Proof of the Hyperplane Zeros Conjecture of Lagarias and Wang

We prove that a real analytic subset of a torus group that is contained in its image under an expanding endomorphism is a finite union of translates of closed subgroups. This confirms the hyperplane zeros conjecture of Lagarias and Wang for real analytic varieties. Our proof uses real analytic geometry, topological dynamics and Fourier analysis.Comment: 25 page

Exact Lagrangian submanifolds in simply-connected cotangent bundles

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler, using a different approach.Comment: 28 pages, 3 figures. Version 2 -- derivation and discussion of the spectral sequence considerably expanded. Other minor change

Analytic curves in algebraic varieties over number fields

We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'olya-Bertrandias valid over the projective line to arbitrary algebraic curves over a number field. The formulation and the proof of these criteria involve some basic notions in Arakelov geometry, combined with complex and rigid analytic geometry (notably, potential theory over complex and $p$-adic curves). We also discuss geometric analogues, pertaining to the algebraic geometry of projective surfaces, of these arithmetic criteria.Comment: 55 pages. To appear in "Algebra, Arithmetic, and Geometry: In Honor of Y.i. Manin", Y. Tschinkel & Yu. Manin editors, Birkh\"auser, 200

Singular open book structures from real mappings

We prove extensions of Milnor's theorem for germs with nonisolated singularity and use them to find new classes of genuine real analytic mappings $\psi$ with positive dimensional singular locus \Sing \psi \subset \psi^{-1}(0), for which the Milnor fibration exists and yields an open book structure with singular binding.Comment: more remark

Characterizing normal crossing hypersurfaces

The objective of this article is to give an effective algebraic characterization of normal crossing hypersurfaces in complex manifolds. It is shown that a hypersurface has normal crossings if and only if it is a free divisor, has a radical Jacobian ideal and a smooth normalization. Using K. Saito's theory of free divisors, also a characterization in terms of logarithmic differential forms and vector fields is found and and finally another one in terms of the logarithmic residue using recent results of M. Granger and M. Schulze.Comment: v2: typos fixed, final version to appear in Math. Ann.; 24 pages, 2 figure

Techniques for the study of singularities with applications to resolution of 2-dimensional schemes

We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.Comment: 26 pages; minor changes have been adde

Dexfenfluramine and the oestrogen-metabolizing enzyme CYP1B1 in the development of pulmonary arterial hypertension

<p>Aims: Pulmonary arterial hypertension (PAH) occurs more frequently in women than men. Oestrogen and the oestrogen-metabolising enzyme cytochrome P450 1B1 (CYP1B1) play a role in the development of PAH. Anorectic drugs such as dexfenfluramine (Dfen) have been associated with the development of PAH. Dfen mediates PAH via a serotonergic mechanism and we have shown serotonin to up-regulate expression of CYP1B1 in human pulmonary artery smooth muscle cells (PASMCs). Thus here we assess the role of CYP1B1 in the development of Dfen-induced PAH.</p> <p>Methods and results: Dfen (5 mg kg−1 day−1 PO for 28 days) increased right ventricular pressure and pulmonary vascular remodelling in female mice only. Mice dosed with Dfen showed increased whole lung expression of CYP1B1 and Dfen-induced PAH was ablated in CYP1B1−/− mice. In line with this, Dfen up-regulated expression of CYP1B1 in PASMCs from PAH patients (PAH-PASMCs) and Dfen-mediated proliferation of PAH-PASMCs was ablated by pharmacological inhibition of CYP1B1. Dfen increased expression of tryptophan hydroxylase 1 (Tph1; the rate-limiting enzyme in the synthesis of serotonin) in PAH-PASMCs and both Dfen-induced proliferation and Dfen-induced up-regulation of CYP1B1 were ablated by inhibition of Tph1. 17β-Oestradiol increased expression of both Tph1 and CYP1B1 in PAH-PASMCs, and Dfen and 17β-oestradiol had synergistic effects on proliferation of PAH-PASMCs. Finally, ovariectomy protected against Dfen-induced PAH in female mice.</p> <p>Conclusion: CYP1B1 is critical in the development of Dfen-induced PAH in mice in vivo and proliferation of PAH-PASMCs in vitro. CYP1B1 may provide a novel therapeutic target for PAH.</p&gt

Affine modifications and affine hypersurfaces with a very transitive automorphism group

We study a kind of modification of an affine domain which produces another affine domain. First appeared in passing in the basic paper of O. Zariski (1942), it was further considered by E.D. Davis (1967). The first named author applied its geometric counterpart to construct contractible smooth affine varieties non-isomorphic to Euclidean spaces. Here we provide certain conditions which guarantee preservation of the topology under a modification. As an application, we show that the group of biregular automorphisms of the affine hypersurface $X \subset C^{k+2}$ given by the equation $uv=p(x_1,...,x_k)$ where $p \in C[x_1,...,x_k],$ acts $m-$transitively on the smooth part reg$X$ of $X$ for any $m \in N.$ We present examples of such hypersurfaces diffeomorphic to Euclidean spaces.Comment: 39 Pages, LaTeX; a revised version with minor changes and correction

Development of an experimental platform for the investigation of laser-plasma interaction in conditions relevant to shock ignition regime

The shock ignition (SI) approach to inertial confinement fusion is a promising scheme for achieving energy production by nuclear fusion. SI relies on using a high intensity laser pulse (≈1016 W/cm2, with a duration of several hundred ps) at the end of the fuel compression stage. However, during laser-plasma interaction (LPI), several parametric instabilities, such as stimulated Raman scattering and two plasmon decay, nonlinearly generate hot electrons (HEs). The whole behavior of HE under SI conditions, including their generation, transport, and final absorption, is still unclear and needs further experimental investigation. This paper focuses on the development of an experimental platform for SI-related experiments, which simultaneously makes use of multiple diagnostics to characterize LPI and HE generation, transport, and energy deposition. Such diagnostics include optical spectrometers, streaked optical shadowgraph, an x-ray pinhole camera, a two-dimensional x-ray imager, a Cu Kα line spectrometer, two hot-electron spectrometers, a hard x-ray (bremsstrahlung) detector, and a streaked optical pyrometer. Diagnostics successfully operated simultaneously in single-shot mode, revealing the features of HEs under SI-relevant conditions.T. Tamagawa, Y. Hironaka, K. Kawasaki, D. Tanaka, T. Idesaka, N. Ozaki, R. Kodama, R. Takizawa, S. Fujioka, A. Yogo, D. Batani, Ph. Nicolai, G. Cristoforetti, P. Koester, L. A. Gizzi, and K. Shigemori, "Development of an experimental platform for the investigation of laser–plasma interaction in conditions relevant to shock ignition regime", Review of Scientific Instruments 93, 063505 (2022) https://doi.org/10.1063/5.008996