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End date: 2019 × Start date: 2010 × DDC: 510 × Type: report × Publisher: Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH ×

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Now showing 1 - 10 of 90
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    Estimating the volume of a convex body
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2018) Baldin, Nicolai
    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.
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    Modelling the spread of brain tumours
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2015) Swan, Amanda; Murtha, Albert
    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 outcomes.
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    Tropical geometry
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2018) Brugallé, Erwan; Itenberg, Ilia; Shaw, Kristin; Viro, Oleg
    What kind of strange spaces hide behind the enigmatic name of tropical geometry? In the tropics, just as in other geometries, one of the simplest objects is a line. Therefore, we begin our exploration by considering tropical lines. Afterwards, we take a look at tropical arithmetic and algebra, and describe how to define tropical curves using tropical polynomials.
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    The adaptive finite element method
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Gallistl, Dietmar
    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 hand, a larger number of unknowns can improve the precision of the simulation. The adaptive finite element method (AFEM) is an algorithm for optimizing the choice of parameters so accurate simulation results can be obtained with as little computational effort as possible.
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    Drugs, herbicides, and numerical simulation
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Benner, Peter; Mena, Hermann; Schneider, René
    The Colombian government sprays coca fields with herbicides in an effort to reduce drug production. Spray drifts at the Ecuador-Colombia border became an international issue. We developed a mathematical model for the herbicide aerial spray drift, enabling simulations of the phenomenon.
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    Polyhedra and commensurability
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Guglielmetti, Rafael; Jacquement, Matthieu
    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 subsequently. Finally, we discuss intriguing connections with other fields of mathematics.
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    The mystery of sleeping sickness – why does it keep waking up?
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2015) Funk, Sebastian
    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 its transmission cycle remain unanswered. One of them is whether transmission is limited to humans, or whether other species play a role in maintaining circulation of the disease. In this snapshot, we introduce a mathematical model for the spread of Trypanosoma brucei, the parasite responsible for causing sleeping sickness, and present some results based on data collected in Cameroon. Understanding how important animals are in harbouring Trypanosoma brucei that can infect humans is important for assessing whether the disease could be reintroduced in human populations even after all infected people have been successfully treated.
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    Arrangements of lines
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Harbourne, Brian; Szemberg, Tomasz
    We discuss certain open problems in the context of arrangements of lines in the plane.
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    Footballs and donuts in four dimensions
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Klee, Steven
    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 and then discuss the ways one may generalize these ideas into higher dimensions.
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    Profinite groups
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Bartholdi, Laurent
    Profinite objects are mathematical constructions used to collect, in a uniform manner, facts about infinitely many finite objects. We shall review recent progress in the theory of profinite groups, due to Nikolov and Segal, and its implications for finite groups.