Browsing 2  Snapshots of Modern Mathematics from Oberwolfach by Title
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Searching for structure in complex data: a modern statistical quest
[SNAP2021003EN] (Mathematisches Forschungsinstitut Oberwolfach, 20210329)Current research in statistics has taken interesting new directions, as data collected from scientific studies has become increasingly complex. At first glance, the number of experiments conducted by a scientist must ... 
Searching for the Monster in the Trees
[SNAP2022003EN] (Mathematisches Forschungsinstitut Oberwolfach, 20220413)The Monster finite simple group is almost unimaginably large, with about 8 × 1053 elements in it. Trying to understand such an immense object requires both theory and computer programs. In this snapshot, we discuss finite ... 
Seeing through rock with help from optimal transport
[SNAP2022004EN] (Mathematisches Forschungsinstitut Oberwolfach, 20220506)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 ... 
Shape space – a paradigm for character animation in computer graphics
[SNAP2020007EN] (Mathematisches Forschungsinstitut Oberwolfach, 20201007)Nowadays 3D computer animation is increasingly realistic as the models used for the characters become more and more complex. These models are typically represented by meshes of hundreds of thousands or even millions ... 
A short story on optimal transport and its many applications
[SNAP2018013EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180808)We present some examples of optimal transport problems and of applications to different sciences (logistics, economics, image processing, and a little bit of evolution equations) through the crazy story of an industrial ... 
Snake graphs, perfect matchings and continued fractions
[SNAP2019001EN] (Mathematisches Forschungsinstitut Oberwolfach, 20190213)A continued fraction is a way of representing a real number by a sequence of integers. We present a new way to think about these continued fractions using snake graphs, which are sequences of squares in the plane. You ... 
Solving inverse problems with Bayes’ theorem
[SNAP2022006EN] (Mathematisches Forschungsinstitut Oberwolfach, 20220905)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 ... 
Solving quadratic equations in many variables
[SNAP2017012EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171230)Fields are number systems in which every linear equation has a solution, such as the set of all rational numbers $\mathbb{Q}$ or the set of all real numbers $\mathbb{R}$. All fields have the same properties in relation ... 
Spaces of Riemannian metrics
[SNAP2017010ENSNAP2017010ES] (Mathematisches Forschungsinstitut Oberwolfach, 20171228)Riemannian metrics endow smooth manifolds such as surfaces with intrinsic geometric properties, for example with curvature. They also allow us to measure quantities like distances, angles and volumes. These are the ... 
Special values of zeta functions and areas of triangles
[SNAP2015010EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)In this snapshot we give a glimpse of the interplay of special values of zeta functions and volumes of triangles. Special values of zeta functions and their generalizations arise in the computation of volumes of moduli ... 
Statistics and dynamical phenomena
[SNAP2014006EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)A friend of mine, an expert in statistical genomics, told me the following story: At a dinner party, an attractive lady asked him, "What do you do for a living?" He replied, "I model." As my friend is a handsome man, the ... 
A surprising connection between quantum mechanics and shallow water waves
[SNAP2019018EN] (Mathematisches Forschungsinstitut Oberwolfach, 20191211)We describe a connection between quantum mechanics and nonlinear wave equations and highlight a few problems at the forefront of modern research in the intersection of these areas. 
Swallowtail on the shore
[SNAP2014007EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)Platonic solids, Felix Klein, H.S.M. Coxeter and a flap of a swallowtail: The five Platonic solids tetrahedron, cube, octahedron, icosahedron and dodecahedron have always attracted much curiosity from mathematicians, not ... 
Swarming robots
[SNAP2016001EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)When lots of robots come together to form shapes, spread in an area, or move in one direction, their motion has to be planned carefully. We discuss how mathematicians devise strategies to help swarms of robots behave like ... 
Symmetry and characters of finite groups
[SNAP2016005EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)Over the last two centuries mathematicians have developed an elegant abstract framework to study the natural idea of symmetry. The aim of this snapshot is to gently guide the interested reader through these ideas. In ... 
The ternary Goldbach problem
[SNAP2014003ENSNAP2014003DE] (Mathematisches Forschungsinstitut Oberwolfach, 2014)[also available in German] Leonhard Euler (1707–1783) – one of the greatest mathematicians of the eighteenth century and of all times – often corresponded with a friend of his, Christian Goldbach (1690–1764), an amateur ... 
Topological Complexity, Robotics and Social Choice
[SNAP2018005EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180810)Topological complexity is a number that measures how hard it is to plan motions (for robots, say) in terms of a particular space associated to the kind of motion to be planned. This is a burgeoning subject within the ... 
Topological recursion
[SNAP2018002EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180305)In this snapshot we present the concept of topological recursion – a new, surprisingly powerful formalism at the border of mathematics and physics, which has been actively developed within the last decade. After introducing ... 
Touching the transcendentals: tractional motion from the bir th of calculus to future perspectives
[SNAP2019013EN] (Mathematisches Forschungsinstitut Oberwolfach, 20191121)When the rigorous foundation of calculus was developed, it marked an epochal change in the approach of mathematicians to geometry. Tools from geometry had been one of the foundations of mathematics until the 17th century ... 
Towards a Mathematical Theory of Turbulence in Fluids
[SNAP2016015EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)Fluid mechanics is the theory of how liquids and gases move around. For the most part, the basic physics are well understood and the mathematical models look relatively simple. Despite this, fluids display a dazzling mystery ...