Browsing 2  Snapshots of modern mathematics from Oberwolfach by Author "Cederbaum, Carla"
Now showing items 120 of 47

The adaptive finite element method
[SNAP2016013EN] Gallistl, Dietmar (Mathematisches Forschungsinstitut Oberwolfach, 2016)Computer simulations of many physical phenomena rely on approximations by models with a finite number of unknowns. The number of these parameters determines the computational effort needed for the simulation. On the other ... 
The Algebraic Statistics of an Oberwolfach Workshop
[SNAP2018001EN] Seigal, Anna (Mathematisches Forschungsinstitut Oberwolfach, 20180227)Algebraic Statistics builds on the idea that statistical models can be understood via polynomials. Many statistical models are parameterized by polynomials in the model parameters; others are described implicitly by ... 
Aperiodic Order and Spectral Properties
[SNAP2017003EN] Baake, Michael; Damanik, David; Grimm, Uwe (Mathematisches Forschungsinstitut Oberwolfach, 20170914)Periodic structures like a typical tiled kitchen floor or the arrangement of carbon atoms in a diamond crystal certainly possess a high degree of order. But what is order without periodicity? In this snapshot, we are ... 
Closed geodesics on surfaces and Riemannian manifolds
[SNAP2017005EN] Radeschi, Marco (Mathematisches Forschungsinstitut Oberwolfach, 20171207)Geodesics are special paths in surfaces and socalled Riemannian manifolds which connect close points in the shortest way. Closed geodesics are geodesics which go back to where they started. In this snapshot we talk ... 
The codimension
[SNAP2018009EN] Lerario, Antonio (Mathematisches Forschungsinstitut Oberwolfach, 20180619)In this snapshot we discuss the notion of codimension, which is, in a sense, “dual” to the notion of dimension and is useful when studying the relative position of one object insider another one. 
Computational Optimal Transport
[SNAP2017008EN] Solomon, Justin (Mathematisches Forschungsinstitut Oberwolfach, 20171221)Optimal transport is the mathematical discipline of matching supply to demand while minimizing shipping costs. This matching problem becomes extremely challenging as the quantity of supply and demand points increases; ... 
Computing the long term evolution of the solar system with geometric numerical integrators
[SNAP2017009EN] Fiorelli Vilmart, Shaula; Vilmart, Gilles (Mathematisches Forschungsinstitut Oberwolfach, 20171227)Simulating the dynamics of the Sun–Earth–Moon system with a standard algorithm yields a dramatically wrong solution, predicting that the Moon is ejected from its orbit. In contrast, a well chosen algorithm with the ... 
Computing with symmetries
[SNAP2018003EN] RoneyDougal, Colva M. (Mathematisches Forschungsinstitut Oberwolfach, 20180306)Group theory is the study of symmetry, and has many applications both within and outside mathematics. In this snapshot, we give a brief introduction to symmetries, and how to compute with them. 
Data assimilation: mathematics for merging models and data
[SNAP2018011EN] Morzfeld, Matthias; Reich, Sebastian (Mathematisches Forschungsinstitut Oberwolfach, 20180710)When you describe a physical process, for example, the weather on Earth, or an engineered system, such as a selfdriving car, you typically have two sources of information. The first is a mathematical model, and the ... 
Drugs, herbicides, and numerical simulation
[SNAP2014010EN] Benner, Peter; Mena, Hermann; Schneider, René (Mathematisches Forschungsinstitut Oberwolfach, 2014)[also available in German] The Colombian government sprays coca fields with herbicides in an effort to reduce drug production. Spray drifts at the EcuadorColombia border became an international issue. We developed a ... 
Estimating the volume of a convex body
[SNAP2018015EN] Baldin, Nicolai (Mathematisches Forschungsinstitut Oberwolfach, 20181230)Sometimes the volume of a convex body needs to be estimated, if we cannot calculate it analytically. We explain how statistics can be used not only to approximate the volume of the convex body, but also its shape. 
Fast Solvers for Highly Oscillatory Problems
[SNAP2018006EN] Barnett, Alex (Mathematisches Forschungsinstitut Oberwolfach, 20180626)Waves of diverse types surround us. Sound, light and other waves, such as microwaves, are crucial for speech, mobile phones, and other communication technologies. Elastic waves propagating through the Earth bounce ... 
A few shades of interpolation
[SNAP2017007EN] Szpond, Justyna (Mathematisches Forschungsinstitut Oberwolfach, 20171207)The topic of this snapshot is interpolation. In the ordinary sense, interpolation means to insert something of a different nature into something else. In mathematics, interpolation means constructing new data points ... 
FokusErkennung bei Epilepsiepatienten mithilfe moderner Verfahren der Zeitreihenanalyse
[SNAP2016008DE] Deistler, Manfred; Graef, Andreas (Mathematisches Forschungsinstitut Oberwolfach, 2016)Viele epileptische Anfälle entstehen in einer begrenzten Region im Gehirn, dem sogenannten Anfallsursprung. Eine chirurgische Entfernung dieser Region kann in vielen Fällen zu Anfallsfreiheit führen. Aus diesem Grund ist ... 
Footballs and donuts in four dimensions
[SNAP2016012EN] Klee, Steven (Mathematisches Forschungsinstitut Oberwolfach, 2016)In this snapshot, we explore connections between the mathematical areas of counting and geometry by studying objects called simplicial complexes. We begin by exploring many familiar objects in our three dimensional world ... 
Geometry behind one of the Painlevé III differential equations
[SNAP2018010EN] Hertling, Claus (Mathematisches Forschungsinstitut Oberwolfach, 20180620)The Painlevé equations are second order differential equations, which were first studied more than 100 years ago. Nowadays they arise in many areas in mathematics and mathematical physics. This snapshot discusses the ... 
High performance computing on smartphones
[SNAP2016006EN] Patera, Anthony T.; Urban, Karsten (Mathematisches Forschungsinstitut Oberwolfach, 2016)Nowadays there is a strong demand to simulate even realworld engineering problems on small computing devices with very limited capacity, such as a smartphone. We explain, using a concrete example, how we can obtain a ... 
How to choose a winner: the mathematics of social choice
[SNAP2015009ENSNAP2015009DE] Powers, Victoria Ann (Mathematisches Forschungsinstitut Oberwolfach, 2015)[also available in German] Suppose a group of individuals wish to choose among several options, for example electing one of several candidates to a political office or choosing the best contestant in a skating competition. ... 
The mathematics of aquatic locomotion
[SNAP2018008EN] Tucsnak, Marius (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 ... 
Mathematics plays a key role in scientific computing
[SNAP2017011EN] Shu, ChiWang (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 ...