Browsing 2  Snapshots of Modern Mathematics from Oberwolfach by Title
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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 ... 
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 ... 
The Periodic Tables of Algebraic Geometry
[SNAP2023002EN] (Mathematisches Forschungsinstitut Oberwolfach, 20230904)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 ... 
Polyhedra and commensurability
[SNAP2016009EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)This snapshot introduces the notion of commensurability of polyhedra. At its bottom, this concept can be developed from constructions with paper, scissors, and glue. Starting with an elementary example, we formalize it ... 
Positive Scalar Curvature and Applications
[SNAP2019004EN] (Mathematisches Forschungsinstitut Oberwolfach, 20190425)We introduce the idea of curvature, including how it developed historically, and focus on the scalar curvature of a manifold. A major current research topic involves understanding positive scalar curvature. We discuss why ... 
Prime tuples in function fields
[SNAP2016010EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)How many prime numbers are there? How are they distributed among other numbers? These are questions that have intrigued mathematicians since ancient times. However, many questions in this area have remained unsolved, and ... 
Das Problem der Kugelpackung
[SNAP2016004DE] (Mathematisches Forschungsinstitut Oberwolfach, 2016)Wie würdest du Tennisbälle oder Orangen stapeln? Oder allgemeiner formuliert: Wie dicht lassen sich identische 3dimensionale Objekte überschneidungsfrei anordnen? Das Problem, welches auch Anwendungen in der digitalen ... 
Le problème ternaire de Goldbach
[SNAP2014003FR] (Mathematisches Forschungsinstitut Oberwolfach, 2024)Leonhard Euler (1707–1783), l’un des plus grands mathématiciens du XVIIIe siècle et de tous les temps, entretenait une correspondance régulière avec l’un de ses amis: Christian Goldbach (1690–1764), un amateur polymathe ...