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Periodic table of shapes could uncover the structure of the universe
Hailed as one of the most significant achievements in the field of science, the Mendeleev Periodic Table of Chemical Elements is celebrating its 150th anniversary in 2019. Not only has it revolutionised the way that scientists understand the basis…Hailed as one of the most significant achievements in the field of science, the Mendeleev Periodic Table of Chemical Elements is celebrating its 150th anniversary in 2019. Not only has…Hailed as one of the most significant achievements in the field of science, the Mendeleev Periodic Table of Chemical Elements is celebrating its…Hailed as one of the most significant achievements in the field of science, the Mendeleev Periodic Table of Chemical Elements is celebrating its 150th anniversary in 2019…Hailed as one of the most significant achievements in the field of science, the Mendeleev Periodic Table of Chemical… -
Classifying von Neumann algebras
Group theory, functional analysis and ergodic theory – three distinct areas of mathematics that meet within the theory of von Neumann algebras. The RIGIDITY project, funded by the ERC, aims to classify families of von Neumann algebras.Group theory, functional analysis and ergodic theory – three distinct areas of mathematics that meet within the theory of von Neumann algebras. The RIGIDITY project, funded by the ERC,…Group theory, functional analysis and ergodic theory – three distinct areas of mathematics that meet within the theory of von Neumann algebras. The…Group theory, functional analysis and ergodic theory – three distinct areas of mathematics that meet within the theory of von Neumann algebras. The RIGIDITY project, funded…Group theory, functional analysis and ergodic theory – three distinct areas of mathematics that meet within the theory of… -
New tools to understand the large-scale behaviour of complex systems
Understanding complex structures means separating irrelevant information to get to something simpler and easier to understand. When you look at something from a distance – although you don’t see all the details, you can still describe what you see…Understanding complex structures means separating irrelevant information to get to something simpler and easier to understand. When you look at something from a distance – although you…Understanding complex structures means separating irrelevant information to get to something simpler and easier to understand. When you look at…Understanding complex structures means separating irrelevant information to get to something simpler and easier to understand. When you look at something from a distance –…Understanding complex structures means separating irrelevant information to get to something simpler and easier to… -
New approaches to controlling dynamics
Once limited to modelling physical problems in engineering, today Partial Differential Equations (PDEs) are used by a diverse array of fields, from natural resources to meteorology, aeronautics, oil and gas and biomedicine – to name only a few. But…Once limited to modelling physical problems in engineering, today Partial Differential Equations (PDEs) are used by a diverse array of fields, from natural resources to meteorology,…Once limited to modelling physical problems in engineering, today Partial Differential Equations (PDEs) are used by a diverse array of fields, from…Once limited to modelling physical problems in engineering, today Partial Differential Equations (PDEs) are used by a diverse array of fields, from natural resources to…Once limited to modelling physical problems in engineering, today Partial Differential Equations (PDEs) are used by a… -
Statistical inference for random functions and measures
How does one infer the dynamics of a DNA minicircle in solution? How does one align the neuronal firing patterns of several neurons across individuals? These questions are intrinsically statistical, but nevertheless escape the traditional tools of…How does one infer the dynamics of a DNA minicircle in solution? How does one align the neuronal firing patterns of several neurons across individuals? These questions are…How does one infer the dynamics of a DNA minicircle in solution? How does one align the neuronal firing patterns of several neurons across…How does one infer the dynamics of a DNA minicircle in solution? How does one align the neuronal firing patterns of several neurons across individuals? These questions are…How does one infer the dynamics of a DNA minicircle in solution? How does one align the neuronal firing patterns of several… -
Understanding the deformation spaces of geometric structures
Funded by the ERC, Prof. Anna Wienhard studies several new geometric forms that have been discovered over the past 20 years. These structures are closely related to the generalisation of Teichmüller space, which describes how the surface of a…Funded by the ERC, Prof. Anna Wienhard studies several new geometric forms that have been discovered over the past 20 years. These structures are closely related to the generalisation…Funded by the ERC, Prof. Anna Wienhard studies several new geometric forms that have been discovered over the past 20 years. These structures are…Funded by the ERC, Prof. Anna Wienhard studies several new geometric forms that have been discovered over the past 20 years. These structures are closely related to the…Funded by the ERC, Prof. Anna Wienhard studies several new geometric forms that have been discovered over the past 20 years… -
Unravelling the mysteries of homogeneous dynamics
How do you study arithmetic objects like integer points using the theory of dynamical systems? The answer is homogenous dynamics, and this connection goes both ways. The GMODGAMMADYNAMICS project, funded by an ERC grant, took a broad approach…How do you study arithmetic objects like integer points using the theory of dynamical systems? The answer is homogenous dynamics, and this connection goes both ways. The…How do you study arithmetic objects like integer points using the theory of dynamical systems? The answer is homogenous dynamics, and this connection…How do you study arithmetic objects like integer points using the theory of dynamical systems? The answer is homogenous dynamics, and this connection goes both ways. The…How do you study arithmetic objects like integer points using the theory of dynamical systems? The answer is homogenous… -
Getting to grips with (slow) chaos
Chaotic systems are everywhere: the weather, molecules in a gas, the stock market. Small variations in initial conditions can lead to a drastically different time evolution, a phenomenon known as the butterfly effect. Systems can be classified…Chaotic systems are everywhere: the weather, molecules in a gas, the stock market. Small variations in initial conditions can lead to a drastically different time evolution, a…Chaotic systems are everywhere: the weather, molecules in a gas, the stock market. Small variations in initial conditions can lead to a drastically…Chaotic systems are everywhere: the weather, molecules in a gas, the stock market. Small variations in initial conditions can lead to a drastically different time evolution,…Chaotic systems are everywhere: the weather, molecules in a gas, the stock market. Small variations in initial conditions… -
Interview with Artur Avila, Fields Medal Awardee and Brazilian ERC starting grant awardee
Artur Avila is a franco-brazilian leading mathematician and an ERC grantee since 2010. At the age of 16, he won the International Mathematical Olympic gold medal and before finishing high school, he received a scholarship for the Instituto Nacional…Artur Avila is a franco-brazilian leading mathematician and an ERC grantee since 2010. At the age of 16, he won the International Mathematical Olympic gold medal and before finishing…Artur Avila is a franco-brazilian leading mathematician and an ERC grantee since 2010. At the age of 16, he won the International Mathematical…Artur Avila is a franco-brazilian leading mathematician and an ERC grantee since 2010. At the age of 16, he won the International Mathematical Olympic gold medal and before…Artur Avila is a franco-brazilian leading mathematician and an ERC grantee since 2010. At the age of 16, he won the…Career -
Proving the power of collaboration in mathematics
Artur Avila is a franco-brazilian leading mathematician and an ERC grantee since 2010. At the age of 16, he won the International Mathematical Olympic gold medal and before finishing high school, he received a scholarship for the Instituto Nacional…Artur Avila is a franco-brazilian leading mathematician and an ERC grantee since 2010. At the age of 16, he won the International Mathematical Olympic gold medal and before finishing…Artur Avila is a franco-brazilian leading mathematician and an ERC grantee since 2010. At the age of 16, he won the International Mathematical…Artur Avila is a franco-brazilian leading mathematician and an ERC grantee since 2010. At the age of 16, he won the International Mathematical Olympic gold medal and before…Artur Avila is a franco-brazilian leading mathematician and an ERC grantee since 2010. At the age of 16, he won the…