Hungary

Combinatorics is a branch of mathematics studying finite structures. The generality of these questions suggests wide applicability of combinatorics in other areas of pure mathematics (most notably in algebra, number theory, probability, and topology), as well as in real-world applications (discrete optimization, computer science).One of the oldest and most central parts of combinatorics are graph theory and enumerative combinatorics. Graph theory models networks (such as road connections, or internet users), and enumerative combinatorics concerns studying counting questions of various kinds.Extremal graph theory is a broad part of graph theory which investigates interplay between various graph parameters. One of the main tools in Extremal graph theory is the so-called Szemeredi Regularity Lemma. This tool (developed in the 70's) has become one of the corner-stones of modern mathematics. Recently, using the insights gained from the Regularity Lemma, Lovasz and Szegedy initiated study of graph limits.The proposed research project addresses major open questions in extremal graph theory and aims contribute to general theories the Regularity Lemma, graph limits, and by developing novel tools which will be used in enumerative combinatorics.

There are around 304 million lakes globally. These provide essential resources for human survival and are an important component of global biogeochemical cycles. Lakes are also fragile systems that are sensitive to multiple pressures including nutrient enrichment, climate change and hydrological modification, making them important 'sentinels' of environmental perturbation. However, traditional monitoring has only produced data from a tiny fraction of the global population of lakes and disentangling the causes of change requires consistently-produced data from a large number of lakes, along with measurements of possible causes of change. Satellite observations (remote sensing) and the establishment of a global lake observatory would produce a step-change in our ability to detect and attribute the causes of changes in lakes world-wide. This is now possible for three reasons: (1) the improved wavebands, spatial resolution and frequency of data collection from satellite sensors is now sufficient to monitor inland waters; (2) formulae to correct for atmospheric properties and to convert the detected reflected light to useful lake properties have been developed; and (3) computing power has increased to the point that allows near real time and archived information from satellites to be processed. GloboLakes will analyse 20 years of data from more than 1000 large lakes across the globe to determine 'what controls the differential sensitivity of lakes to environmental perturbation'. This is an ambitious project that is only possible by bringing together a consortium of scientists with complementary skills. These include expertise in remote sensing of freshwaters and processing large volumes of satellite images, collation and analysis of large-scale environmental data, environmental statistics and the assessment of data uncertainty, freshwater ecology and mechanisms of environmental change and the ability to produce lake models to forecast future lake conditions. The eight objectives of GloboLakes are to: (i) develop remote sensing algorithms to estimate lake biogeochemical and physical parameters; (ii) make these algorithms operational and process satellite data; (iii) compile integrated spatio-temporal information on climatic and catchment data for >1000 lakes; (iv) integrate data and assess uncertainty in data sources; (v) detect spatial and temporal patterns in lake water quality; (vi) attribute the causes of lake response to environmental conditions; (vii) forecast lake sensitivity to environmental change; (viii) apply data to lake management and the monitoring of freshwater resources. The project will focus on the retrieval of surface water temperature as this has a fundamental effect on lake ecology, the concentration of coloured dissolved organic matter and suspended solids that derive largely from the catchment, the abundance of phytoplankton measured as the concentration of the pigment, chlorophyll a, and the abundance of cyanobacteria (blue-green algae) that can potentially be toxic. Knowledge of the conditions of lakes and their sensitivity to change is also extremely valuable for the management of lakes and reservoirs and GloboLakes will provide information and products specifically for environmental managers. A satellite due to be launched during the course of the project, called Sentinel 2, will provide even greater spatial resolution allowing data to be collected and exploited from even smaller lakes. This will be investigated by GloboLakes and incorporated into the framework of a global lake observatory.