90 research outputs found
On the cohomology of pseudoeffective line bundles
The goal of this survey is to present various results concerning the
cohomology of pseudoeffective line bundles on compact K{\"a}hler manifolds, and
related properties of their multiplier ideal sheaves. In case the curvature is
strictly positive, the prototype is the well known Nadel vanishing theorem,
which is itself a generalized analytic version of the fundamental
Kawamata-Viehweg vanishing theorem of algebraic geometry. We are interested
here in the case where the curvature is merely semipositive in the sense of
currents, and the base manifold is not necessarily projective. In this
situation, one can still obtain interesting information on cohomology, e.g. a
Hard Lefschetz theorem with pseudoeffective coefficients, in the form of a
surjectivity statement for the Lefschetz map. More recently, Junyan Cao, in his
PhD thesis defended in Grenoble, obtained a general K{\"a}hler vanishing
theorem that depends on the concept of numerical dimension of a given
pseudoeffective line bundle. The proof of these results depends in a crucial
way on a general approximation result for closed (1,1)-currents, based on the
use of Bergman kernels, and the related intersection theory of currents.
Another important ingredient is the recent proof by Guan and Zhou of the strong
openness conjecture. As an application, we discuss a structure theorem for
compact K{\"a}hler threefolds without nontrivial subvarieties, following a
joint work with F.Campana and M.Verbitsky. We hope that these notes will serve
as a useful guide to the more detailed and more technical papers in the
literature; in some cases, we provide here substantially simplified proofs and
unifying viewpoints.Comment: 39 pages. This survey is a written account of a lecture given at the
Abel Symposium, Trondheim, July 201
Interacting Preformed Cooper Pairs in Resonant Fermi Gases
We consider the normal phase of a strongly interacting Fermi gas, which can
have either an equal or an unequal number of atoms in its two accessible spin
states. Due to the unitarity-limited attractive interaction between particles
with different spin, noncondensed Cooper pairs are formed. The starting point
in treating preformed pairs is the Nozi\`{e}res-Schmitt-Rink (NSR) theory,
which approximates the pairs as being noninteracting. Here, we consider the
effects of the interactions between the Cooper pairs in a Wilsonian
renormalization-group scheme. Starting from the exact bosonic action for the
pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism
with the Wilsonian approach. We compare our findings with the recent
experiments by Harikoshi {\it et al.} [Science {\bf 327}, 442 (2010)] and
Nascimb\`{e}ne {\it et al.} [Nature {\bf 463}, 1057 (2010)], and find very good
agreement. We also make predictions for the population-imbalanced case, that
can be tested in experiments.Comment: 10 pages, 6 figures, accepted version for PRA, discussion of the
imbalanced Fermi gas added, new figure and references adde
Sous-groupes alg\'ebriques du groupe de Cremona
We give a complete classification of maximal algebraic subgroups of the
Cremona group of the plane and provide algebraic varieties that parametrize the
conjugacy classes.
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Nous donnons une classification compl\`ete des sous-groupes alg\'ebriques
maximaux du groupe de Cremona du plan et explicitons les vari\'et\'es qui
param\`etrent les classes de conjugaison.Comment: Text in French, Translated introduction, 35 pages, 1 figure, to
appear in Transform. Group
The masterpieces of John Forbes Nash Jr.
In this set of notes I follow Nash’s four groundbreaking works on real algebraic manifolds, on isometric embeddings of Riemannian manifolds and on the continuity of solutions to parabolic equations. My aim has been to stay as close as possible to Nash’s original arguments, but at the same time present them with a more modern language and notation. Occasionally I have also provided detailed proofs of the points that Nash leaves to the reader
Involvement of regional lymph nodes after penetration of Schistosoma mansoni cercariae in naive and infected mice
The parotid lymph nodes of naive and previously infected Balb/c mice were studied after, respectively, infection and re-infection with cercariae of Schistosoma mansoni via the ears. Schistosomula were able to pass through the lymph node by following the lymph flow or by penetrating the veins of the medullary cords. The number of nodal mast cells was higher from day 2 to 6 of primary infection; and from day 5 to 11 of re-infection. The amount of degranulating mast cells was significantly higher at day 4 of infection and at day 1 of re-infection. Eosinophils characterized the nodal inflammatory processes observed after day 5 in both primarily-infected and re-infected mice. However, only in the latter the eosinophils were able to adhere to the larval surface. In primarily-infected mice, no intranodal larva presented signs of degeneration. In contrast, in re-infected animals, some degenerating larvae were found inside eosinophilic infiltrates. The eosinophils reached the nodal tissue by migrating through the high endothelial venules and their collecting veins
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