L)αw) into weak-L1(w). The interest in questions of this type goes back to the beginnings of the weighted theory, with prior results, due to Coifman–Fefferman, P´erez, and Hyt¨onen–P´erez, on the L(log L) scale. Also, for square functions Sf,and…

Hamilton’s theory of kin selection is the best-known framework for understanding the evolution of social behavior but has long been a source of controversy in evolutionary biology. A recent critique of the theory by Nowak, Tarnita, and Wilson sparked a new round of debate, which shows no signs of abating. In this overview, we highlight a number of conceptual issues that lie at the heart of th…

Tahun Terbit

2010

Aquatic and terrestrial ecosystems are tightly linked through the fluxes of organisms and matter. However, aquatic and terrestrial ecologists have mainly studied these ecosystems separately, a “splendid isolation” historically fostered by disciplinary boundaries between institutes and funding schemes. Here, we synthesize the progress made in joint aquatic and terrestrial research and sugges…

The proliferation of a number of pressures affecting the ocean is leading to a growing concern that the state of the ocean is compromised, which is driving society into pessimism. Ocean calamities are disruptive changes to ocean ecosystems that have profound impacts and that are widespread or global in scope. However, scrutiny of ocean calamities to ensure that they can be confidently attribute…

Tahun Terbit

2010