Computing top intersections in the tautological ring of MgM_g

We derive effective recursion formulae of top intersections in the tautological ring $R^*(M_g)$ of the moduli space of curves of genus $g\geq 2$. As an application, we prove a convolution-type tautological relation in $R^{g-2}(M_g)$.Comment: 18 page

Dessins, their delta-matroids and partial duals

Given a map $\mathcal M$ on a connected and closed orientable surface, the delta-matroid of $\mathcal M$ is a combinatorial object associated to $\mathcal M$ which captures some topological information of the embedding. We explore how delta-matroids associated to dessins d'enfants behave under the action of the absolute Galois group. Twists of delta-matroids are considered as well; they correspond to the recently introduced operation of partial duality of maps. Furthermore, we prove that every map has a partial dual defined over its field of moduli. A relationship between dessins, partial duals and tropical curves arising from the cartography groups of dessins is observed as well.Comment: 34 pages, 20 figures. Accepted for publication in the SIGMAP14 Conference Proceeding

Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds

We investigate the relationship between the Lagrangian Floer superpotentials for a toric orbifold and its toric crepant resolutions. More specifically, we study an open string version of the crepant resolution conjecture (CRC) which states that the Lagrangian Floer superpotential of a Gorenstein toric orbifold $\mathcal{X}$ and that of its toric crepant resolution $Y$ coincide after analytic continuation of quantum parameters and a change of variables. Relating this conjecture with the closed CRC, we find that the change of variable formula which appears in closed CRC can be explained by relations between open (orbifold) Gromov-Witten invariants. We also discover a geometric explanation (in terms of virtual counting of stable orbi-discs) for the specialization of quantum parameters to roots of unity which appears in Y. Ruan's original CRC ["The cohomology ring of crepant resolutions of orbifolds", Gromov-Witten theory of spin curves and orbifolds, 117-126, Contemp. Math., 403, Amer. Math. Soc., Providence, RI, 2006]. We prove the open CRC for the weighted projective spaces $\mathcal{X}=\mathbb{P}(1,\ldots,1,n)$ using an equality between open and closed orbifold Gromov-Witten invariants. Along the way, we also prove an open mirror theorem for these toric orbifolds.Comment: 48 pages, 1 figure; v2: references added and updated, final version, to appear in CM

Advances in Sea-Ice Research Based on Remotely Sensed Passive Microwave Data

The contributions made to our knowledge of polar sea ice since the early 1970s by passive microwave remote sensing are surveyed

Research needs towards a resilient community: Vulnerability reduction, infrastructural systems model, loss assessment, resilience-based design and emergency management

Most of the literature on resilience is devoted to its assessment. It seems time to move from analysis to design, to develop the tools needed to enhance resilience. Resilience enhancement, a close relative of the less fashionable risk mitigation, adds to the latter, at least in the general perception, a systemic dimension. Resilience is often paired with community, and the latter is a system. This chapter therefore discusses strategies to enhance resilience, endorses one of prevention rather than cure, and focuses in the remainder on the role played by systemic analysis, i.e. the analysis of the built environment modelled beyond a simple collection of physical assets, with due care to the associated interdependencies. Research needs are identified and include challenges in network modelling, the replacement of generic fragility curves for components, how to deal with evolving state of information

Extreme timescale core-level spectroscopy with tailored XUV pulses

A new approach for few-femtosecond time-resolved photoelectron spectroscopy in condensed matter that balances the combined needs for both temporal and energy resolution is demonstrated. Here, the method is designed to investigate a prototypical Mott insulator, tantalum disulphide (1T-TaS2), which transforms from its charge-density-wave ordered Mott insulating state to a conducting state in a matter of femtoseconds. The signature to be observed through the phase transition is a charge-density-wave induced splitting of the Ta 4f core-levels, which can be resolved with sub-eV spectral resolution. Combining this spectral resolution with few-femtosecond time resolution enables the collapse of the charge ordered Mott state to be clocked. Precise knowledge of the sub-20-femtosecond dynamics will provide new insight into the physical mechanism behind the collapse and may reveal Mott physics on the timescale of electronic hopping.Comment: 20 pages, 6 figure

Supersonic strain front driven by a dense electron-hole plasma

We study coherent strain in (001) Ge generated by an ultrafast laser-initiated high density electron-hole plasma. The resultant coherent pulse is probed by time-resolved x-ray diffraction through changes in the anomalous transmission. The acoustic pulse front is driven by ambipolar diffusion of the electron-hole plasma and propagates into the crystal at supersonic speeds. Simulations of the strain including electron-phonon coupling, modified by carrier diffusion and Auger recombination, are in good agreement with the observed dynamics.Comment: 4 pages, 6 figure