Geometric invariant theory of syzygies, with applications to moduli spaces

We define syzygy points of projective schemes, and introduce a program of studying their GIT stability. Then we describe two cases where we have managed to make some progress in this program, that of polarized K3 surfaces of odd genus, and of genus six canonical curves. Applications of our results include effectivity statements for divisor classes on the moduli space of odd genus K3 surfaces, and a new construction in the Hassett-Keel program for the moduli space of genus six curves.Comment: v1: 23 pages, submitted to the Proceedings of the Abel Symposium 2017, v2: final version, corrects a sign error and resulting divisor class calculations on the moduli space of K3 surfaces in Section 5, other minor changes, In: Christophersen J., Ranestad K. (eds) Geometry of Moduli. Abelsymposium 2017. Abel Symposia, vol 14. Springer, Cha

Electron Signatures of Reconnection in a Global eVlasiator Simulation

Geospace plasma simulations have progressed toward more realistic descriptions of the solar wind-magnetosphere interaction from magnetohydrodynamic to hybrid ion-kinetic, such as the state-of-the-art Vlasiator model. Despite computational advances, electron scales have been out of reach in a global setting. eVlasiator, a novel Vlasiator submodule, shows for the first time how electromagnetic fields driven by global hybrid-ion kinetics influence electrons, resulting in kinetic signatures. We analyze simulated electron distributions associated with reconnection sites and compare them with Magnetospheric Multiscale (MMS) spacecraft observations. Comparison with MMS shows that key electron features, such as reconnection inflows, heated outflows, flat-top distributions, and bidirectional streaming, are in remarkable agreement. Thus, we show that many reconnection-related features can be reproduced despite strongly truncated electron physics and an ion-scale spatial resolution. Ion-scale dynamics and ion-driven magnetic fields are shown to be significantly responsible for the environment that produces electron dynamics observed by spacecraft in near-Earth plasmas.Peer reviewe

Torus equivariant K-stability

It is conjectured that to test the K-polystability of a polarised variety it is enough to consider test-configurations which are equivariant with respect to a torus in the automorphism group. We prove partial results towards this conjecture. We also show that it would give a new proof of the K-polystability of constant scalar curvature polarised manifolds

Roadmap on Superoscillations

Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern studies originated in quantum theory, but there were anticipations in radar and optics. The mathematical understanding—still being explored—recognises that functions are extremely small where they superoscillate; this has implications for information theory. Applications to optical vortices, sub-wavelength microscopy and related areas of nanoscience are now moving from the theoretical and the demonstrative to the practical. This Roadmap surveys all these areas, providing background, current research, and anticipating future developments

Roadmap on superoscillations

Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern studies originated in quantum theory, but there were anticipations in radar and optics. The mathematical understanding—still being explored—recognises that functions are extremely small where they superoscillate; this has implications for information theory. Applications to optical vortices, sub-wavelength microscopy and related areas of nanoscience are now moving from the theoretical and the demonstrative to the practical. This Roadmap surveys all these areas, providing background, current research, and anticipating future developments

Ten lessons on the resilience of the EU common fisheries policy towards climate change and fuel efficiency - A call for adaptive, flexible and well-informed fisheries management

To effectively future-proof the management of the European Union fishing fleets we have explored a suite of case studies encompassing the northeast and tropical Atlantic, the Mediterranean, Baltic and Black Seas. This study shows that European Union (EU) fisheries are likely resilient to climate-driven short-term stresses, but may be negatively impacted by long-term trends in climate change. However, fisheries' long-term stock resilience can be improved (and therefore be more resilient to increasing changes in climate) by adopting robust and adaptive fisheries management, provided such measures are based on sound scientific advice which includes uncertainty. Such management requires regular updates of biological reference points. Such updates will delineate safe biological limits for exploitation, providing both high long-term yields with reduced risk of stock collapse when affected by short-term stresses, and enhanced compliance with advice to avoid higher than intended fishing mortality. However, high resilience of the exploited ecosystem does not necessarily lead to the resilience of the economy of EU fisheries from suffering shocks associated with reduced yields, neither to a reduced carbon footprint if fuel use increases from lower stock abundances. Fuel consumption is impacted by stock development, but also by changes in vessel and gear technologies, as well as fishing techniques. In this respect, energy-efficient fishing technologies already exist within the EU, though implementing them would require improving the uptake of innovations and demonstrating to stakeholders the potential for both reduced fuel costs and increased catch rates. A transition towards reducing fuel consumption and costs would need to be supported by the setup of EU regulatory instruments. Overall, to effectively manage EU fisheries within a changing climate, flexible, adaptive, well-informed and well-enforced management is needed, with incentives provided for innovations and ocean literacy to cope with the changing conditions, while also reducing the dependency of the capture fishing industry on fossil fuels. To support such management, we provide 10 lessons to characterize 'win-win' fishing strategies for the European Union, which develop leverages in which fishing effort deployed corresponds to Maximum Sustainable Yield targets and Common Fisheries Policy minimal effects objectives. In these strategies, higher catch is obtained in the long run, less fuel is spent to attain the catch, and the fisheries have a higher resistance and resilience to shock and long-term factors to face climate-induced stresses