Browsing 2  Snapshots of Modern Mathematics from Oberwolfach by Snapshot Mathematical Subject "Analysis"
Now showing items 2140 of 42

Mathematische Modellierung von Krebswachstum
[SNAP2017004DE] (Mathematisches Forschungsinstitut Oberwolfach, 20171017)Krebs ist eine der größten Herausforderungen der modernen Medizin. Der WHO zufolge starben 2012 weltweit 8,2 Millionen Menschen an Krebs. Bis heute sind dessen molekulare Mechanismen nur in Teilen verstanden, was eine ... 
Minimizing energy
[SNAP2015002EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)What is the most efficient way to fence land when you’ve only got so many metres of fence? Or, to put it differently, what is the largest area bounded by a simple closed planar curve of fixed length? We consider the answer ... 
Mixed volumes and mixed integrals
[SNAP2018014EN] (Mathematisches Forschungsinstitut Oberwolfach, 20181229)In recent years, mathematicians have developed new approaches to study convex sets: instead of considering convex sets themselves, they explore certain functions or measures that are related to them. Problems from ... 
Molecular Quantum Dynamics
[SNAP2017006EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171024)We provide a brief introduction to some basic ideas of Molecular Quantum Dynamics. We discuss the scope, strengths and main applications of this field of science. Finally, we also mention open problems of current ... 
News on quadratic polynomials
[SNAP2017002EN] (Mathematisches Forschungsinstitut Oberwolfach, 20170718)Many problems in mathematics have remained unsolved because of missing links between mathematical disciplines, such as algebra, geometry, analysis, or number theory. Here we introduce a recently discovered result concerning ... 
Nonlinear Acoustics
[SNAP2019008EN] (Mathematisches Forschungsinstitut Oberwolfach, 20190904)Nonlinear acoustics has been a topic of research for more than 250 years. Driven by a wide range and a large number of highly relevant industrial and medical applications, this area has expanded enormously in the last ... 
On Logic, Choices and Games
[SNAP2019009EN] (Mathematisches Forschungsinstitut Oberwolfach, 20190904)Can we always mathematically formalise our taste and preferences? We discuss how this has been done historically in the field of game theory, and how recent ideas from logic and computer science have brought an interesting ... 
Operator theory and the singular value decomposition
[SNAP2014009EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)This is a snapshot about operator theory and one of its fundamental tools: the singular value decomposition (SVD). The SVD breaks up linear transformations into simpler mappings, thus unveiling their geometric properties. ... 
Patterns and Waves in Theory, Experiment, and Application
[SNAP2023001EN] (Mathematisches Forschungsinstitut Oberwolfach, 20230704)In this snapshot of modern mathematics we describe some of the most prevalent waves and patterns that can arise in mathematical models and which are used to describe a number of biological, chemical, physical, and social ... 
Quantum diffusion
[SNAP2015014EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)If you place a drop of ink into a glass of water, the ink will slowly dissipate into the surrounding water until it is perfectly mixed. If you record your experiment with a camera and play the film backwards, you will see ... 
Quantum symmetry
[SNAP2020005EN] (Mathematisches Forschungsinstitut Oberwolfach, 20200604)In mathematics, symmetry is usually captured using the formalism of groups. However, the developments of the past few decades revealed the need to go beyond groups: to “quantum groups”. We explain the passage from ... 
Quantum symmetry
[SNAP2020009EN] (Mathematisches Forschungsinstitut Oberwolfach, 20201231)The symmetry of objects plays a crucial role in many branches of mathematics and physics. It allowed, for example, the early prediction of the existence of new small particles. “Quantum symmetry” concerns a generalized ... 
Rotating needles, vibrating strings, and Fourier summation
[SNAP2020006EN] (Mathematisches Forschungsinstitut Oberwolfach, 20200921)We give a brief survey of the connection between seemingly unrelated problems such as sets in the plane containing lines pointing in many directions, vibrating strings and drum heads, and a classical problem from Fourier analysis. 
Route planning for bacteria
[SNAP2022012EN] (Mathematisches Forschungsinstitut Oberwolfach, 20221208)Bacteria have been fascinating biologists since their discovery in the late 17th century. By analysing their movements, mathematical models have been developed as a tool to understand their behaviour. However, adapting ... 
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 ... 
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. 
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 ... 
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 ... 
Waves and Incidences
[SNAP2024001EN] (Mathematisches Forschungsinstitut Oberwolfach, 20240409)The wave equation in Euclidean spaces describes many natural phenomena such as sound, light, or water waves. We explore how its solutions are related to the geometric problem of how long thin cylinders can intersect each ...