Browsing 2  Snapshots of Modern Mathematics from Oberwolfach by Title
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The KadisonSinger problem
[SNAP2014008EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)In quantum mechanics, unlike in classical mechanics, one cannot make precise predictions about how a system will behave. Instead, one is concerned with mere probabilities. Consequently, it is a very important task to ... 
Limits of graph sequences
[SNAP2019010EN] (Mathematisches Forschungsinstitut Oberwolfach, 20190904)Graphs are simple mathematical structures used to model a wide variety of reallife objects. With the rise of computers, the size of the graphs used for these models has grown enormously. The need to efficiently represent ... 
The mathematics of aquatic locomotion
[SNAP2018008EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180619)Aquatic locomotion is a selfpropelled motion through a liquid medium. It can be of biological nature (fish, microorganisms,. . .) or performed by robotic swimmers. This snapshot aims to introduce the reader to some ... 
The Mathematics of Fluids and Solids
[SNAP2019019EN] (Mathematisches Forschungsinstitut Oberwolfach, 20191218)Fluidstructure interaction is a rich and active field of mathematics that studies the interaction between fluids and solid objects. In this short article, we give a glimpse into this exciting field, as well as a ... 
Mathematics plays a key role in scientific computing
[SNAP2017011EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171229)I attended a very interesting workshop at the research center MFO in Oberwolfach on “Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws”. The title sounds a bit technical, but in plain language ... 
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 ... 
Matrixfaktorisierungen
[SNAP2014002DE] (Mathematisches Forschungsinstitut Oberwolfach, 2014)Im Folgenden soll ein kurzer Abriss des Themas Matrixfaktorisierungen gegeben werden. Wir werden darlegen, warum dieses recht simple Konzept zu erstaunlich tiefen mathematischen Gedankengängen führt und auch in der modernen ... 
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 ... 
Mixeddimensional models for realworld applications
[SNAP2019014EN] (Mathematisches Forschungsinstitut Oberwolfach, 20191121)We explore mathematical models for physical problems in which it is necessary to simultaneously consider equations in different dimensions; these are called mixeddimensional models. We first give several examples, and ... 
Modeling communication and movement: from cells to animals and humans
[SNAP2015006EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)Communication forms the basis of biological interactions. While the use of a single communication mechanism (for example visual communication) by a species is quite well understood, in nature the majority of species ... 
Modelling the spread of brain tumours
[SNAP2015013EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)The study of mathematical biology attempts to use mathematical models to draw useful conclusions about biological systems. Here, we consider the modelling of brain tumour spread with the ultimate goal of improving treatment ... 
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 ... 
The mystery of sleeping sickness – why does it keep waking up?
[SNAP2015015EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)Sleeping sickness is a neglected tropical disease that affects rural populations in Africa. Deadly when untreated, it is being targeted for elimination through case finding and treatment. Yet, fundamental questions about ... 
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 ... 
Number theory in quantum computing
[SNAP2018012EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180807)Algorithms are mathematical procedures developed to solve a problem. When encoded on a computer, algorithms must be "translated" to a series of simple steps, each of which the computer knows how to do. This task is ... 
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 ... 
On radial basis functions
[SNAP2019002EN] (Mathematisches Forschungsinstitut Oberwolfach, 20190313)Many sciences and other areas of research and applications from engineering to economics require the approximation of functions that depend on many variables. This can be for a variety of reasons. Sometimes we have a ... 
On the containment problem
[SNAP2016003EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)Mathematicians routinely speak two languages: the language of geometry and the language of algebra. When translating between these languages, curves and lines become sets of polynomials called “ideals”. Often there are ...