Complex structures of splitting type

We study the six-dimensional solvmanifolds that admit complex structures of splitting type classifying the underlying solvable Lie algebras. In particular, many complex structures of this type exist on the Nakamura manifold $X$, and they allow us to construct a countable family of compact complex non-$\partial\overline\partial$ manifolds $X_k$, $k\in\mathbb{Z}$, that admit a small holomorphic deformation $\{(X_{k})_{t}\}_{t\in\Delta_k}$ satisfying the $\partial\overline\partial$-Lemma for any $t\in\Delta_k$ except for the central fibre. Moreover, a study of the existence of special Hermitian metrics is also carried out on six-dimensional solvmanifolds with splitting-type complex structures

Limit points of lines of minima in Thurston's boundary of Teichmueller space

Given two measured laminations mu and nu in a hyperbolic surface which fill up the surface, Kerckhoff [Lines of Minima in Teichmueller space, Duke Math J. 65 (1992) 187-213] defines an associated line of minima along which convex combinations of the length functions of mu and nu are minimised. This is a line in Teichmueller space which can be thought as analogous to the geodesic in hyperbolic space determined by two points at infinity. We show that when mu is uniquely ergodic, this line converges to the projective lamination [mu], but that when mu is rational, the line converges not to [mu], but rather to the barycentre of the support of mu. Similar results on the behaviour of Teichmueller geodesics have been proved by Masur [Two boundaries of Teichmueller space, Duke Math. J. 49 (1982) 183-190].Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-9.abs.htm

Solutions of the Laplacian flow and coflow of a locally conformal parallel G2-structure

We study the Laplacian flow of a G 2-structure where this latter structure is claimed to be locally conformal parallel. The first examples of long time solutions of this flow with the locally conformal parallel condition are given. All of the solutions are ancient and Laplacian soliton of shrinking type. These examples are one-parameter families of locally conformal parallel G2-structures on rank-one solvable extensions of six-dimensional nilpotent Lie groups. The found solutions are used to construct long time solutions to the Laplacian coflow starting from a locally conformal parallel structure. We also study the behavior of the curvature of the solutions obtaining that for one of the examples the induced metric is Einstein along all the flow (resp. coflow)

Laplacian coflow for warped G2-structures

We consider the Laplacian coflow of a G2-structure on warped products of the form M7=M6×fS1 with M6 a compact 6-manifold endowed with an SU(3)-structure. We give an explicit reinterpretation of this flow as a set of evolution equations of the differential forms defining the SU(3)-structure on M6 and the warping function f. Necessary and sufficient conditions for the existence of solution for this flow are given. Finally we describe new solutions for this flow where the SU(3)-structure on M6 is nearly Kähler, symplectic half-flat or balanced. © 2020 Elsevier B.V

Caracterització de l'episodi "Glòria" a la Conca del Tordera mitjançant modelització hidrològica distribuïda

El gener del 2020 es va produir un gran temporal “Glòria” que va causar afectacions a tota Catalunya, sobretot a la conca de la Tordera, on hi va haver infraestructures greument danyades i inundacions. L’estudi de temporals és molt important actualment per la construcció d’infraestructures que no es vegin afectades i reduir així el risc de inundacions. No obstant, l’episodi Glòria encara segueix sense estar caracteritzat hidrològicament amb precisió degut a les discrepàncies entre dades d’aforaments d’estacions existents. L’objectiu principal del treball és caracteritzar des del punt de vista hidrològic l'episodi Glòria a tota la conca del Tordera, utilitzant la modelització numèrica distribuïda. Per portar-ho a terme, s’han obtingut i analitzat dades hidrològiques de la conca de la Tordera, s’ha construït un model hidrològic amb Iber, una eina que integra la modelització hidràulica bidimensional amb la modelització hidrològica distribuïda i s’ha refinat el model per tal de caracteritzar hidrològicament el temporal Glòria a la conca de la Tordera amb la màxima precisió possible.En enero de 2020 se produjo un gran temporal “Glòria” que causó afectaciones en toda Cataluña, sobre todo en la cuenca del Tordera, donde hubo infraestructuras gravemente dañadas e inundaciones. El estudio de temporales es muy importante en la actualidad por la construcción de infraestructuras que no se vean afectadas y reducir así el riesgo de inundaciones. Sin embargo, el episodio Glòria todavía sigue sin estar caracterizado hidrológicamente con precisión debido a las discrepancias entre datos de aforos de estaciones existentes. El objetivo principal del trabajo es caracterizar desde el punto de vista hidrológico el episodio Glòria en toda la cuenca del Tordera, utilizando la modelización numérica distribuida. Para ello, se han obtenido y analizado datos hidrológicos de la cuenca del Tordera, se ha construido un modelo hidrológico con Iber, una herramienta que integra la modelización hidráulica bidimensional con la modelización hidrológica distribuida y se ha refinado el modelo para caracterizar hidrológicamente el temporal Glòria en la cuenca del Tordera con la máxima precisión posible.In January 2020 there was a great storm "Gloria" that affected all Catalonia, especially in the basin of the Tordera, where there were severely damaged infrastructures and floods. Nowadays, the study of storms is very important for the construction of infrastructure that is not affected and thus reduce the risk of flooding. However, the Gloria episode is still not accurately hydrologically characterized due to discrepancies between gauging data from existing stations. The main objective of the document is to characterize from the hydrological point of view the Glòria episode throughout the Tordera basin, using distributed numerical modeling. To carry it out, hydrological data from the Tordera basin have been obtained and analyzed, a hydrological model has been built with Iber, a tool that integrates two-dimensional hydraulic modeling with distributed hydrological modelin. The model has been refined in order to hydrologically characterize the Gloria storm in the Tordera basin with the maximum possible precision

Fishing Nets and String at the Final Mesolithic and Early Neolithic Site of Zamostje 2, Sergiev Posad (Russia)

Altres ajuts: Funding information: O.L. was funded by the Program of FSR SAS no FMZF-2022-0012. M.B.-A. is currently funded by a MSCA-IF-2019 (GA No. 893735) and during part of this research was an Alexander von Humboldt post-doc fellow. R.P. was funded by ICREA Academia Program.The site Zamostje 2, located in Sergiev-Posad district of Moscow (Russia) on the west bank of the Dubna River, has provided two Mesolithic and one Early Neolithic occupations dated from 7000 to 5400 cal BC. Thanks to the waterlogged environment, the site has an exceptional preservation. The site has yielded fishing screens, fishing fences, wooden fishing traps, and several small cordage remains elaborated with plant fibres, pine bark floats, fragments of paddles, and other wooden objects. In this work, we present the study of the fragments of cordage and fishing nets with the objective of providing new insights into the production and use of implements made of plant fibres. We have characterized the production process by analysing the morphological and technical characteristics by carrying out experimentation with plant fibres in order to obtain reference material to recognize them at an archaeological level. The analysis of 82 knots and 23 fragments of strings has allowed to determine that they were elaborated with single threads from 0.5 to 1.5 mm thick, which is noticeably smaller than most examples from other sites. All of them were elaborated with woody bast fibres

Invariant complex structures on 6-nilmanifolds classification, Frölicher spectral sequence and special Hermitian metrics

We classify invariant complex structures on 6-dimensional nilmanifolds up to equivalence. As an application, the behaviour of the associated Frölicher sequence is studied as well as its relation to the existence of strongly Gauduchon metrics. We also show that the strongly Gauduchon property and the balanced property are not closed under holomorphic deformation.Ministerio de Ciencia e Innovació