Cohomologies of locally conformally symplectic manifolds and solvmanifolds

We study the Morse-Novikov cohomology and its almost-symplectic counterpart on manifolds admitting locally conformally symplectic structures. More precisely, we introduce lcs cohomologies and we study elliptic Hodge theory, dualities, Hard Lefschetz Condition. We consider solvmanifolds and Oeljeklaus-Toma manifolds. In particular, we prove that Oeljeklaus-Toma manifolds with precisely one complex place, and under an additional arithmetic condition, satisfy the Mostow property. This holds in particular for the Inoue surface of type $S^0$

Classification of simple linearly compact Kantor triple systems over the complex numbers

Simple finite dimensional Kantor triple systems over the complex numbers are classified in terms of Satake diagrams. We prove that every simple and linearly compact Kantor triple system has finite dimension and give an explicit presentation of all the classical and exceptional systems.Comment: 46 pages, 3 tables; v2: Major revision of the introduction; v3: Final version to appear in Journal of Algebr

Symplectic cohomologies and deformations

In this note we study the behavior of symplectic cohomology groups under symplectic deformations. Moreover, we show that for compact almost-K\"ahler manifolds $(X,J,g,\omega)$ with $J$ $\mathcal{C}^\infty$-pure and full the space of de Rham harmonic forms is contained in the space of symplectic-Bott-Chern harmonic forms. Furthermore, we prove that the second non-HLC degree measures the gap between the de Rham and the symplectic-Bott-Chern harmonic forms

Some remarks on Hermitian manifolds satisfying K\"ahler-like conditions

We study Hermitian metrics whose Bismut connection $\nabla^B$ satisfies the first Bianchi identity in relation to the SKT condition and the parallelism of the torsion of the Bimut connection. We obtain a characterization of complex surfaces admitting Hermitian metrics whose Bismut connection satisfy the first Bianchi identity and the condition $R^B(x,y,z,w)=R^B(Jx,Jy,z,w)$, for every tangent vectors $x,y,z,w$, in terms of Vaisman metrics. These conditions, also called Bismut K\"ahler-like, have been recently studied in [D. Angella, A. Otal, L. Ugarte, R. Villacampa, On Gauduchon connections with K\"ahler-like curvature, to appear in Commun. Anal. Geom., arXiv:1809.02632 [math.DG]], [Q. Zhao, F. Zheng, Strominger connection and pluriclosed metrics, arXiv:1904.06604 [math.DG]], [S. T. Yau, Q. Zhao, F. Zheng, On Strominger K\"ahler-like manifolds with degenerate torsion, arXiv:1908.05322 [math.DG]]. Using the characterization of SKT almost abelian Lie groups in [R. M. Arroyo, R. Lafuente, The long-time behavior of the homogeneous pluriclosed flow, Proc. London Math. Soc. (3), 119, (2019), 266-289], we construct new examples of Hermitian manifolds satisfying the Bismut K\"ahler-like condition. Moreover, we prove some results in relation to the pluriclosed flow on complex surfaces and on almost abelian Lie groups. In particular, we show that, if the initial metric has constant scalar curvature, then the pluriclosed flow preserves the Vaisman condition on complex surfaces.Comment: Theorem B and Lemma 5.1 modified. Added Remark 5.

Under What Conditions Can Inflation Targeting Be Adopted? The Experience of Emerging Markets

While there have been numerous studies of inflation targeting in industrial countries, there has been much less analysis of the effects of inflation targeting in emerging market countries. Based on a new and detailed survey of 31 central banks, this paper shows that inflation targeting in emerging-market countries brings significant benefits to the countries that adopt it relative to other strategies, such as money or exchange rate targeting. Indeed, by comparing the performance of the inflation-targeting countries with a sample of countries that pursue other regimes we show that there are significant improvements in anchoring both inflation and inflation expectations with no adverse effects on output. In addition, under inflation targeting interest rates, exchange rates, and international reserves are less volatile, and the risk of currency crises relative to money or exchange rate targets is smaller. Interestingly, IT seems to outperform exchange rate pegs—even when only successful pegs are chosen in comparison. The survey evidence indicates that it is unnecessary for countries to meet a stringent set of institutional, technical, and economic “preconditions” for the successful adoption of inflation targeting.

Strong pressure-energy correlations in liquids as a configuration space property: Simulations of temperature down jumps and crystallization

Computer simulations recently revealed that several liquids exhibit strong correlations between virial and potential energy equilibrium fluctuations in the NVT ensemble [U. R. Pedersen {\it et al.}, Phys. Rev. Lett. {\bf 100}, 015701 (2008)]. In order to investigate whether these correlations are present also far from equilibrium constant-volume aging following a temperature down jump from equilibrium was simulated for two strongly correlating liquids, an asymmetric dumbbell model and Lewis-Wahnstr{\"o}m OTP, as well as for SPC water that is not strongly correlating. For the two strongly correlating liquids virial and potential energy follow each other closely during the aging towards equilibrium. For SPC water, on the other hand, virial and potential energy vary with little correlation as the system ages towards equilibrium. Further proof that strong pressure-energy correlations express a configuration space property comes from monitoring pressure and energy during the crystallization (reported here for the first time) of supercooled Lewis-Wahnstr{\"o}m OTP at constant temperature