ERC FUNDED PROJECTS

The global marine ecosystem is being deeply altered by human activity. On the one hand, rising concentrations of atmospheric greenhouse gases are changing the physical and chemical state of the ocean, exerting pressure from the bottom up. Meanwhile, the global fishery has provided large economic benefits, but in so doing has restructured ecosystems by removing most of the large animal biomass, a major top-down change. Although there has been a tremendous amount of research into isolated aspects of these impacts, the development of a holistic understanding of the full interactions between physics, chemistry, ecology and economic activity might appear impossible, given the myriad complexities. This proposal lays out a strategy to assemble a team of trans-disciplinary expertise, that will develop a unified, data-constrained, grid-based modeling framework to represent the most important interactions of the global human-ocean system. Building this framework requires solving a series of fundamental problems that currently hinder the development of the full model. If these problems can be solved, the resulting model will reveal novel emergent properties and open the doors to a range of previously unexplored questions of high impact across a range of disciplines. Key questions include the ways in which animals interact with oxygen minimum zones with implications for fisheries, the impacts fish harvesting may have on nutrient recycling, spatio-temporal interactions between managed and unmanaged fisheries, and fundamental questions about the relationships between fish price, fishing cost, and multiple markets in a changing world. Just as the first coupled ocean-atmosphere models revealed a wealth of new behaviours, the coupled human-ocean model proposed here has the potential to launch multiple new fields of enquiry. It is hoped that the novel approach will contribute to a paradigm shift that treats human activity as one component within the framework of the Earth System.

1 600 000 €

Start date: 2016-07-01, End date: 2021-12-31

In order to celebrate mathematics in the new millennium, the Clay Mathematics Institute established seven $1.000.000 Prize Problems. One of these is the conjecture of Birch and Swinnerton-Dyer (BSD), widely open since the 1960's. The main object of this proposal is developing innovative and unconventional strategies for proving groundbreaking results towards the resolution of this problem and their generalizations by Bloch and Kato (BK). Breakthroughs on BSD were achieved by Coates-Wiles, Gross, Zagier and Kolyvagin, and Kato. Since then, there have been nearly no new ideas on how to tackle BSD. Only very recently, three independent revolutionary approaches have seen the light: the works of (1) the Fields medalist Bhargava, (2) Skinner and Urban, and (3) myself and my collaborators. In spite of that, our knowledge of BSD is rather poor. In my proposal I suggest innovating strategies for approaching new horizons in BSD and BK that I aim to develop with the team of PhD and postdoctoral researchers that the CoG may allow me to consolidate. The results I plan to prove represent a departure from the achievements obtained with my coauthors during the past years: I. BSD over totally real number fields. I plan to prove new ground-breaking instances of BSD in rank 0 for elliptic curves over totally real number fields, generalizing the theorem of Kato (by providing a new proof) and covering many new scenarios that have never been considered before. II. BSD in rank r=2. Most of the literature on BSD applies when r=0 or 1. I expect to prove p-adic versions of the theorems of Gross-Zagier and Kolyvagin in rank 2. III. Darmon's 2000 conjecture on Stark-Heegner points. I plan to prove Darmon’s striking conjecture announced at the ICM2000 by recasting it in terms of special values of p-adic L-functions.

1 428 588 €

Start date: 2016-09-01, End date: 2022-08-31

The enormous quantities of frozen carbon in the Arctic, held in shallow soils and sediments, act as “capacitors” of the global carbon system. Thawing permafrost (PF) and collapsing methane hydrates are top candidates to cause a net transfer of carbon from land/ocean to the atmosphere this century, yet uncertainties abound. Our program targets the East Siberian Arctic Ocean (ESAO), the World’s largest shelf sea, as it holds 80% of coastal PF, 80% of subsea PF and 75% of shallow hydrates. Our initial findings (e.g., Science, 2010; Nature, 2012; PNAS; 2013; Nature Geoscience, 2013, 2014) are challenging earlier notions by showing complexities in terrestrial PF-Carbon remobilization and extensive venting of methane from subsea PF/hydrates. The objective of the CC-Top Program is to transform descriptive and data-lean pictures into quantitative understanding of the CC system, to pin down the present and predict future releases from these “Sleeping Giants” of the global carbon system. The CC-Top program combines unique Arctic field capacities with powerful molecular-isotopic characterization of PF-carbon/methane to break through on: The “awakening” of terrestrial PF-C pools: CC-Top will employ great pan-arctic rivers as natural integrators and by probing the δ13C/Δ14C and molecular fingerprints, apportion release fluxes of different PF-C pools. The ESAO subsea cryosphere/methane: CC-Top will use recent spatially-extensive observations, deep sediment cores and gap-filling expeditions to (i) estimate distribution of subsea PF and hydrates; (ii) establish thermal state (thawing rate) of subsea PF-C; (iii) apportion sources of releasing methane btw subsea-PF, shallow hydrates vs seepage from the deep petroleum megapool using source-diagnostic triple-isotope fingerprinting. Arctic Ocean slope hydrates: CC-Top will investigate sites (discovered by us 2008-2014) of collapsed hydrates venting methane, to characterize geospatial distribution and causes of destabilization.

2 499 756 €

Start date: 2016-11-01, End date: 2021-10-31

Computer-generated imagery is now ubiquitous in our society, spanning fields such as games and movies, architecture, engineering, or virtual prototyping, while also helping create novel ones such as computational materials. With the increase in computational power and the improvement of acquisition techniques, there has been a paradigm shift in the field towards data-driven techniques, which has yielded an unprecedented level of realism in visual appearance. Unfortunately, this leads to a series of problems, identified in this proposal: First, there is a disconnect between the mathematical representation of the data and any meaningful parameters that humans understand; the captured data is machine-friendly, but not human friendly. Second, the many different acquisition systems lead to heterogeneous formats and very large datasets. And third, real-world appearance functions are usually nonlinear and high-dimensional. As a result, visual appearance datasets are increasingly unfit to editing operations, which limits the creative process for scientists, engineers, artists and practitioners in general. There is an immense gap between the complexity, realism and richness of the captured data, and the flexibility to edit such data. We believe that the current research path leads to a fragmented space of isolated solutions, each tailored to a particular dataset and problem. We propose a research plan at the theoretical, algorithmic and application levels, putting the user at the core. We will learn key relevant appearance features in terms humans understand, from which intuitive, predictable editing spaces, algorithms, and workflows will be defined. In order to ensure usability and foster creativity, we will also extend our research to efficient simulation of visual appearance, exploiting the extra dimensionality of the captured datasets. Achieving our goals will finally enable us to reach the true potential of real-world captured datasets in many aspects of society.

1 629 519 €

Start date: 2016-11-01, End date: 2023-04-30