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A bijection transforms one type of mathematical object into another. Such transformations provide new perspectives on these objects, revealing surprising properties and uncovering new mysteries. We discuss bijections from alternating sign matrices to other objects in mathematics and physics and recent progress in the search for a missing bijection.
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Richard Brauer (1901–1977) was a German–American mathematician who is regarded as the founder of a highly active mathematical area known as modular representation theory. This area grew from group theory, which can be thought of as the mathematical study of symmetries. In this snapshot, we hope to impress on the reader the legacy left by Brauer and celebrate the 60th anniversary of “Brauer’s problems”, a list of 43 conjectures and objectives suggested by Brauer in 1963. These problems inspired an entire branch within character theory, studying “local-global conjectures”.
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The Dutch catalog for the exhibition “Pracht en kracht van wiskunde,” which toured Belgium and the Netherlands in 2022 and 2023, is available here.
This gallery contains additional information about the exhibition, posters in English and Dutch, and other materials.
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Differential equations make predictions on the future state of a system given the present. In order to get a sensible prediction, sometimes it is necessary to include randomness in differential equations, taking microscopic effects into account. Surprisingly, despite the presence of randomness, our probabilistic prediction of future states is stable with respect to changes in the surrounding environment, even if the original prediction was unstable. This snapshot will unveil the core mathematical mechanism underlying this “regularisation by noise” phenomenon.
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To understand our world, we classify things. A famous example is the periodic table of elements, which describes the properties of all known chemical elements and gives us a classification of the building blocks we can use in physics, chemistry, and biology. In mathematics, and algebraic geometry in particular, there are many instances of similar periodic tables”, describing fundamental classification results. We will go on a tour of some of these.
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The goal of inverse problems is to find an unknown parameter based on noisy data. Such problems appear in a wide range of applications including geophysics, medicine, and chemistry. One method of solving them is known as the Bayesian approach. In this approach, the unknown parameter is modelled as a random variable to reflect its uncertain value. Bayes’ theorem is applied to update our knowledge given new information from noisy data.
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Geophysicists and mathematicians work together to detect geological structures located deep within the earth by measuring and interpreting echoes from manmade earthquakes. This inverse problem naturally involves the mathematics of wave propagation, but we will see that a different mathematical theory – optimal transport – also turns out to be very useful.
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We explore mathematical models for physical problems in which it is necessary to simultaneously consider equations in different dimensions; these are called mixed-dimensional models. We first give several examples, and then an overview of recent progress made towards finding a general method of solution of such problems.
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When you describe a physical process, for example, the weather on Earth, or an engineered system, such as a self-driving car, you typically have two sources of information. The first is a mathematical model, and the second is information obtained by collecting data. To make the best predictions for the weather, or most effectively operate the self-driving car, you want to use both sources of information. Data assimilation describes the mathematical, numerical and computational framework for doing just that.
Submitted by Bianca Violet on
We introduce and outline a workshop concept called Science Spaces aimed at High School students, which combines mathematics and natural sciences with art to strengthen creativity, imagination, and perceptual abilities. The workshop guides the participants through the process of designing and implementing a public exhibition.