Mathematics

We prove the nonexistence of stable immersed minimal surfaces uniformly conformally equivalent to C in any complete orientable four-dimensional Riemannian manifold with uniformly positive isotropic curvature. We also generalize the same nonexistence result to higher dimensions provided that the ambient manifold has uniformly positive complex sectional curvature. The proof consists of two parts, assuming an "eigenvalue condition" on the ∂operator of a holomorphic bundle, we prove (1) a vanishing theorem for these holomorphic bundles on C;

Soviet propaganda often used the Soviet space program as a symbol of a much larger and more ambitious political/engineering project-the construction of communism. Both projects involved the construction of a new self, and the cosmonaut was often regarded as a model for the "new Soviet man." The Soviet cosmonauts publicly represented a communist ideal, an active human agency of sociopolitical and economic change. At the same time, space engineers and psychologists viewed human operators as integral parts of a complex technological system and assigned the cosmonauts a very limited role in spacecraft control. This article examines how the cosmonaut self became the subject of "human engineering," explores the tension between the public image of the cosmonauts and their professional identity, and draws parallels between the iconic roles of the cosmonaut and the astronaut in the cold war context. 2007, 22 : 135-157 135

This article explores the impact of the professional culture of rocket engineering in Stalin's Soviet Union on the engineering and organizational practices of the space program during the Khrushchev era. The Stalinist legacy and the dual military / civilian character of rocket engineers' work profoundly affected the identity of this elite part of Soviet technical intelligentsia. Focusing on such notions as control, authority, and responsibility, this article examines the role of engineering culture in shaping the Soviet approach to the automation of piloted spacecraft control. Through patronage and networking, rocket engineers were able to overcome the ineffi ciency of Soviet industrial management and to advance their agenda of space exploration.

The set of orbits of GL(V ) in F l(V ) × F l(V ) × V is finite, and is parametrized by the set of certain decorated permutations in a work of Solomon. We describe a Mirabolic RSK correspondence (bijective) between this set of decorated permutations and the set of triples: a pair of standard Young tableaux, and an extra partition. It gives rise to a partition of the set of orbits into combinatorial cells. We prove that the same partition is given by the type of a general conormal vector to an orbit. We conjecture that the same partition is given by the bimodule Kazhdan-Lusztig cells in the bimodule over the Iwahori-Hecke algebra of GL(V ) arising from F l(V ) × F l(V ) × V . We also give conjectural applications to the classification of unipotent mirabolic character sheaves on GL(V ) × V .

Let C be a smooth connected projective curve of genus > 1 over an algebraically closed field k of characteristic p > 0, and c ∈ k \ Fp. Let Bun N be the stack of rank N vector bundles on C and L det the line bundle on Bun N given by determinant of derived global sections. We construct an equivalence of derived categories of modules for certain localizations of the twisted crystalline differential operator algebras D Bun N ,L c det and D Bun N ,L −1/c det . The first step of the argument is the same as that of [BB] for the nonquantum case: based on the Azumaya property of crystalline differential operators, the equivalence is constructed as a twisted version of Fourier-Mukai transform on the Hitchin fibration. However, there are some new ingredients. Along the way we introduce a generalization of p-curvature for line bundles with non-flat connections, and construct a Liouville vector field on the space of de Rham local systems on C.

Nanomaterials modified with biological recognition motifs acquire a myriad of functions that can be exploited for the diagnosis and treatment of cancer. Nevertheless, while bioactive domains can be used to target nanoparticles to cell receptors, shuttle them across cell membranes, and activate cell signaling, such modifications typically include cationic or hydrophobic regions that lead to rapid reticuloendothelial system (RES) clearance of particles from the blood, ultimately reducing particle accumulation in tumors. Further functionalization with hydrophilic polymers like poly(ethylene glycol) (PEG) can improve blood half-lives and tumor accumulation, but often at the expense of efficient ligandmediated nanoparticle binding. To address this tradeoff between improved biodistribution and optimal functionality on nanoparticles, we present a general strategy for reversibly veiling bioactive domains on nanoparticles using sterically protective polymers. We demonstrate that these materials effectively accumulate via the hyperpermeable vasculature of tumors and can be activated by cancer-secreted proteases to unveil hidden functional domains.