The discovery that matter is made up of atoms ranks as one ofmankind's greatest achievements. Twenty first century science isdominated by a quest for the mastery (both in terms of control andunderstanding) of our environment at the atomic level.In biology, understanding life (preserving it, or even attempting tocreate it) revolves around large, complex, molecules -- RNA, DNA, andproteins.Global warming is dictated by the particular way atoms are arrangedto make small greenhouse gas molecules, carbon dioxide and so on.The drive for faster, more efficient, cheaper computer chips forcesnanotechnology upon us. As the transistors that make up themicroscopic circuits are packed ever closer together, electronicengineers must understand where the atoms are placed, or misplaced, inthe semiconducting and insulating materials.Astronomers are currently, daily, discovering new planets outside oursolar system, orbiting alien stars. The largest are the easiest tospot, and many are far larger than Jupiter. The more massive theplanet the higher pressures endured by the matter that makes up itsbulk. How can we hope to determine the structure of matter at theseconditions?The atomic theory of matter leads to quantum mechanics -- a mechanicsof the every small. In principle, to understand and predict thebehaviour of matter at the atomic scale simply requires the solutionof the quantum mechanical Schroedinger equations. This is a challengein itself, but in an approximate way it is now possible to quicklycompute the energies and properties of fairly large collections ofatoms. But is it possible to predict how those atoms will be arrangedin Nature - ex nihilo, from nothing but our understanding ofphysics?Some have referred to it as a scandal that the physical sciencescannot routinely predict the structure of even simple crystals -- butmost have assumed it to be a very difficult problem. A minimum energymust be found in a many dimensional space of all the possiblestructures. Those researchers brave enough to tackle this challengehave done so by reaching for complex algorithms -- such as geneticalgorithms, which appeal to evolution to breed ever betterstructures (with better taken to mean more stable). However, Ihave discovered to my surprise, and to others', that the very simplestalgorithm -- throw the collection of atoms into a box, and move theatoms downhill on the energy landscape -- is remarkably effectiveif it is repeated many times.This approach needs no prior knowledge of chemistry. Indeed thescientist is taught chemistry by its results -- this is critical ifthe method is to be used to predict the behaviour of matter underextreme conditions, where learned intuition will typically fail.I have used this approach, which I call random structure searching to predict the structure of crystals ex nihilo. My firstapplication of it has been to silane at very high pressures, and thestructure I predicted has recently been seen in experiments. Butprobably the most impressive application so far has been to predictingthe structure of hydrogen at the huge pressures found in the gas giantplanets, where it may be a room temperature superconductor.In the course of my fellowship I will extend this work to try toanticipate the structure of matter in the newly discovered exoplanets,to try to discover and design materials with extreme (and hopefully,extremely useful) properties, and to help pharmaceutical researchersunderstand the many forms that their drug molecules adopt when theycrystallise.

The context of the proposal mainly concerns singular stochastic PDEs and related statistical physics models. By saying singular, we mean that the solution (or some of its derivatives) has wild oscillations with a frequency and magnitude blowing up to infinity at small scales. The singularities in the solutions to stochastic PDEs are typically almost everywhere. As a consequence, nonlinear operations of the solutions may not make sense as they take these high frequency oscillations into quantities that are typically infinity. Thus, the correct interpretation of the solutions to these equations usually requires renormalisation. In the past three years, there have been major advances in the development of solution theories to a number of important singular SPDEs, including the three dimensional stochastic quantisation equation, the KPZ equation and the parabolic Anderson model in two and three dimensions. These equations are widely believed to be the universal models for the large scale behaviours of many systems in statistical mechanics. The successful construction of the solutions opens a way to study in detail these equations as well as the natural phenomena they represent. In this proposal, we aim to deepen the understanding of the quantitative behaviour of the solutions to these equations, and rigorously prove the universality phenomena for their related statistical physics models. We will also investigate how certain perturbations of the system (for example, asymmetry in phase coexistence models) can force its large scale behaviour to deviate from the expected universal limit.

The discovery that matter is made up of atoms ranks as one ofmankind's greatest achievements. Twenty first century science isdominated by a quest for the mastery (both in terms of control andunderstanding) of our environment at the atomic level.In biology, understanding life (preserving it, or even attempting tocreate it) revolves around large, complex, molecules -- RNA, DNA, andproteins.Global warming is dictated by the particular way atoms are arrangedto make small greenhouse gas molecules, carbon dioxide and so on.The drive for faster, more efficient, cheaper computer chips forcesnanotechnology upon us. As the transistors that make up themicroscopic circuits are packed ever closer together, electronicengineers must understand where the atoms are placed, or misplaced, inthe semiconducting and insulating materials.Astronomers are currently, daily, discovering new planets outside oursolar system, orbiting alien stars. The largest are the easiest tospot, and many are far larger than Jupiter. The more massive theplanet the higher pressures endured by the matter that makes up itsbulk. How can we hope to determine the structure of matter at theseconditions?The atomic theory of matter leads to quantum mechanics -- a mechanicsof the every small. In principle, to understand and predict thebehaviour of matter at the atomic scale simply requires the solutionof the quantum mechanical Schroedinger equations. This is a challengein itself, but in an approximate way it is now possible to quicklycompute the energies and properties of fairly large collections ofatoms. But is it possible to predict how those atoms will be arrangedin Nature - ex nihilo, from nothing but our understanding ofphysics?Some have referred to it as a scandal that the physical sciencescannot routinely predict the structure of even simple crystals -- butmost have assumed it to be a very difficult problem. A minimum energymust be found in a many dimensional space of all the possiblestructures. Those researchers brave enough to tackle this challengehave done so by reaching for complex algorithms -- such as geneticalgorithms, which appeal to evolution to breed ever betterstructures (with better taken to mean more stable). However, Ihave discovered to my surprise, and to others', that the very simplestalgorithm -- throw the collection of atoms into a box, and move theatoms downhill on the energy landscape -- is remarkably effectiveif it is repeated many times.This approach needs no prior knowledge of chemistry. Indeed thescientist is taught chemistry by its results -- this is critical ifthe method is to be used to predict the behaviour of matter underextreme conditions, where learned intuition will typically fail.I have used this approach, which I call random structure searching to predict the structure of crystals ex nihilo. My firstapplication of it has been to silane at very high pressures, and thestructure I predicted has recently been seen in experiments. Butprobably the most impressive application so far has been to predictingthe structure of hydrogen at the huge pressures found in the gas giantplanets, where it may be a room temperature superconductor.In the course of my fellowship I will extend this work to try toanticipate the structure of matter in the newly discovered exoplanets,to try to discover and design materials with extreme (and hopefully,extremely useful) properties, and to help pharmaceutical researchersunderstand the many forms that their drug molecules adopt when theycrystallise.

Stochastic partial differential equations (SPDE) describe the behaviour of spatially extended systems under the influence of noise. They arise naturally in various fields of applications as diverse as data mining, mathematical finance, and population dynamics and genetics. The present proposal aims to study a class of stochastic partial differential equations from statistical mechanics. Many particle models exhibit a behaviour called phase transition, where the behaviour of the system changes drastically when one changes a given system parameter beyond a critical point. It is a very exciting question to understand the behaviour of such a system near a critical point. In such a regime one expects the dynamics to be governed by a non-linear SPDE. Analytically the understanding of these equations is very challenging, because of the interaction between the rough noise term and the non-linear evolution. But this is also what gives rise to interesting phenomena. In this proposal, we aim to deepen the understanding of these equations. On the one hand we will study the behaviour under the influence of a small noise term. Then we will establish that two different kinds of particle models can indeed be described by such an SPDE.

The shift from hunting and gathering to an agricultural way of life was one of the most profound events in the history of our species and one which continues to impact our existence today. Understanding this process is key to understanding the origins and rise of human civilization. Despite decades of study, however, fundamental questions regarding why, where and how it occurred remain largely unanswered. Such a fundamental change in human existence could not have been possible without the domestication of selected animals and plants. The dog is crucial in this story since it was not only the first ever domestic animal, but also the only animal to be domesticated by hunter-gatherers several thousand years before the appearance of farmers. The bones and teeth of early domestic dogs and their wild wolf ancestors hold important clues to our understanding of how, where and when humans and wild animals began the relationship we still depend upon today. These remains have been recovered from as early as 15,000 years ago in numerous archaeological sites across Eurasia suggesting that dogs were either domesticated independently on several occasions across the Old World, or that dogs were domesticated just once and subsequently spreading with late Stone Age hunter gatherers across the Eurasian continent and into North America. There are also those who suggest that wolves were involved in an earlier, failed domestication experiment by Ice Age Palaeolithic hunters about 32,000 years ago. Despite the fact that we generally know the timing and locations of the domestication of all the other farmyard animals, we still know very little for certain about the origins of our most iconic domestic animal. New scientific techniques that include the combination of genetics and statistical analyses of the shapes of ancient bones and teeth are beginning to provide unique insights into the biology of the domestication process itself, as well as new ways of tracking the spread of humans and their domestic animals around the globe. By employing these techniques we will be able to observe the variation that existed in early wolf populations at different levels of biological organization, identify diagnostic signatures that pinpoint which ancestral wolf populations were involved in early dog domestication, reveal the shape (and possibly the genetic) signatures specifically linked to the domestication process and track those signatures through time and space. We have used this combined approach successfully in our previous research enabling us to definitively unravel the complex story of pig domestication in both Europe and the Far East. We have shown that pigs were domesticated multiple times and in multiple places across Eurasia, and the fine-scale resolution of the data we have generated has also allowed us to reveal the migration routes pigs took with early farmers across Europe and into the Pacific. By applying this successful research model to ancient dogs and wolves, we will gain much deeper insight into the fundamental questions that still surround the story of dog domestication.